NH and the interchanged -NH2 / -O- groups in the incorrect structure.","X-ray crystallography\n\nRelationship to other scattering techniques","X-ray crystallography\n\nElastic vs. inelastic scattering","X-ray crystallography\n\nX-ray crystallography is a form of elastic scattering; the outgoing X-rays have the same energy, and thus same wavelength, as the incoming X-rays, only with altered direction. By contrast, inelastic scattering occurs when energy is transferred from the incoming X-ray to the crystal, e.g., by exciting an inner-shell electron to a higher energy level. Such inelastic scattering reduces the energy (or increases the wavelength) of the outgoing beam. Inelastic scattering is useful for probing such excitations of matter, but not in determining the distribution of scatterers within the matter, which is the goal of X-ray crystallography.","X-ray crystallography\n\nX-rays range in wavelength from 10 to 0.01 nanometers; a typical wavelength used for crystallography is 1 Å (0.1 nm), which is on the scale of covalent chemical bonds and the radius of a single atom. Longer-wavelength photons (such as ultraviolet radiation) would not have sufficient resolution to determine the atomic positions. At the other extreme, shorter-wavelength photons such as gamma rays are difficult to produce in large numbers, difficult to focus, and interact too strongly with matter, producing particle-antiparticle pairs. Therefore, X-rays are the \"sweetspot\" for wavelength when determining atomic-resolution structures from the scattering of electromagnetic radiation.","X-ray crystallography\n\nOther X-ray techniques","X-ray crystallography\n\nOther forms of elastic X-ray scattering include powder diffraction, Small-Angle X-ray Scattering (SAXS) and several types of X-ray fiber diffraction, which was used by Rosalind Franklin in determining the double-helix structure of DNA. In general, single-crystal X-ray diffraction offers more structural information than these other techniques; however, it requires a sufficiently large and regular crystal, which is not always available.","X-ray crystallography\n\nThese scattering methods generally use monochromatic X-rays, which are restricted to a single wavelength with minor deviations. A broad spectrum of X-rays (that is, a blend of X-rays with different wavelengths) can also be used to carry out X-ray diffraction, a technique known as the Laue method. This is the method used in the original discovery of X-ray diffraction. Laue scattering provides much structural information with only a short exposure to the X-ray beam, and is therefore used in structural studies of very rapid events (Time resolved crystallography). However, it is not as well-suited as monochromatic scattering for determining the full atomic structure of a crystal and therefore works better with crystals with relatively simple atomic arrangements.","X-ray crystallography\n\nThe Laue back reflection mode records X-rays scattered backwards from a broad spectrum source. This is useful if the sample is too thick for X-rays to transmit through it. The diffracting planes in the crystal are determined by knowing that the normal to the diffracting plane bisects the angle between the incident beam and the diffracted beam. A Greninger chart can be used to interpret the back reflection Laue photograph.","X-ray crystallography\n\nElectron and neutron diffraction","X-ray crystallography\n\nOther particles, such as electrons and neutrons, may be used to produce a diffraction pattern. Although electron, neutron, and X-ray scattering are based on different physical processes, the resulting diffraction patterns are analyzed using the same coherent diffraction imaging techniques.","X-ray crystallography\n\nAs derived below, the electron density within the crystal and the diffraction patterns are related by a simple mathematical method, the Fourier transform, which allows the density to be calculated relatively easily from the patterns. However, this works only if the scattering is weak, i.e., if the scattered beams are much less intense than the incoming beam. Weakly scattered beams pass through the remainder of the crystal without undergoing a second scattering event. Such re-scattered waves are called \"secondary scattering\" and hinder the analysis. Any sufficiently thick crystal will produce secondary scattering, but since X-rays interact relatively weakly with the electrons, this is generally not a significant concern. By contrast, electron beams may produce strong secondary scattering even for relatively thin crystals (>100 nm). Since this thickness corresponds to the diameter of many viruses, a promising direction is the electron diffraction of isolated macromolecular assemblies, such as viral capsids and molecular machines, which may be carried out with a cryo-electron microscope. Moreover, the strong interaction of electrons with matter (about 1000 times stronger than for X-rays) allows determination of the atomic structure of extremely small volumes.","X-ray crystallography\n\nThe field of applications for electron crystallography ranges from bio molecules like membrane proteins over organic thin films to the complex structures of (nanocrystalline) intermetallic compounds and zeolites.","X-ray crystallography\n\nNeutron diffraction is an excellent method for structure determination, although it has been difficult to obtain intense, monochromatic beams of neutrons in sufficient quantities. Traditionally, nuclear reactors have been used, although sources producing neutrons by spallation are becoming increasingly available. Being uncharged, neutrons scatter much more readily from the atomic nuclei rather than from the electrons. Therefore, neutron scattering is very useful for observing the positions of light atoms with few electrons, especially hydrogen, which is essentially invisible in the X-ray diffraction. Neutron scattering also has the remarkable property that the solvent can be made invisible by adjusting the ratio of normal water, H2O, and heavy water, D2O.","X-ray crystallography\n\nMethods","X-ray crystallography\n\nOverview of single-crystal X-ray diffraction","X-ray crystallography\n\nThe oldest and most precise method of X-ray crystallography is single-crystal X-ray diffraction, in which a beam of X-rays strikes a single crystal, producing scattered beams. When they land on a piece of film or other detector, these beams make a diffraction pattern of spots; the strengths and angles of these beams are recorded as the crystal is gradually rotated. Each spot is called a reflection, since it corresponds to the reflection of the X-rays from one set of evenly spaced planes within the crystal. For single crystals of sufficient purity and regularity, X-ray diffraction data can determine the mean chemical bond lengths and angles to within a few thousandths of an angstrom and to within a few tenths of a degree, respectively. The atoms in a crystal are not static, but oscillate about their mean positions, usually by less than a few tenths of an angstrom. X-ray crystallography allows measuring the size of these oscillations.","X-ray crystallography\n\nProcedure","X-ray crystallography\n\nThe technique of single-crystal X-ray crystallography has three basic steps. The first—and often most difficult—step is to obtain an adequate crystal of the material under study. The crystal should be sufficiently large (typically larger than 0.1 mm in all dimensions), pure in composition and regular in structure, with no significant internal imperfections such as cracks or twinning.","X-ray crystallography\n\nIn the second step, the crystal is placed in an intense beam of X-rays, usually of a single wavelength (monochromatic X-rays), producing the regular pattern of reflections. As the crystal is gradually rotated, previous reflections disappear and new ones appear; the intensity of every spot is recorded at every orientation of the crystal. Multiple data sets may have to be collected, with each set covering slightly more than half a full rotation of the crystal and typically containing tens of thousands of reflections.","X-ray crystallography\n\nIn the third step, these data are combined computationally with complementary chemical information to produce and refine a model of the arrangement of atoms within the crystal. The final, refined model of the atomic arrangement—now called a crystal structure—is usually stored in a public database.","X-ray crystallography\n\nLimitations","X-ray crystallography\n\nAs the crystal's repeating unit, its unit cell, becomes larger and more complex, the atomic-level picture provided by X-ray crystallography becomes less well-resolved (more \"fuzzy\") for a given number of observed reflections. Two limiting cases of X-ray crystallography—\"small-molecule\" and \"macromolecular\" crystallography—are often discerned. Small-molecule crystallography typically involves crystals with fewer than 100 atoms in their asymmetric unit; such crystal structures are usually so well resolved that the atoms can be discerned as isolated \"blobs\" of electron density. By contrast, macromolecular crystallography often involves tens of thousands of atoms in the unit cell. Such crystal structures are generally less well-resolved (more \"smeared out\"); the atoms and chemical bonds appear as tubes of electron density, rather than as isolated atoms. In general, small molecules are also easier to crystallize than macromolecules; however, X-ray crystallography has proven possible even for viruses with hundreds of thousands of atoms. Though normally x-ray crystallography can only be performed if the sample is in crystal form, new research has been done into sampling non-crystalline forms of samples.","X-ray crystallography\n\nCrystallization","X-ray crystallography\n\nAlthough crystallography can be used to characterize the disorder in an impure or irregular crystal, crystallography generally requires a pure crystal of high regularity to solve the structure of a complicated arrangement of atoms. Pure, regular crystals can sometimes be obtained from natural or synthetic materials, such as samples of metals, minerals or other macroscopic materials. The regularity of such crystals can sometimes be improved with macromolecular crystal annealing and other methods. However, in many cases, obtaining a diffraction-quality crystal is the chief barrier to solving its atomic-resolution structure.","X-ray crystallography\n\nSmall-molecule and macromolecular crystallography differ in the range of possible techniques used to produce diffraction-quality crystals. Small molecules generally have few degrees of conformational freedom, and may be crystallized by a wide range of methods, such as chemical vapor deposition and recrystallization. By contrast, macromolecules generally have many degrees of freedom and their crystallization must be carried out so as to maintain a stable structure. For example, proteins and larger RNA molecules cannot be crystallized if their tertiary structure has been unfolded; therefore, the range of crystallization conditions is restricted to solution conditions in which such molecules remain folded.","X-ray crystallography\n\nProtein crystals are almost always grown in solution. The most common approach is to lower the solubility of its component molecules very gradually; if this is done too quickly, the molecules will precipitate from solution, forming a useless dust or amorphous gel on the bottom of the container. Crystal growth in solution is characterized by two steps: nucleation of a microscopic crystallite (possibly having only 100 molecules), followed by growth of that crystallite, ideally to a diffraction-quality crystal. The solution conditions that favor the first step (nucleation) are not always the same conditions that favor the second step (subsequent growth). The crystallographer's goal is to identify solution conditions that favor the development of a single, large crystal, since larger crystals offer improved resolution of the molecule. Consequently, the solution conditions should disfavor the first step (nucleation) but favor the second (growth), so that only one large crystal forms per droplet. If nucleation is favored too much, a shower of small crystallites will form in the droplet, rather than one large crystal; if favored too little, no crystal will form whatsoever.","X-ray crystallography\n\nOther approaches involves, crystallizing proteins under oil, where aqueous protein solutions are dispensed under liquid oil, and water evaporates through the layer of oil. Different oils have different evaporation permeabilities, therefore yielding changes in concentration rates from different percipient/protein mixture. The technique relies on bringing the protein directly into the nucleation zone by mixing protein with the appropriate amount of percipient to prevent the diffusion of water out of the drop.","X-ray crystallography\n\nIt is extremely difficult to predict good conditions for nucleation or growth of well-ordered crystals. In practice, favorable conditions are identified by screening; a very large batch of the molecules is prepared, and a wide variety of crystallization solutions are tested. Hundreds, even thousands, of solution conditions are generally tried before finding the successful one. The various conditions can use one or more physical mechanisms to lower the solubility of the molecule; for example, some may change the pH, some contain salts of the Hofmeister series or chemicals that lower the dielectric constant of the solution, and still others contain large polymers such as polyethylene glycol that drive the molecule out of solution by entropic effects. It is also common to try several temperatures for encouraging crystallization, or to gradually lower the temperature so that the solution becomes supersaturated. These methods require large amounts of the target molecule, as they use high concentration of the molecule(s) to be crystallized. Due to the difficulty in obtaining such large quantities (milligrams) of crystallization-grade protein, robots have been developed that are capable of accurately dispensing crystallization trial drops that are in the order of 100 nanoliters in volume.","X-ray crystallography\n\nThis means that 10-fold less protein is used per experiment when compared to crystallization trials set up by hand (in the order of 1 microliter).","X-ray crystallography\n\nSeveral factors are known to inhibit or mar crystallization. The growing crystals are generally held at a constant temperature and protected from shocks or vibrations that might disturb their crystallization. Impurities in the molecules or in the crystallization solutions are often inimical to crystallization. Conformational flexibility in the molecule also tends to make crystallization less likely, due to entropy. Ironically, molecules that tend to self-assemble into regular helices are often unwilling to assemble into crystals . Crystals can be marred by twinning, which can occur when a unit cell can pack equally favorably in multiple orientations; although recent advances in computational methods may allow solving the structure of some twinned crystals. Having failed to crystallize a target molecule, a crystallographer may try again with a slightly modified version of the molecule; even small changes in molecular properties can lead to large differences in crystallization behavior.","X-ray crystallography\n\nData collection","X-ray crystallography\n\nMounting the crystal","X-ray crystallography\n\nThe crystal is mounted for measurements so that it may be held in the X-ray beam and rotated. There are several methods of mounting. In the past, crystals were loaded into glass capillaries with the crystallization solution (the mother liquor). Nowadays, crystals of small molecules are typically attached with oil or glue to a glass fiber or a loop, which is made of nylon or plastic and attached to a solid rod. Protein crystals are scooped up by a loop, then flash-frozen with liquid nitrogen. This freezing reduces the radiation damage of the X-rays, as well as the noise in the Bragg peaks due to thermal motion (the Debye-Waller effect). However, untreated protein crystals often crack if flash-frozen; therefore, they are generally pre-soaked in a cryoprotectant solution before freezing. Unfortunately, this pre-soak may itself cause the crystal to crack, ruining it for crystallography. Generally, successful cryo-conditions are identified by trial and error.","X-ray crystallography\n\nThe capillary or loop is mounted on a goniometer, which allows it to be positioned accurately within the X-ray beam and rotated. Since both the crystal and the beam are often very small, the crystal must be centered within the beam to within ~25 micrometers accuracy, which is aided by a camera focused on the crystal. The most common type of goniometer is the \"kappa goniometer\", which offers three angles of rotation: the ω angle, which rotates about an axis perpendicular to the beam; the κ angle, about an axis at ~50° to the ω axis; and, finally, the φ angle about the loop/capillary axis. When the κ angle is zero, the ω and φ axes are aligned. The κ rotation allows for convenient mounting of the crystal, since the arm in which the crystal is mounted may be swung out towards the crystallographer. The oscillations carried out during data collection (mentioned below) involve the ω axis only. An older type of goniometer is the four-circle goniometer, and its relatives such as the six-circle goniometer.","X-ray crystallography\n\nX-ray Sources","X-ray crystallography\n\nRotating Anode","X-ray crystallography\n\nSmall scale can be done on a local X-ray tube source, typically coupled with an image plate detector. These have the advantage of being (relatively) inexpensive and easy to maintain, and allow for quick screening and collection of samples. However, the wavelength light produced is limited by anode material, typically copper. Further, intensity is limited by the power applied and cooling capacity available to avoid melting the anode. In such systems, electrons are boiled off of a cathode and accelerated through a strong electric potential of ~50 kV; having reached a high speed, the electrons collide with a metal plate, emitting bremsstrahlung and some strong spectral lines corresponding to the excitation of inner-shell electrons of the metal. The most common metal used is copper, which can be kept cool easily, due to its high thermal conductivity, and which produces strong Kα and Kβ lines. The Kβ line is sometimes suppressed with a thin (~10 µm) nickel foil. The simplest and cheapest variety of sealed X-ray tube has a stationary anode (the Crookes tube) and run with ~2 kW of electron beam power. The more expensive variety has a rotating-anode type source that run with ~14 kW of e-beam power.","X-ray crystallography\n\nX-rays are generally filtered (by use of X-Ray Filters) to a single wavelength (made monochromatic) and collimated to a single direction before they are allowed to strike the crystal. The filtering not only simplifies the data analysis, but also removes radiation that degrades the crystal without contributing useful information. Collimation is done either with a collimator (basically, a long tube) or with a clever arrangement of gently curved mirrors. Mirror systems are preferred for small crystals (under 0.3 mm) or with large unit cells (over 150 Å)","X-ray crystallography\n\nSynchrotron Radiation","X-ray crystallography\n\nSynchrotron radiation are some of the brightest lights on earth. It is the single most powerful tool available to X-ray crystallographers. It is made of X-ray beams generated in large machines called synchrotrons. These machines accelerate electrically charged particles, often electrons, to nearly the speed of light and confine them in a (roughly) circular loop using magnetic fields.","X-ray crystallography\n\nSynchrotrons are generally national facilities, each with several dedicated beamlines where data is collected without interruption. Synchrotrons were originally designed for use by high-energy physicists studying subatomic particles and cosmic phenomena. The largest component of each synchrotron is its electron storage ring. This ring is actually not a perfect circle, but a many-sided polygon. At each corner of the polygon, or sector, precisely aligned magnets bend the electron stream. As the electrons’ path is bent, they emit bursts of energy in the form of X-rays.","X-ray crystallography\n\nUsing synchrotron radiation frequently has specific requirements for X-ray crystallography. The intense ionizing radiation can cause radiation damage to samples, particularly macromolecular crystals. Cryo crystallography protects the sample from radiation damage, by freezing the crystal at liquid nitrogen temperatures (~100 K). However, synchrotron radiation frequently has the advantage of user selectable wavelengths, allowing for anomalous scattering experiments which maximizes anomalous signal. This is critical in experiments such as SAD and MAD.","X-ray crystallography\n\nFree Electron Laser","X-ray crystallography\n\nRecently, free electron lasers have been developed for use in X-ray crystallography. These are the brightest X-ray sources currently available; with the X-rays coming in femtosecond bursts. The intensity of the source is such that atomic resolution diffraction patterns can be resolved for crystals otherwise too small for collection. However, the intense light source also destroys the sample, requiring multiple crystals to be shot. As each crystal is randomly oriented in the beam, hundreds of thousands of individual diffraction images must be collected in order to get a complete data-set. This method, serial femtosecond crystallography, has been used in solving the structure of a number of protein crystal structures, sometimes noting differences with equivalent structures collected from synchrotron sources.","X-ray crystallography\n\nRecording the reflections","X-ray crystallography\n\nWhen a crystal is mounted and exposed to an intense beam of X-rays, it scatters the X-rays into a pattern of spots or reflections that can be observed on a screen behind the crystal. A similar pattern may be seen by shining a laser pointer at a compact disc. The relative intensities of these spots provide the information to determine the arrangement of molecules within the crystal in atomic detail. The intensities of these reflections may be recorded with photographic film, an area detector or with a charge-coupled device (CCD) image sensor. The peaks at small angles correspond to low-resolution data, whereas those at high angles represent high-resolution data; thus, an upper limit on the eventual resolution of the structure can be determined from the first few images. Some measures of diffraction quality can be determined at this point, such as the mosaicity of the crystal and its overall disorder, as observed in the peak widths. Some pathologies of the crystal that would render it unfit for solving the structure can also be diagnosed quickly at this point.","X-ray crystallography\n\nOne image of spots is insufficient to reconstruct the whole crystal; it represents only a small slice of the full Fourier transform. To collect all the necessary information, the crystal must be rotated step-by-step through 180°, with an image recorded at every step; actually, slightly more than 180° is required to cover reciprocal space, due to the curvature of the Ewald sphere. However, if the crystal has a higher symmetry, a smaller angular range such as 90° or 45° may be recorded. The rotation axis should be changed at least once, to avoid developing a \"blind spot\" in reciprocal space close to the rotation axis. It is customary to rock the crystal slightly (by 0.5–2°) to catch a broader region of reciprocal space.","X-ray crystallography\n\nMultiple data sets may be necessary for certain phasing methods. For example, MAD phasing requires that the scattering be recorded at least three (and usually four, for redundancy) wavelengths of the incoming X-ray radiation. A single crystal may degrade too much during the collection of one data set, owing to radiation damage; in such cases, data sets on multiple crystals must be taken.","X-ray crystallography\n\nData analysis","X-ray crystallography\n\nCrystal symmetry, unit cell, and image scaling","X-ray crystallography\n\nThe recorded series of two-dimensional diffraction patterns, each corresponding to a different crystal orientation, is converted into a three-dimensional model of the electron density; the conversion uses the mathematical technique of Fourier transforms, which is explained below. Each spot corresponds to a different type of variation in the electron density; the crystallographer must determine which variation corresponds to which spot (indexing), the relative strengths of the spots in different images (merging and scaling) and how the variations should be combined to yield the total electron density (phasing).","X-ray crystallography\n\nData processing begins with indexing the reflections. This means identifying the dimensions of the unit cell and which image peak corresponds to which position in reciprocal space. A byproduct of indexing is to determine the symmetry of the crystal, i.e., its space group. Some space groups can be eliminated from the beginning. For example, reflection symmetries cannot be observed in chiral molecules; thus, only 65 space groups of 230 possible are allowed for protein molecules which are almost always chiral. Indexing is generally accomplished using an autoindexing routine. Having assigned symmetry, the data is then integrated. This converts the hundreds of images containing the thousands of reflections into a single file, consisting of (at the very least) records of the Miller index of each reflection, and an intensity for each reflection (at this state the file often also includes error estimates and measures of partiality (what part of a given reflection was recorded on that image)).","X-ray crystallography\n\nA full data set may consist of hundreds of separate images taken at different orientations of the crystal. The first step is to merge and scale these various images, that is, to identify which peaks appear in two or more images (merging) and to scale the relative images so that they have a consistent intensity scale. Optimizing the intensity scale is critical because the relative intensity of the peaks is the key information from which the structure is determined. The repetitive technique of crystallographic data collection and the often high symmetry of crystalline materials cause the diffractometer to record many symmetry-equivalent reflections multiple times. This allows calculating the symmetry-related R-factor, a reliability index based upon how similar are the measured intensities of symmetry-equivalent reflections, thus assessing the quality of the data.","X-ray crystallography\n\nInitial phasing","X-ray crystallography\n\nThe data collected from a diffraction experiment is a reciprocal space representation of the crystal lattice. The position of each diffraction 'spot' is governed by the size and shape of the unit cell, and the inherent symmetry within the crystal. The intensity of each diffraction 'spot' is recorded, and this intensity is proportional to the square of the structure factor amplitude. The structure factor is a complex number containing information relating to both the amplitude and phase of a wave. In order to obtain an interpretable electron density map, both amplitude and phase must be known (an electron density map allows a crystallographer to build a starting model of the molecule). The phase cannot be directly recorded during a diffraction experiment: this is known as the phase problem. Initial phase estimates can be obtained in a variety of ways:\n* Ab initio phasing or direct methods – This is usually the method of choice for small molecules (\n* Anomalous X-ray scattering (MAD or SAD phasing) – the X-ray wavelength may be scanned past an absorption edge of an atom, which changes the scattering in a known way.","X-ray crystallography\n\nBy recording full sets of reflections at three different wavelengths (far below, far above and in the middle of the absorption edge) one can solve for the substructure of the anomalously diffracting atoms and hence the structure of the whole molecule. The most popular method of incorporating anomalous scattering atoms into proteins is to express the protein in a methionine auxotroph (a host incapable of synthesizing methionine) in a media rich in seleno-methionine, which contains selenium atoms. A MAD experiment can then be conducted around the absorption edge, which should then yield the position of any methionine residues within the protein, providing initial phases. * Heavy atom methods (multiple isomorphous replacement) – If electron-dense metal atoms can be introduced into the crystal, direct methods or Patterson-space methods can be used to determine their location and to obtain initial phases. Such heavy atoms can be introduced either by soaking the crystal in a heavy atom-containing solution, or by co-crystallization (growing the crystals in the presence of a heavy atom). As in MAD phasing, the changes in the scattering amplitudes can be interpreted to yield the phases.","X-ray crystallography\n\nAlthough this is the original method by which protein crystal structures were solved, it has largely been superseded by MAD phasing with selenomethionine.","X-ray crystallography\n\nModel building and phase refinement","X-ray crystallography\n\nHaving obtained initial phases, an initial model can be built. This model can be used to refine the phases, leading to an improved model, and so on. Given a model of some atomic positions, these positions and their respective Debye-Waller factors (or B-factors, accounting for the thermal motion of the atom) can be refined to fit the observed diffraction data, ideally yielding a better set of phases. A new model can then be fit to the new electron density map and a further round of refinement is carried out. This continues until the correlation between the diffraction data and the model is maximized. The agreement is measured by an R-factor defined as","X-ray crystallography\n\nR = \\frac{\\sum_{\\mathrm{all\\ reflections}} \\left|F_{o} - F_{c} \\right|}{\\sum_{\\mathrm{all\\ reflections}} \\left|F_{o} \\right|}","X-ray crystallography\n\nwhere F is the structure factor. A similar quality criterion is Rfree, which is calculated from a subset (~10%) of reflections that were not included in the structure refinement. Both R factors depend on the resolution of the data. As a rule of thumb, Rfree should be approximately the resolution in angstroms divided by 10; thus, a data-set with 2 Å resolution should yield a final Rfree ~ 0.2. Chemical bonding features such as stereochemistry, hydrogen bonding and distribution of bond lengths and angles are complementary measures of the model quality. Phase bias is a serious problem in such iterative model building. Omit maps are a common technique used to check for this.","X-ray crystallography\n\nIt may not be possible to observe every atom of the crystallized molecule – it must be remembered that the resulting electron density is an average of all the molecules within the crystal. In some cases, there is too much residual disorder in those atoms, and the resulting electron density for atoms existing in many conformations is smeared to such an extent that it is no longer detectable in the electron density map. Weakly scattering atoms such as hydrogen are routinely invisible. It is also possible for a single atom to appear multiple times in an electron density map, e.g., if a protein sidechain has multiple (f(\\mathbf{r}) = \\frac{1}{\\left(2\\pi\\right)^{3}} \\int F(\\mathbf{q}) e^{\\mathrm{i}\\mathbf{q}\\cdot\\mathbf{r}} \\mathrm{d}\\mathbf{q}","X-ray crystallography\n\nwhere the integral is taken over all values of q. The three-dimensional real vector q represents a point in reciprocal space, that is, to a particular oscillation in the electron density as one moves in the direction in which q points. The length of q corresponds to 2\\pi divided by the wavelength of the oscillation. The corresponding formula for a Fourier transform will be used below\nF(\\mathbf{q}) = \\int f(\\mathbf{r}) \\mathrm{e}^{-\\mathrm{i}\\mathbf{q}\\cdot\\mathbf{r}}\\mathrm{d}\\mathbf{r}\nwhere the integral is summed over all possible values of the position vector r within the crystal.","X-ray crystallography\n\nThe Fourier transform F(q) is generally a complex number, and therefore has a magnitude |F(q)| and a phase φ(q) related by the equation\nF(\\mathbf{q}) = \\left|F(\\mathbf{q}) \\right|\\mathrm{e}^{\\mathrm{i}\\phi(\\mathbf{q})}\nThe intensities of the reflections observed in X-ray diffraction give us the magnitudes |F(q)| but not the phases φ(q). To obtain the phases, full sets of reflections are collected with known alterations to the scattering, either by modulating the wavelength past a certain absorption edge or by adding strongly scattering (i.e., electron-dense) metal atoms such as mercury. Combining the magnitudes and phases yields the full Fourier transform F(q), which may be inverted to obtain the electron density f(r).","X-ray crystallography\n\nCrystals are often idealized as being perfectly periodic. In that ideal case, the atoms are positioned on a perfect lattice, the electron density is perfectly periodic, and the Fourier transform F(q) is zero except when q belongs to the reciprocal lattice (the so-called Bragg peaks). In reality, however, crystals are not perfectly periodic; atoms vibrate about their mean position, and there may be disorder of various types, such as mosaicity, dislocations, various point defects, and heterogeneity in the conformation of crystallized molecules. Therefore, the Bragg peaks have a finite width and there may be significant diffuse scattering, a continuum of scattered X-rays that fall between the Bragg peaks.","X-ray crystallography\n\nIntuitive understanding by Bragg's law","X-ray crystallography\n\nAn intuitive understanding of X-ray diffraction can be obtained from the Bragg model of diffraction. In this model, a given reflection is associated with a set of evenly spaced sheets running through the crystal, usually passing through the centers of the atoms of the crystal lattice. The orientation of a particular set of sheets is identified by its three Miller indices (h, k, l), and let their spacing be noted by d. William Lawrence Bragg proposed a model in which the incoming X-rays are scattered specularly (mirror-like) from each plane; from that assumption, X-rays scattered from adjacent planes will combine constructively (constructive interference) when the angle θ between the plane and the X-ray results in a path-length difference that is an integer multiple n of the X-ray wavelength λ. 2 d\\sin\\theta = n\\lambda\\,\nA reflection is said to be indexed when its Miller indices (or, more correctly, its reciprocal lattice vector components) have been identified from the known wavelength and the scattering angle 2θ. Such indexing gives the unit-cell parameters, the lengths and angles of the unit-cell, as well as its space group.","X-ray crystallography\n\nSince Bragg's law does not interpret the relative intensities of the reflections, however, it is generally inadequate to solve for the arrangement of atoms within the unit-cell; for that, a Fourier transform method must be carried out.","X-ray crystallography\n\nScattering as a Fourier transform","X-ray crystallography\n\nThe incoming X-ray beam has a polarization and should be represented as a vector wave; however, for simplicity, let it be represented here as a scalar wave. We also ignore the complication of the time dependence of the wave and just concentrate on the wave's spatial dependence. Plane waves can be represented by a wave vector kin, and so the strength of the incoming wave at time t=0 is given by\nA \\mathrm{e}^{\\mathrm{i}\\mathbf{k}_{\\mathrm{in}} \\cdot \\mathbf{r}}","X-ray crystallography\n\nAt position r within the sample, let there be a density of scatterers f(r); these scatterers should produce a scattered spherical wave of amplitude proportional to the local amplitude of the incoming wave times the number of scatterers in a small volume dV about r\n\\mathrm{amplitude\\ of\\ scattered\\ wave} = A \\mathrm{e}^{\\mathrm{i}\\mathbf{k} \\cdot \\mathbf{r}} S f(\\mathbf{r}) \\mathrm{d}V\nwhere S is the proportionality constant.","X-ray crystallography\n\nLet's consider the fraction of scattered waves that leave with an outgoing wave-vector of kout and strike the screen at rscreen. Since no energy is lost (elastic, not inelastic scattering), the wavelengths are the same as are the magnitudes of the wave-vectors |kin|=|kout|. From the time that the photon is scattered at r until it is absorbed at rscreen, the photon undergoes a change in phase\ne^{i \\mathbf{k}_{out} \\cdot \\left( \\mathbf{r}_{\\mathrm{screen}} - \\mathbf{r} \\right)}","X-ray crystallography\n\nThe net radiation arriving at rscreen is the sum of all the scattered waves throughout the crystal\nA S \\int \\mathrm{d}\\mathbf{r} f(\\mathbf{r}) \\mathrm{e}^{\\mathrm{i} \\mathbf{k}_{in} \\cdot \\mathbf{r}}\ne^{i \\mathbf{k}_{out} \\cdot \\left( \\mathbf{r}_{\\mathrm{screen}} - \\mathbf{r} \\right)} =\nA S e^{i \\mathbf{k}_{out} \\cdot \\mathbf{r}_{\\mathrm{screen}}}\n\\int \\mathrm{d}\\mathbf{r} f(\\mathbf{r}) \\mathrm{e}^{\\mathrm{i} \\left( \\mathbf{k}_{in} - \\mathbf{k}_{out} \\right) \\cdot \\mathbf{r}}","X-ray crystallography\n\nwhich may be written as a Fourier transform\nA S \\mathrm{e}^{\\mathrm{i} \\mathbf{k}_{out} \\cdot \\mathbf{r}_{\\mathrm{screen}}}\n\\int d\\mathbf{r} f(\\mathbf{r}) \\mathrm{e}^{-\\mathrm{i} \\mathbf{q} \\cdot \\mathbf{r}} =\nA S \\mathrm{e}^{\\mathrm{i} \\mathbf{k}_{out} \\cdot \\mathbf{r}_{\\mathrm{screen}}} F(\\mathbf{q})","X-ray crystallography\n\nwhere q = kout – kin. The measured intensity of the reflection will be square of this amplitude\nA^{2} S^{2} \\left|F(\\mathbf{q}) \\right|^{2}","X-ray crystallography\n\nFriedel and Bijvoet mates","X-ray crystallography\n\nFor every reflection corresponding to a point q in the reciprocal space, there is another reflection of the same intensity at the opposite point -q. This opposite reflection is known as the Friedel mate of the original reflection. This symmetry results from the mathematical fact that the density of electrons f(r) at a position r is always a real number. As noted above, f(r) is the inverse transform of its Fourier transform F(q); however, such an inverse transform is a complex number in general. To ensure that f(r) is real, the Fourier transform F(q) must be such that the Friedel mates F(−q) and F(q) are complex conjugates of one another. Thus, F(−q) has the same magnitude as F(q) but they have the opposite phase, i.e., φ(q) = −φ(q)\nF(-\\mathbf{q}) \\left|F(-\\mathbf{q}) \\right|\\mathrm{e}^{\\mathrm{i}\\phi(-\\mathbf{q})} \n F^{*}(\\mathbf{q}) = \\left| F(\\mathbf{q}) \\right|\\mathrm{e}^{-\\mathrm{i}\\phi(\\mathbf{q})}","X-ray crystallography\n\nThe equality of their magnitudes ensures that the Friedel mates have the same intensity |F|2. This symmetry allows one to measure the full Fourier transform from only half the reciprocal space, e.g., by rotating the crystal slightly more than 180° instead of a full 360° revolution. In crystals with significant symmetry, even more reflections may have the same intensity (Bijvoet mates); in such cases, even less of the reciprocal space may need to be measured. In favorable cases of high symmetry, sometimes only 90° or even only 45° of data are required to completely explore the reciprocal space.","X-ray crystallography\n\nThe Friedel-mate constraint can be derived from the definition of the inverse Fourier transform\nf(\\mathbf{r}) \\int \\frac{d\\mathbf{q}}{\\left(2\\pi\\right)^{3}} F(\\mathbf{q}) \\mathrm{e}^{\\mathrm{i}\\mathbf{q}\\cdot\\mathbf{r}}","X-ray crystallography\n\n\\int \\frac{d\\mathbf{q}}{\\left(2\\pi\\right)^{3}} \\left|F(\\mathbf{q}) \\right|\\mathrm{e}^{\\mathrm{i}\\phi(\\mathbf{q})} \\mathrm{e}^{\\mathrm{i}\\mathbf{q}\\cdot\\mathbf{r}}","X-ray crystallography\n\nSince Euler's formula states that eix = cos(x) + i sin(x), the inverse Fourier transform can be separated into a sum of a purely real part and a purely imaginary part\nf(\\mathbf{r}) \\int \\frac{d\\mathbf{q}}{\\left(2\\pi\\right)^{3}} \\left|F(\\mathbf{q}) \\right|\\mathrm{e}^{\\mathrm{i}\\left(\\phi+\\mathbf{q}\\cdot\\mathbf{r}\\right)}","X-ray crystallography\n\n\\int \\frac{d\\mathbf{q}}{\\left(2\\pi\\right)^{3}} \\left|F(\\mathbf{q}) \\right|\n\\cos\\left(\\phi+\\mathbf{q}\\cdot\\mathbf{r}\\right) +\ni \\int \\frac{d\\mathbf{q}}{\\left(2\\pi\\right)^{3}} \\left|F(\\mathbf{q}) \\right|\n\\sin\\left(\\phi+\\mathbf{q}\\cdot\\mathbf{r}\\right) = I_{\\mathrm{cos}} + iI_{\\mathrm{sin}}","X-ray crystallography\n\nThe function f(r) is real if and only if the second integral Isin is zero for all values of r. In turn, this is true if and only if the above constraint is satisfied\nI_{\\mathrm{sin}} \\int \\frac{d\\mathbf{q}}{\\left(2\\pi\\right)^{3}} \\left|F(\\mathbf{q}) \\right|\\sin\\left(\\phi+\\mathbf{q}\\cdot\\mathbf{r}\\right)","X-ray crystallography\n\n\\int \\frac{d\\mathbf{q}}{\\left(2\\pi\\right)^{3}} \\left|F(\\mathbf{-q}) \\right|\n\\sin\\left(-\\phi-\\mathbf{q}\\cdot\\mathbf{r}\\right) = -I_{\\mathrm{sin}}","X-ray crystallography\n\nsince Isin −Isin implies that Isin\n0.","X-ray crystallography\n\nEwald's sphere","X-ray crystallography\n\nEach X-ray diffraction image represents only a slice, a spherical slice of reciprocal space, as may be seen by the Ewald sphere construction. Both kout and kin have the same length, due to the elastic scattering, since the wavelength has not changed. Therefore, they may be represented as two radial vectors in a sphere in reciprocal space, which shows the values of q that are sampled in a given diffraction image. Since there is a slight spread in the incoming wavelengths of the incoming X-ray beam, the values of|F(q)|can be measured only for q vectors located between the two spheres corresponding to those radii. Therefore, to obtain a full set of Fourier transform data, it is necessary to rotate the crystal through slightly more than 180°, or sometimes less if sufficient symmetry is present. A full 360° rotation is not needed because of a symmetry intrinsic to the Fourier transforms of real functions (such as the electron density), but \"slightly more\" than 180° is needed to cover all of reciprocal space within a given resolution because of the curvature of the Ewald sphere.","X-ray crystallography\n\nIn practice, the crystal is rocked by a small amount (0.25-1°) to incorporate reflections near the boundaries of the spherical Ewald's shells.","X-ray crystallography\n\nPatterson function","X-ray crystallography\n\nA well-known result of Fourier transforms is the autocorrelation theorem, which states that the autocorrelation c(r) of a function f(r)\nc(\\mathbf{r}) \\int d\\mathbf{x} f(\\mathbf{x}) f(\\mathbf{x} + \\mathbf{r}) \n \\int \\frac{d\\mathbf{q}}{\\left(2\\pi\\right)^{3}} C(\\mathbf{q}) e^{i\\mathbf{q}\\cdot\\mathbf{r}}","X-ray crystallography\n\nhas a Fourier transform C(q) that is the squared magnitude of F(q)\nC(\\mathbf{q}) = \\left|F(\\mathbf{q}) \\right|^{2}","X-ray crystallography\n\nTherefore, the autocorrelation function c(r) of the electron density (also known as the Patterson function ) can be computed directly from the reflection intensities, without computing the phases. In principle, this could be used to determine the crystal structure directly; however, it is difficult to realize in practice. The autocorrelation function corresponds to the distribution of vectors between atoms in the crystal; thus, a crystal of N atoms in its unit cell may have N(N-1) peaks in its Patterson function. Given the inevitable errors in measuring the intensities, and the mathematical difficulties of reconstructing atomic positions from the interatomic vectors, this technique is rarely used to solve structures, except for the simplest crystals.","X-ray crystallography\n\nAdvantages of a crystal","X-ray crystallography\n\nIn principle, an atomic structure could be determined from applying X-ray scattering to non-crystalline samples, even to a single molecule. However, crystals offer a much stronger signal due to their periodicity. A crystalline sample is by definition periodic; a crystal is composed of many unit cells repeated indefinitely in three independent directions. Such periodic systems have a Fourier transform that is concentrated at periodically repeating points in reciprocal space known as Bragg peaks; the Bragg peaks correspond to the reflection spots observed in the diffraction image. Since the amplitude at these reflections grows linearly with the number N of scatterers, the observed intensity of these spots should grow quadratically, like N2. In other words, using a crystal concentrates the weak scattering of the individual unit cells into a much more powerful, coherent reflection that can be observed above the noise. This is an example of constructive interference.","X-ray crystallography\n\nIn a liquid, powder or amorphous sample, molecules within that sample are in random orientations. Such samples have a continuous Fourier spectrum that uniformly spreads its amplitude thereby reducing the measured signal intensity, as is observed in SAXS. More importantly, the orientational information is lost. Although theoretically possible, it is experimentally difficult to obtain atomic-resolution structures of complicated, asymmetric molecules from such rotationally averaged data. An intermediate case is fiber diffraction in which the subunits are arranged periodically in at least one dimension.","X-ray crystallography\n\nNobel Prizes for X-ray Crystallography","DNA\n\nDeoxyribonucleic acid (; DNA) is a molecule that carries the genetic instructions used in the growth, development, functioning and reproduction of all known living organisms and many viruses. DNA and RNA are nucleic acids; alongside proteins and complex carbohydrates (polysaccharides), they are one of the three major types of macromolecule that are essential for all known forms of life. Most DNA molecules consist of two biopolymer strands coiled around each other to form a double helix.","DNA\n\nThe two DNA strands are known as polynucleotides since they are composed of simpler units called nucleotides. Each nucleotide is composed of a nitrogen-containing nucleobase—either cytosine (C), guanine (G), adenine (A), or thymine (T)—as well as a sugar called deoxyribose and a phosphate group. The nucleotides are joined to one another in a chain by covalent bonds between the sugar of one nucleotide and the phosphate of the next, resulting in an alternating sugar-phosphate backbone. According to base pairing rules (A with T, and C with G), hydrogen bonds bind the nitrogenous bases of the two separate polynucleotide strands to make double-stranded DNA. The total amount of related DNA base pairs on Earth is estimated at 5.0 x 1037, and weighs 50 billion tonnes. In comparison, the total mass of the biosphere has been estimated to be as much as 4 TtC (trillion tons of carbon).","DNA\n\nDNA stores biological information. The DNA backbone is resistant to cleavage, and both strands of the double-stranded structure store the same biological information. Biological information is replicated as the two strands are separated. A significant portion of DNA (more than 98% for humans) is non-coding, meaning that these sections do not serve as patterns for protein sequences.","DNA\n\nThe two strands of DNA run in opposite directions to each other and are therefore anti-parallel. Attached to each sugar is one of four types of nucleobases (informally, bases). It is the sequence of these four nucleobases along the backbone that encodes biological information. Under the genetic code, RNA strands are translated to specify the sequence of amino acids within proteins. These RNA strands are initially created using DNA strands as a template in a process called transcription.","DNA\n\nWithin eukaryotic cells, DNA is organized into long structures called chromosomes. During cell division these chromosomes are duplicated in the process of DNA replication, providing each cell its own complete set of chromosomes. Eukaryotic organisms (animals, plants, fungi, and protists) store most of their DNA inside the cell nucleus and some of their DNA in organelles, such as mitochondria or chloroplasts. In contrast, prokaryotes (bacteria and archaea) store their DNA only in the cytoplasm. Within the eukaryotic chromosomes, chromatin proteins such as histones compact and organize DNA. These compact structures guide the interactions between DNA and other proteins, helping control which parts of the DNA are transcribed.","DNA\n\nDNA was first isolated by Friedrich Miescher in 1869. Its molecular structure was identified by James Watson and Francis Crick in 1953, whose model-building efforts were guided by X-ray diffraction data acquired by Rosalind Franklin. DNA is used by researchers as a molecular tool to explore physical laws and theories, such as the ergodic theorem and the theory of elasticity. The unique material properties of DNA have made it an attractive molecule for material scientists and engineers interested in micro- and nano-fabrication. Among notable advances in this field are DNA origami and DNA-based hybrid materials.","DNA\n\nProperties","DNA\n\nDNA is a long polymer made from repeating units called nucleotides. The structure of DNA is non-static, all species comprises two helical chains each coiled round the same axis, and each with a pitch of 34 ångströms (3.4 nanometres) and a radius of 10 ångströms (1.0 nanometre). According to another study, when measured in a particular solution, the DNA chain measured 22 to 26 ångströms wide (2.2 to 2.6 nanometres), and one nucleotide unit measured 3.3 Å (0.33 nm) long. Although each individual repeating unit is very small, DNA polymers can be very large molecules containing millions of nucleotides. For instance, the DNA in the largest human chromosome, chromosome number 1, consists of approximately 220 million base pairs and would be 85 mm long if straightened.","DNA\n\nIn living organisms DNA does not usually exist as a single molecule, but instead as a pair of molecules that are held tightly together.Berg J., Tymoczko J. and Stryer L. (2002) Biochemistry. W. H. Freeman and Company ISBN 0-7167-4955-6 These two long strands entwine like vines, in the shape of a double helix. The nucleotide repeats contain both the segment of the backbone of the molecule, which holds the chain together, and a nucleobase, which interacts with the other DNA strand in the helix. A nucleobase linked to a sugar is called a nucleoside and a base linked to a sugar and one or more phosphate groups is called a nucleotide. A polymer comprising multiple linked nucleotides (as in DNA) is called a polynucleotide.","DNA\n\nThe backbone of the DNA strand is made from alternating phosphate and sugar residues. The sugar in DNA is 2-deoxyribose, which is a pentose (five-carbon) sugar. The sugars are joined together by phosphate groups that form phosphodiester bonds between the third and fifth carbon atoms of adjacent sugar rings. These asymmetric bonds mean a strand of DNA has a direction. In a double helix the direction of the nucleotides in one strand is opposite to their direction in the other strand: the strands are antiparallel. The asymmetric ends of DNA strands are called the 5′ (five prime) and 3′ (three prime) ends, with the 5′ end having a terminal phosphate group and the 3′ end a terminal hydroxyl group. One major difference between DNA and RNA is the sugar, with the 2-deoxyribose in DNA being replaced by the alternative pentose sugar ribose in RNA.","DNA\n\nThe DNA double helix is stabilized primarily by two forces: hydrogen bonds between nucleotides and base-stacking interactions among aromatic nucleobases. In the aqueous environment of the cell, the conjugated bonds of nucleotide bases align perpendicular to the axis of the DNA molecule, minimizing their interaction with the solvation shell and therefore, the Gibbs free energy. The four bases found in DNA are adenine (abbreviated A), cytosine (C), guanine (G) and thymine (T). These four bases are attached to the sugar/phosphate to form the complete nucleotide, as shown for adenosine monophosphate. Adenine pairs with thymine and guanine pairs with cytosine. It was represented by A-T base pairs and G-C base pairs.","DNA\n\nNucleobase classification","DNA\n\nThe nucleobases are classified into two types: the purines, A and G, being fused five- and six-membered heterocyclic compounds, and the pyrimidines, the six-membered rings C and T. A fifth pyrimidine nucleobase, uracil (U), usually takes the place of thymine in RNA and differs from thymine by lacking a methyl group on its ring. In addition to RNA and DNA a large number of artificial nucleic acid analogues have also been created to study the properties of nucleic acids, or for use in biotechnology.","DNA\n\nUracil is not usually found in DNA, occurring only as a breakdown product of cytosine. However, in a number of bacteriophages – Bacillus subtilis bacteriophages PBS1 and PBS2 and Yersinia bacteriophage piR1-37 – thymine has been replaced by uracil. Another phage - Staphylococcal phage S6 - has been identified with a genome where thymine has been replaced by uracil.","DNA\n\nBase J (beta-d-glucopyranosyloxymethyluracil), a modified form of uracil, is also found in a number of organisms: the flagellates Diplonema and Euglena, and all the kinetoplastid genera. Biosynthesis of J occurs in two steps: in the first step a specific thymidine in DNA is converted into hydroxymethyldeoxyuridine; in the second HOMedU is glycosylated to form J. Proteins that bind specifically to this base have been identified. These proteins appear to be distant relatives of the Tet1 oncogene that is involved in the pathogenesis of acute myeloid leukemia. J appears to act as a termination signal for RNA polymerase II.","DNA\n\nGrooves","DNA\n\nTwin helical strands form the DNA backbone. Another double helix may be found tracing the spaces, or grooves, between the strands. These voids are adjacent to the base pairs and may provide a binding site. As the strands are not symmetrically located with respect to each other, the grooves are unequally sized. One groove, the major groove, is 22 Å wide and the other, the minor groove, is 12 Å wide. The width of the major groove means that the edges of the bases are more accessible in the major groove than in the minor groove. As a result, proteins such as transcription factors that can bind to specific sequences in double-stranded DNA usually make contact with the sides of the bases exposed in the major groove. This situation varies in unusual conformations of DNA within the cell (see below), but the major and minor grooves are always named to reflect the differences in size that would be seen if the DNA is twisted back into the ordinary B form.","DNA\n\nBase pairing","DNA\n\nIn a DNA double helix, each type of nucleobase on one strand bonds with just one type of nucleobase on the other strand. This is called complementary base pairing. Here, purines form hydrogen bonds to pyrimidines, with adenine bonding only to thymine in two hydrogen bonds, and cytosine bonding only to guanine in three hydrogen bonds. This arrangement of two nucleotides binding together across the double helix is called a base pair. As hydrogen bonds are not covalent, they can be broken and rejoined relatively easily. The two strands of DNA in a double helix can therefore be pulled apart like a zipper, either by a mechanical force or high temperature. As a result of this complementarity, all the information in the double-stranded sequence of a DNA helix is duplicated on each strand, which is vital in DNA replication. Indeed, this reversible and specific interaction between complementary base pairs is critical for all the functions of DNA in living organisms.","DNA\n\nTop, a GC base pair with three hydrogen bonds. Bottom, an AT base pair with two hydrogen bonds. Non-covalent hydrogen bonds between the pairs are shown as dashed lines.\nThe two types of base pairs form different numbers of hydrogen bonds, AT forming two hydrogen bonds, and GC forming three hydrogen bonds (see figures, right).\nDNA with high GC-content is more stable than DNA with low GC-content.","DNA\n\nAs noted above, most DNA molecules are actually two polymer strands, bound together in a helical fashion by noncovalent bonds; this double stranded structure (dsDNA) is maintained largely by the intrastrand base stacking interactions, which are strongest for G,C stacks. The two strands can come apart – a process known as melting – to form two single-stranded DNA molecules (ssDNA) molecules. Melting occurs at high temperature, low salt and high pH (low pH also melts DNA, but since DNA is unstable due to acid depurination, low pH is rarely used).","DNA\n\nThe stability of the dsDNA form depends not only on the GC-content (% G,C basepairs) but also on sequence (since stacking is sequence specific) and also length (longer molecules are more stable). The stability can be measured in various ways; a common way is the \"melting temperature\", which is the temperature at which 50% of the ds molecules are converted to ss molecules; melting temperature is dependent on ionic strength and the concentration of DNA.\nAs a result, it is both the percentage of GC base pairs and the overall length of a DNA double helix that determines the strength of the association between the two strands of DNA. Long DNA helices with a high GC-content have stronger-interacting strands, while short helices with high AT content have weaker-interacting strands. In biology, parts of the DNA double helix that need to separate easily, such as the TATAAT Pribnow box in some promoters, tend to have a high AT content, making the strands easier to pull apart.","DNA\n\nIn the laboratory, the strength of this interaction can be measured by finding the temperature necessary to break the hydrogen bonds, their melting temperature (also called Tm value). When all the base pairs in a DNA double helix melt, the strands separate and exist in solution as two entirely independent molecules. These single-stranded DNA molecules (ssDNA) have no single common shape, but some conformations are more stable than others.","DNA\n\nSense and antisense","DNA\n\nA DNA sequence is called \"sense\" if its sequence is the same as that of a messenger RNA copy that is translated into protein. The sequence on the opposite strand is called the \"antisense\" sequence. Both sense and antisense sequences can exist on different parts of the same strand of DNA (i.e. both strands can contain both sense and antisense sequences). In both prokaryotes and eukaryotes, antisense RNA sequences are produced, but the functions of these RNAs are not entirely clear. One proposal is that antisense RNAs are involved in regulating gene expression through RNA-RNA base pairing.","DNA\n\nA few DNA sequences in prokaryotes and eukaryotes, and more in plasmids and viruses, blur the distinction between sense and antisense strands by having overlapping genes. In these cases, some DNA sequences do double duty, encoding one protein when read along one strand, and a second protein when read in the opposite direction along the other strand. In bacteria, this overlap may be involved in the regulation of gene transcription, while in viruses, overlapping genes increase the amount of information that can be encoded within the small viral genome.","DNA\n\nSupercoiling","DNA\n\nDNA can be twisted like a rope in a process called DNA supercoiling. With DNA in its \"relaxed\" state, a strand usually circles the axis of the double helix once every 10.4 base pairs, but if the DNA is twisted the strands become more tightly or more loosely wound. If the DNA is twisted in the direction of the helix, this is positive supercoiling, and the bases are held more tightly together. If they are twisted in the opposite direction, this is negative supercoiling, and the bases come apart more easily. In nature, most DNA has slight negative supercoiling that is introduced by enzymes called topoisomerases. These enzymes are also needed to relieve the twisting stresses introduced into DNA strands during processes such as transcription and DNA replication.","DNA\n\nAlternative DNA structures","DNA\n\nDNA exists in many possible conformations that include A-DNA, B-DNA, and Z-DNA forms, although, only B-DNA and Z-DNA have been directly observed in functional organisms. The conformation that DNA adopts depends on the hydration level, DNA sequence, the amount and direction of supercoiling, chemical modifications of the bases, the type and concentration of metal ions, as well as the presence of polyamines in solution.","DNA\n\nThe first published reports of A-DNA X-ray diffraction patterns—and also B-DNA—used analyses based on Patterson transforms that provided only a limited amount of structural information for oriented fibers of DNA. An alternative analysis was then proposed by Wilkins et al., in 1953, for the in vivo B-DNA X-ray diffraction/scattering patterns of highly hydrated DNA fibers in terms of squares of Bessel functions. In the same journal, James Watson and Francis Crick presented their molecular modeling analysis of the DNA X-ray diffraction patterns to suggest that the structure was a double-helix.","DNA\n\nAlthough the \"B-DNA form\" is most common under the conditions found in cells, it is not a well-defined conformation but a family of related DNA conformations that occur at the high hydration levels present in living cells. Their corresponding X-ray diffraction and scattering patterns are characteristic of molecular paracrystals with a significant degree of disorder.","DNA\n\nCompared to B-DNA, the A-DNA form is a wider right-handed spiral, with a shallow, wide minor groove and a narrower, deeper major groove. The A form occurs under non-physiological conditions in partially dehydrated samples of DNA, while in the cell it may be produced in hybrid pairings of DNA and RNA strands, as well as in enzyme-DNA complexes. Segments of DNA where the bases have been chemically modified by methylation may undergo a larger change in conformation and adopt the Z form. Here, the strands turn about the helical axis in a left-handed spiral, the opposite of the more common B form. These unusual structures can be recognized by specific Z-DNA binding proteins and may be involved in the regulation of transcription.","DNA\n\nAlternative DNA chemistry","DNA\n\nFor a number of years exobiologists have proposed the existence of a shadow biosphere, a postulated microbial biosphere of Earth that uses radically different biochemical and molecular processes than currently known life. One of the proposals was the existence of lifeforms that use arsenic instead of phosphorus in DNA. A report in 2010 of the possibility in the bacterium GFAJ-1, was announced, though the research was disputed, and evidence suggests the bacterium actively prevents the incorporation of arsenic into the DNA backbone and other biomolecules.","DNA\n\nQuadruplex structures","DNA\n\nAt the ends of the linear chromosomes are specialized regions of DNA called telomeres. The main function of these regions is to allow the cell to replicate chromosome ends using the enzyme telomerase, as the enzymes that normally replicate DNA cannot copy the extreme 3′ ends of chromosomes. These specialized chromosome caps also help protect the DNA ends, and stop the DNA repair systems in the cell from treating them as damage to be corrected. In human cells, telomeres are usually lengths of single-stranded DNA containing several thousand repeats of a simple TTAGGG sequence.","DNA\n\nThese guanine-rich sequences may stabilize chromosome ends by forming structures of stacked sets of four-base units, rather than the usual base pairs found in other DNA molecules. Here, four guanine bases form a flat plate and these flat four-base units then stack on top of each other, to form a stable G-quadruplex structure. These structures are stabilized by hydrogen bonding between the edges of the bases and chelation of a metal ion in the centre of each four-base unit. Other structures can also be formed, with the central set of four bases coming from either a single strand folded around the bases, or several different parallel strands, each contributing one base to the central structure.","DNA\n\nIn addition to these stacked structures, telomeres also form large loop structures called telomere loops, or T-loops. Here, the single-stranded DNA curls around in a long circle stabilized by telomere-binding proteins. At the very end of the T-loop, the single-stranded telomere DNA is held onto a region of double-stranded DNA by the telomere strand disrupting the double-helical DNA and base pairing to one of the two strands. This triple-stranded structure is called a displacement loop or D-loop.","DNA\n\nBranched DNA can form networks containing multiple branches.","DNA\n\nBranched DNA","DNA\n\nIn DNA, fraying occurs when non-complementary regions exist at the end of an otherwise complementary double-strand of DNA. However, branched DNA can occur if a third strand of DNA is introduced and contains adjoining regions able to hybridize with the frayed regions of the pre-existing double-strand. Although the simplest example of branched DNA involves only three strands of DNA, complexes involving additional strands and multiple branches are also possible. Branched DNA can be used in nanotechnology to construct geometric shapes, see the section on uses in technology below.","DNA\n\nChemical modifications and altered DNA packaging","DNA\n\nStructure of cytosine with and without the 5-methyl group. Deamination converts 5-methylcytosine into thymine.","DNA\n\nBase modifications and DNA packaging","DNA\n\nThe expression of genes is influenced by how the DNA is packaged in chromosomes, in a structure called chromatin. Base modifications can be involved in packaging, with regions that have low or no gene expression usually containing high levels of methylation of cytosine bases. DNA packaging and its influence on gene expression can also occur by covalent modifications of the histone protein core around which DNA is wrapped in the chromatin structure or else by remodeling carried out by chromatin remodeling complexes (see Chromatin remodeling). There is, further, crosstalk between DNA methylation and histone modification, so they can coordinately affect chromatin and gene expression.","DNA\n\nFor one example, cytosine methylation, produces 5-methylcytosine, which is important for X-chromosome inactivation. The average level of methylation varies between organisms – the worm Caenorhabditis elegans lacks cytosine methylation, while vertebrates have higher levels, with up to 1% of their DNA containing 5-methylcytosine. Despite the importance of 5-methylcytosine, it can deaminate to leave a thymine base, so methylated cytosines are particularly prone to mutations. Other base modifications include adenine methylation in bacteria, the presence of 5-hydroxymethylcytosine in the brain, and the glycosylation of uracil to produce the \"J-base\" in kinetoplastids.","DNA\n\nDamage","DNA\n\nDNA can be damaged by many sorts of mutagens, which change the DNA sequence. Mutagens include oxidizing agents, alkylating agents and also high-energy electromagnetic radiation such as ultraviolet light and X-rays. The type of DNA damage produced depends on the type of mutagen. For example, UV light can damage DNA by producing thymine dimers, which are cross-links between pyrimidine bases. On the other hand, oxidants such as free radicals or hydrogen peroxide produce multiple forms of damage, including base modifications, particularly of guanosine, and double-strand breaks. A typical human cell contains about 150,000 bases that have suffered oxidative damage. Of these oxidative lesions, the most dangerous are double-strand breaks, as these are difficult to repair and can produce point mutations, insertions and deletions from the DNA sequence, as well as chromosomal translocations. These mutations can cause cancer. Because of inherent limitations in the DNA repair mechanisms, if humans lived long enough, they would all eventually develop cancer. DNA damages that are naturally occurring, due to normal cellular processes that produce reactive oxygen species, the hydrolytic activities of cellular water, etc., also occur frequently.","DNA\n\nAlthough most of these damages are repaired, in any cell some DNA damage may remain despite the action of repair processes. These remaining DNA damages accumulate with age in mammalian postmitotic tissues. This accumulation appears to be an important underlying cause of aging.","DNA\n\nMany mutagens fit into the space between two adjacent base pairs, this is called intercalation. Most intercalators are aromatic and planar molecules; examples include ethidium bromide, acridines, daunomycin, and doxorubicin. For an intercalator to fit between base pairs, the bases must separate, distorting the DNA strands by unwinding of the double helix. This inhibits both transcription and DNA replication, causing toxicity and mutations. As a result, DNA intercalators may be carcinogens, and in the case of thalidomide, a teratogen. Others such as benzo(a)pyrene|benzo[a]pyrene diol epoxide and aflatoxin form DNA adducts that induce errors in replication. Nevertheless, due to their ability to inhibit DNA transcription and replication, other similar toxins are also used in chemotherapy to inhibit rapidly growing cancer cells.","DNA\n\nBiological functions","DNA\n\nDNA usually occurs as linear chromosomes in eukaryotes, and circular chromosomes in prokaryotes. The set of chromosomes in a cell makes up its genome; the human genome has approximately 3 billion base pairs of DNA arranged into 46 chromosomes. The information carried by DNA is held in the sequence of pieces of DNA called genes. Transmission of genetic information in genes is achieved via complementary base pairing. For example, in transcription, when a cell uses the information in a gene, the DNA sequence is copied into a complementary RNA sequence through the attraction between the DNA and the correct RNA nucleotides. Usually, this RNA copy is then used to make a matching protein sequence in a process called translation, which depends on the same interaction between RNA nucleotides. In alternative fashion, a cell may simply copy its genetic information in a process called DNA replication. The details of these functions are covered in other articles; here the focus is on the interactions between DNA and other molecules that mediate the function of the genome.","DNA\n\nGenes and genomes","DNA\n\nGenomic DNA is tightly and orderly packed in the process called DNA condensation to fit the small available volumes of the cell. In eukaryotes, DNA is located in the cell nucleus, as well as small amounts in mitochondria and chloroplasts. In prokaryotes, the DNA is held within an irregularly shaped body in the cytoplasm called the nucleoid. The genetic information in a genome is held within genes, and the complete set of this information in an organism is called its genotype. A gene is a unit of heredity and is a region of DNA that influences a particular characteristic in an organism. Genes contain an open reading frame that can be transcribed, as well as regulatory sequences such as promoters and enhancers, which control the transcription of the open reading frame.","DNA\n\nIn many species, only a small fraction of the total sequence of the genome encodes protein. For example, only about 1.5% of the human genome consists of protein-coding exons, with over 50% of human DNA consisting of non-coding repetitive sequences. The reasons for the presence of so much noncoding DNA in eukaryotic genomes and the extraordinary differences in genome size, or C-value, among species represent a long-standing puzzle known as the \"C-value enigma\". However, some DNA sequences that do not code protein may still encode functional non-coding RNA molecules, which are involved in the regulation of gene expression.","DNA\n\nSome noncoding DNA sequences play structural roles in chromosomes. Telomeres and centromeres typically contain few genes, but are important for the function and stability of chromosomes. An abundant form of noncoding DNA in humans are pseudogenes, which are copies of genes that have been disabled by mutation. These sequences are usually just molecular fossils, although they can occasionally serve as raw genetic material for the creation of new genes through the process of gene duplication and divergence.","DNA\n\nTranscription and translation","DNA\n\nA gene is a sequence of DNA that contains genetic information and can influence the phenotype of an organism. Within a gene, the sequence of bases along a DNA strand defines a messenger RNA sequence, which then defines one or more protein sequences. The relationship between the nucleotide sequences of genes and the amino-acid sequences of proteins is determined by the rules of translation, known collectively as the genetic code. The genetic code consists of three-letter 'words' called codons formed from a sequence of three nucleotides (e.g. ACT, CAG, TTT).","DNA\n\nIn transcription, the codons of a gene are copied into messenger RNA by RNA polymerase. This RNA copy is then decoded by a ribosome that reads the RNA sequence by base-pairing the messenger RNA to transfer RNA, which carries amino acids. Since there are 4 bases in 3-letter combinations, there are 64 possible codons (43 combinations). These encode the twenty standard amino acids, giving most amino acids more than one possible codon. There are also three 'stop' or 'nonsense' codons signifying the end of the coding region; these are the TAA, TGA, and TAG codons.","DNA\n\nReplication","DNA\n\nCell division is essential for an organism to grow, but, when a cell divides, it must replicate the DNA in its genome so that the two daughter cells have the same genetic information as their parent. The double-stranded structure of DNA provides a simple mechanism for DNA replication. Here, the two strands are separated and then each strand's complementary DNA sequence is recreated by an enzyme called DNA polymerase. This enzyme makes the complementary strand by finding the correct base through complementary base pairing, and bonding it onto the original strand. As DNA polymerases can only extend a DNA strand in a 5′ to 3′ direction, different mechanisms are used to copy the antiparallel strands of the double helix. In this way, the base on the old strand dictates which base appears on the new strand, and the cell ends up with a perfect copy of its DNA.","DNA\n\nExtracellular nucleic acids","DNA\n\nNaked extracellular DNA (eDNA), most of it released by cell death, is nearly ubiquitous in the environment. Its concentration in soil may be as high as 2 μg/L, and its concentration in natural aquatic environments may be as high at 88 μg/L. Various possible functions have been proposed for eDNA: it may be involved in horizontal gene transfer; it may provide nutrients; and it may act as a buffer to recruit or titrate ions or antibiotics. Extracellular DNA acts as a functional extracellular matrix component in the biofilms of a number of bacterial species. It may act as a recognition factor to regulate the attachment and dispersal of specific cell types in the biofilm; it may contribute to biofilm formation; and it may contribute to the biofilm's physical strength and resistance to biological stress.","DNA\n\nInteractions with proteins","DNA\n\nAll the functions of DNA depend on interactions with proteins. These protein interactions can be non-specific, or the protein can bind specifically to a single DNA sequence. Enzymes can also bind to DNA and of these, the polymerases that copy the DNA base sequence in transcription and DNA replication are particularly important.","DNA\n\nDNA-binding proteins","DNA\n\nInteraction of DNA (shown in orange) with histones (shown in blue). These proteins' basic amino acids bind to the acidic phosphate groups on DNA.","DNA\n\nStructural proteins that bind DNA are well-understood examples of non-specific DNA-protein interactions. Within chromosomes, DNA is held in complexes with structural proteins. These proteins organize the DNA into a compact structure called chromatin. In eukaryotes this structure involves DNA binding to a complex of small basic proteins called histones, while in prokaryotes multiple types of proteins are involved. The histones form a disk-shaped complex called a nucleosome, which contains two complete turns of double-stranded DNA wrapped around its surface. These non-specific interactions are formed through basic residues in the histones making ionic bonds to the acidic sugar-phosphate backbone of the DNA, and are therefore largely independent of the base sequence. Chemical modifications of these basic amino acid residues include methylation, phosphorylation and acetylation. These chemical changes alter the strength of the interaction between the DNA and the histones, making the DNA more or less accessible to transcription factors and changing the rate of transcription. Other non-specific DNA-binding proteins in chromatin include the high-mobility group proteins, which bind to bent or distorted DNA. These proteins are important in bending arrays of nucleosomes and arranging them into the larger structures that make up chromosomes.","DNA\n\nA distinct group of DNA-binding proteins are the DNA-binding proteins that specifically bind single-stranded DNA. In humans, replication protein A is the best-understood member of this family and is used in processes where the double helix is separated, including DNA replication, recombination and DNA repair. These binding proteins seem to stabilize single-stranded DNA and protect it from forming stem-loops or being degraded by nucleases.","DNA\n\nIn contrast, other proteins have evolved to bind to particular DNA sequences. The most intensively studied of these are the various transcription factors, which are proteins that regulate transcription. Each transcription factor binds to one particular set of DNA sequences and activates or inhibits the transcription of genes that have these sequences close to their promoters. The transcription factors do this in two ways. Firstly, they can bind the RNA polymerase responsible for transcription, either directly or through other mediator proteins; this locates the polymerase at the promoter and allows it to begin transcription. Alternatively, transcription factors can bind enzymes that modify the histones at the promoter. This changes the accessibility of the DNA template to the polymerase.","DNA\n\nAs these DNA targets can occur throughout an organism's genome, changes in the activity of one type of transcription factor can affect thousands of genes. Consequently, these proteins are often the targets of the signal transduction processes that control responses to environmental changes or cellular differentiation and development. The specificity of these transcription factors' interactions with DNA come from the proteins making multiple contacts to the edges of the DNA bases, allowing them to \"read\" the DNA sequence. Most of these base-interactions are made in the major groove, where the bases are most accessible.","DNA\n\nDNA-modifying enzymes","DNA\n\nNucleases and ligases","DNA\n\nNucleases are enzymes that cut DNA strands by catalyzing the hydrolysis of the phosphodiester bonds. Nucleases that hydrolyse nucleotides from the ends of DNA strands are called exonucleases, while endonucleases cut within strands. The most frequently used nucleases in molecular biology are the restriction endonucleases, which cut DNA at specific sequences. For instance, the EcoRV enzyme shown to the left recognizes the 6-base sequence 5′-GATATC-3′ and makes a cut at the vertical line. In nature, these enzymes protect bacteria against phage infection by digesting the phage DNA when it enters the bacterial cell, acting as part of the restriction modification system. In technology, these sequence-specific nucleases are used in molecular cloning and DNA fingerprinting.","DNA\n\nEnzymes called DNA ligases can rejoin cut or broken DNA strands. Ligases are particularly important in lagging strand DNA replication, as they join together the short segments of DNA produced at the replication fork into a complete copy of the DNA template. They are also used in DNA repair and genetic recombination.","DNA\n\nTopoisomerases and helicases","DNA\n\nTopoisomerases are enzymes with both nuclease and ligase activity. These proteins change the amount of supercoiling in DNA. Some of these enzymes work by cutting the DNA helix and allowing one section to rotate, thereby reducing its level of supercoiling; the enzyme then seals the DNA break. Other types of these enzymes are capable of cutting one DNA helix and then passing a second strand of DNA through this break, before rejoining the helix. Topoisomerases are required for many processes involving DNA, such as DNA replication and transcription.","DNA\n\nHelicases are proteins that are a type of molecular motor. They use the chemical energy in nucleoside triphosphates, predominantly ATP, to break hydrogen bonds between bases and unwind the DNA double helix into single strands. These enzymes are essential for most processes where enzymes need to access the DNA bases.","DNA\n\nPolymerases","DNA\n\nPolymerases are enzymes that synthesize polynucleotide chains from nucleoside triphosphates. The sequence of their products are created based on existing polynucleotide chains—which are called templates. These enzymes function by repeatedly adding a nucleotide to the 3′ hydroxyl group at the end of the growing polynucleotide chain. As a consequence, all polymerases work in a 5′ to 3′ direction. In the active site of these enzymes, the incoming nucleoside triphosphate base-pairs to the template: this allows polymerases to accurately synthesize the complementary strand of their template. Polymerases are classified according to the type of template that they use.","DNA\n\nIn DNA replication, DNA-dependent DNA polymerases make copies of DNA polynucleotide chains. In order to preserve biological information, it is essential that the sequence of bases in each copy are precisely complementary to the sequence of bases in the template strand. Many DNA polymerases have a proofreading activity. Here, the polymerase recognizes the occasional mistakes in the synthesis reaction by the lack of base pairing between the mismatched nucleotides. If a mismatch is detected, a 3′ to 5′ exonuclease activity is activated and the incorrect base removed. In most organisms, DNA polymerases function in a large complex called the replisome that contains multiple accessory subunits, such as the DNA clamp or helicases.","DNA\n\nRNA-dependent DNA polymerases are a specialized class of polymerases that copy the sequence of an RNA strand into DNA. They include reverse transcriptase, which is a viral enzyme involved in the infection of cells by retroviruses, and telomerase, which is required for the replication of telomeres. Telomerase is an unusual polymerase because it contains its own RNA template as part of its structure.","DNA\n\nTranscription is carried out by a DNA-dependent RNA polymerase that copies the sequence of a DNA strand into RNA. To begin transcribing a gene, the RNA polymerase binds to a sequence of DNA called a promoter and separates the DNA strands. It then copies the gene sequence into a messenger RNA transcript until it reaches a region of DNA called the terminator, where it halts and detaches from the DNA. As with human DNA-dependent DNA polymerases, RNA polymerase II, the enzyme that transcribes most of the genes in the human genome, operates as part of a large protein complex with multiple regulatory and accessory subunits.","DNA\n\nGenetic recombination","DNA\n\nStructure of the Holliday junction intermediate in genetic recombination. The four separate DNA strands are coloured red, blue, green and yellow.","DNA\n\nA DNA helix usually does not interact with other segments of DNA, and in human cells the different chromosomes even occupy separate areas in the nucleus called \"chromosome territories\". This physical separation of different chromosomes is important for the ability of DNA to function as a stable repository for information, as one of the few times chromosomes interact is in chromosomal crossover which occurs during sexual reproduction, when genetic recombination occurs. Chromosomal crossover is when two DNA helices break, swap a section and then rejoin.","DNA\n\nRecombination allows chromosomes to exchange genetic information and produces new combinations of genes, which increases the efficiency of natural selection and can be important in the rapid evolution of new proteins. Genetic recombination can also be involved in DNA repair, particularly in the cell's response to double-strand breaks.","DNA\n\nThe most common form of chromosomal crossover is homologous recombination, where the two chromosomes involved share very similar sequences. Non-homologous recombination can be damaging to cells, as it can produce chromosomal translocations and genetic abnormalities. The recombination reaction is catalyzed by enzymes known as recombinases, such as RAD51. The first step in recombination is a double-stranded break caused by either an endonuclease or damage to the DNA. A series of steps catalyzed in part by the recombinase then leads to joining of the two helices by at least one Holliday junction, in which a segment of a single strand in each helix is annealed to the complementary strand in the other helix. The Holliday junction is a tetrahedral junction structure that can be moved along the pair of chromosomes, swapping one strand for another. The recombination reaction is then halted by cleavage of the junction and re-ligation of the released DNA.","DNA\n\nEvolution","DNA\n\nDNA contains the genetic information that allows all modern living things to function, grow and reproduce. However, it is unclear how long in the 4-billion-year history of life DNA has performed this function, as it has been proposed that the earliest forms of life may have used RNA as their genetic material. RNA may have acted as the central part of early cell metabolism as it can both transmit genetic information and carry out catalysis as part of ribozymes. This ancient RNA world where nucleic acid would have been used for both catalysis and genetics may have influenced the evolution of the current genetic code based on four nucleotide bases. This would occur, since the number of different bases in such an organism is a trade-off between a small number of bases increasing replication accuracy and a large number of bases increasing the catalytic efficiency of ribozymes. However, there is no direct evidence of ancient genetic systems, as recovery of DNA from most fossils is impossible because DNA survives in the environment for less than one million years, and slowly degrades into short fragments in solution.","DNA\n\nClaims for older DNA have been made, most notably a report of the isolation of a viable bacterium from a salt crystal 250 million years old, but these claims are controversial.","DNA\n\nBuilding blocks of DNA (adenine, guanine and related organic molecules) may have been formed extraterrestrially in outer space. Complex DNA and RNA organic compounds of life, including uracil, cytosine and thymine, have also been formed in the laboratory under conditions mimicking those found in outer space, using starting chemicals, such as pyrimidine, found in meteorites. Pyrimidine, like polycyclic aromatic hydrocarbons (PAHs), the most carbon-rich chemical found in the universe, may have been formed in red giants or in interstellar dust and gas clouds.","DNA\n\nUses in technology","DNA\n\nGenetic engineering","DNA\n\nMethods have been developed to purify DNA from organisms, such as phenol-chloroform extraction, and to manipulate it in the laboratory, such as restriction digests and the polymerase chain reaction. Modern biology and biochemistry make intensive use of these techniques in recombinant DNA technology. Recombinant DNA is a man-made DNA sequence that has been assembled from other DNA sequences. They can be transformed into organisms in the form of plasmids or in the appropriate format, by using a viral vector. The genetically modified organisms produced can be used to produce products such as recombinant proteins, used in medical research, or be grown in agriculture.","DNA\n\nDNA profiling","DNA\n\nForensic scientists can use DNA in blood, semen, skin, saliva or hair found at a crime scene to identify a matching DNA of an individual, such as a perpetrator. This process is formally termed DNA profiling, but may also be called \"genetic fingerprinting\". In DNA profiling, the lengths of variable sections of repetitive DNA, such as short tandem repeats and minisatellites, are compared between people. This method is usually an extremely reliable technique for identifying a matching DNA. However, identification can be complicated if the scene is contaminated with DNA from several people. DNA profiling was developed in 1984 by British geneticist Sir Alec Jeffreys, and first used in forensic science to convict Colin Pitchfork in the 1988 Enderby murders case.","DNA\n\nThe development of forensic science, and the ability to now obtain genetic matching on minute samples of blood, skin, saliva or hair has led to a re-examination of a number of cases. Evidence can now be uncovered that was not scientifically possible at the time of the original examination. Combined with the removal of the double jeopardy law in some places, this can allow cases to be reopened where previous trials have failed to produce sufficient evidence to convince a jury. People charged with serious crimes may be required to provide a sample of DNA for matching purposes. The most obvious defence to DNA matches obtained forensically is to claim that cross-contamination of evidence has taken place. This has resulted in meticulous strict handling procedures with new cases of serious crime.\nDNA profiling is also used to identify victims of mass casualty incidents. As well as positively identifying bodies or body parts in serious accidents, DNA profiling is being successfully used to identify individual victims in mass war graves – matching to family members.","DNA\n\nDNA profiling is also used in DNA paternity testing in order to determine if someone is the biologicalparent or grandparent of a child with the probability of parentage is typically 99.99% when the alleged parent is biologically related to the child. Normal DNA sequencing methods happen after birth but there are new methods to test paternity while the mother is still pregnant.","DNA\n\nDNA enzymes or catalytic DNA","DNA\n\nDeoxyribozymes, also called DNAzymes or catalytic DNA are first discovered in 1994. They are mostly single stranded DNA sequences isolated from a large pool of random DNA sequences through a combinatorial approach called in vitro selection or SELEX. DNAzymes catalyze variety of chemical reactions including RNA/DNA cleavage, RNA/DNA ligation, amino acids phosphorylation/dephosphorylation, carbon-carbon bond formation, and etc. DNAzymes can enhance catalytic rate of chemical reactions up to 100,000,000,000-fold over the uncatalyzed reaction. The most extensively studied class of DNAzymes are RNA-cleaving DNAzymes which have been used in detection of different metal ions and designing therapeutic agents. Several metal-specific DNAzymes have been reported including the GR-5 DNAzyme (lead-specific), the CA1-3 DNAzymes (copper-specific), the 39E DNAzyme (uranyl-specific) and the NaA43 DNAzyme (sodium-specific). The NaA43 DNAzyme, which is reported to be more than 10,000-fold selective for sodium over other metal ions, was used to make a real-time sodium sensor in living cells.","DNA\n\nBioinformatics","DNA\n\nBioinformatics involves the development of techniques to store, data mine, search and manipulate biological data, including DNA nucleic acid sequence data. These have led to widely applied advances in computer science, especially string searching algorithms, machine learning and database theory. String searching or matching algorithms, which find an occurrence of a sequence of letters inside a larger sequence of letters, were developed to search for specific sequences of nucleotides. The DNA sequence may be aligned with other DNA sequences to identify homologous sequences and locate the specific mutations that make them distinct. These techniques, especially multiple sequence alignment, are used in studying phylogenetic relationships and protein function. Data sets representing entire genomes' worth of DNA sequences, such as those produced by the Human Genome Project, are difficult to use without the annotations that identify the locations of genes and regulatory elements on each chromosome. Regions of DNA sequence that have the characteristic patterns associated with protein- or RNA-coding genes can be identified by gene finding algorithms, which allow researchers to predict the presence of particular gene products and their possible functions in an organism even before they have been isolated experimentally.","DNA\n\nEntire genomes may also be compared, which can shed light on the evolutionary history of particular organism and permit the examination of complex evolutionary events.","DNA\n\nDNA nanotechnology","DNA\n\nDNA nanotechnology uses the unique molecular recognition properties of DNA and other nucleic acids to create self-assembling branched DNA complexes with useful properties. DNA is thus used as a structural material rather than as a carrier of biological information. This has led to the creation of two-dimensional periodic lattices (both tile-based and using the \"DNA origami\" method) as well as three-dimensional structures in the shapes of polyhedra. Nanomechanical devices and algorithmic self-assembly have also been demonstrated, and these DNA structures have been used to template the arrangement of other molecules such as gold nanoparticles and streptavidin proteins.","DNA\n\nHistory and anthropology","DNA\n\nBecause DNA collects mutations over time, which are then inherited, it contains historical information, and, by comparing DNA sequences, geneticists can infer the evolutionary history of organisms, their phylogeny. This field of phylogenetics is a powerful tool in evolutionary biology. If DNA sequences within a species are compared, population geneticists can learn the history of particular populations. This can be used in studies ranging from ecological genetics to anthropology; For example, DNA evidence is being used to try to identify the Ten Lost Tribes of Israel.","DNA\n\nInformation storage","DNA\n\nIn a paper published in Nature in January 2013, scientists from the European Bioinformatics Institute and Agilent Technologies proposed a mechanism to use DNA's ability to code information as a means of digital data storage. The group was able to encode 739 kilobytes of data into DNA code, synthesize the actual DNA, then sequence the DNA and decode the information back to its original form, with a reported 100% accuracy. The encoded information consisted of text files and audio files. A prior experiment was published in August 2012. It was conducted by researchers at Harvard University, where the text of a 54,000-word book was encoded in DNA.","DNA\n\nHistory of DNA research","DNA\n\nDNA was first isolated by the Swiss physician Friedrich Miescher who, in 1869, discovered a microscopic substance in the pus of discarded surgical bandages. As it resided in the nuclei of cells, he called it \"nuclein\". In 1878, Albrecht Kossel isolated the non-protein component of \"nuclein\", nucleic acid, and later isolated its five primary nucleobases. In 1919, Phoebus Levene identified the base, sugar and phosphate nucleotide unit. Levene suggested that DNA consisted of a string of nucleotide units linked together through the phosphate groups. Levene thought the chain was short and the bases repeated in a fixed order. In 1937, William Astbury produced the first X-ray diffraction patterns that showed that DNA had a regular structure.","DNA\n\nIn 1927, Nikolai Koltsov proposed that inherited traits would be inherited via a \"giant hereditary molecule\" made up of \"two mirror strands that would replicate in a semi-conservative fashion using each strand as a template\". In 1928, Frederick Griffith in his experiment discovered that traits of the \"smooth\" form of Pneumococcus could be transferred to the \"rough\" form of the same bacteria by mixing killed \"smooth\" bacteria with the live \"rough\" form. This system provided the first clear suggestion that DNA carries genetic information—the Avery–MacLeod–McCarty experiment—when Oswald Avery, along with coworkers Colin MacLeod and Maclyn McCarty, identified DNA as the transforming principle in 1943. DNA's role in heredity was confirmed in 1952, when Alfred Hershey and Martha Chase in the Hershey–Chase experiment showed that DNA is the genetic material of the T2 phage.","DNA\n\nIn 1953, James Watson and Francis Crick suggested what is now accepted as the first correct double-helix model of DNA structure in the journal Nature. Their double-helix, molecular model of DNA was then based on a single X-ray diffraction image (labeled as \"Photo 51\") taken by Rosalind Franklin and Raymond Gosling in May 1952, as well as the information that the DNA bases are paired.","DNA\n\nExperimental evidence supporting the Watson and Crick model was published in a series of five articles in the same issue of Nature.Nature Archives [http://www.nature.com/nature/dna50/archive.html Double Helix of DNA: 50 Years] Of these, Franklin and Gosling's paper was the first publication of their own X-ray diffraction data and original analysis method that partially supported the Watson and Crick model; this issue also contained an article on DNA structure by Maurice Wilkins and two of his colleagues, whose analysis and in vivo B-DNA X-ray patterns also supported the presence in vivo of the double-helical DNA configurations as proposed by Crick and Watson for their double-helix molecular model of DNA in the previous two pages of Nature. In 1962, after Franklin's death, Watson, Crick, and Wilkins jointly received the Nobel Prize in Physiology or Medicine. Nobel Prizes are awarded only to living recipients. A debate continues about who should receive credit for the discovery.","DNA\n\nIn an influential presentation in 1957, Crick laid out the central dogma of molecular biology, which foretold the relationship between DNA, RNA, and proteins, and articulated the \"adaptor hypothesis\". Final confirmation of the replication mechanism that was implied by the double-helical structure followed in 1958 through the Meselson–Stahl experiment. Further work by Crick and coworkers showed that the genetic code was based on non-overlapping triplets of bases, called codons, allowing Har Gobind Khorana, Robert W. Holley and Marshall Warren Nirenberg to decipher the genetic code. These findings represent the birth of molecular biology.","Francis Crick\n\nFrancis Harry Compton Crick (8 June 1916 – 28 July 2004) was a British molecular biologist, biophysicist, and neuroscientist, most noted for being a co-discoverer of the structure of the DNA molecule in 1953 with James Watson. Together with Watson and Maurice Wilkins, he was jointly awarded the 1962 Nobel Prize in Physiology or Medicine \"for their discoveries concerning the molecular structure of nucleic acids and its significance for information transfer in living material\".","Francis Crick\n\nCrick was an important theoretical molecular biologist and played a crucial role in research related to revealing the genetic code. He is widely known for use of the term \"central dogma\" to summarize the idea that genetic information flow in cells is essentially one-way, from DNA to RNA to protein.","Francis Crick\n\nDuring the remainder of his career, he held the post of J.W. Kieckhefer Distinguished Research Professor at the Salk Institute for Biological Studies in La Jolla, California. His later research centered on theoretical neurobiology and attempts to advance the scientific study of human consciousness. He remained in this post until his death; \"he was editing a manuscript on his death bed, a scientist until the bitter end\" according to Christof Koch.","Francis Crick\n\nEarly life and education","Francis Crick\n\nCrick was the first son of Harry Crick (1887–1948) and Annie Elizabeth Crick (née Wilkins; 1879–1955). He was born and raised in Weston Favell, then a small village near the English town of Northampton, in which Crick’s father and uncle ran the family’s boot and shoe factory. His grandfather, Walter Drawbridge Crick (1857–1903), an amateur naturalist, wrote a survey of local foraminifera (single-celled protists with shells), corresponded with Charles Darwin, and had two gastropods (snails or slugs) named after him.","Francis Crick\n\nAt an early age, Francis was attracted to science and what he could learn about it from books. As a child, he was taken to church by his parents. But by about age 12, he said he did not want to go anymore, as he preferred a scientific search for answers over religious belief.","Francis Crick\n\nWalter Crick, his uncle, lived in a small house on the south side of Abington Avenue; he had a shed at the bottom of his little garden where he taught Crick to blow glass, do chemical experiments and to make photographic prints. When he was eight or nine he transferred to the most junior form of the Northampton Grammar School, on the Billing Road. This was about from his home so he could walk there and back, by Park Avenue South and Abington Park Crescent, but he more often went by bus or, later, by bicycle. The teacher – a Miss Holding – was an inspired teacher and made everything interesting. The teaching in the higher forms was satisfactory, but not as stimulating. After the age of 14, he was educated at Mill Hill School in London (on scholarship), where he studied mathematics, physics, and chemistry with his best friend John Shilston. He shared the Walter Knox Prize for Chemistry on Mill Hill School's Foundation Day, Friday, 7 July 1933. He declared that his success was inspired by the quality of teaching he received whilst a pupil at Mill Hill.","Francis Crick\n\nAt the age of 21, Crick earned a Bachelor of Science degree in physics from University College London. Crick had failed to gain a place at a Cambridge college, probably through failing their requirement for Latin. Crick began his PhD at UCL but was interrupted by WWII. He later became a PhD student and Honorary Fellow of Gonville and Caius College, Cambridge and mainly worked at the Cavendish Laboratory and the Medical Research Council (MRC) Laboratory of Molecular Biology in Cambridge. He was also an Honorary Fellow of Churchill College, Cambridge and of University College, London.","Francis Crick\n\nCrick began a Ph.D. research project on measuring viscosity of water at high temperatures (which he later described as \"the dullest problem imaginable\" ) in the laboratory of physicist Edward Neville da Costa Andrade at University College, London, but with the outbreak of World War II (in particular, an incident during the Battle of Britain when a bomb fell through the roof of the laboratory and destroyed his experimental apparatus), Crick was deflected from a possible career in physics. During his second year as a PhD student, however, he was awarded the Carey Foster Research Prize, a great honour. He did postdoctoral work at the Polytechnic Institute of Brooklyn.","Francis Crick\n\nDuring World War II, he worked for the Admiralty Research Laboratory, from which emerged a group of many notable scientists, including David Bates, Robert Boyd, George Deacon, John Gunn, Harrie Massey, and Nevill Mott; he worked on the design of magnetic and acoustic mines, and was instrumental in designing a new mine that was effective against German minesweepers.","Francis Crick\n\nPost-World War II life and work","Francis Crick\n\nIn 1947, aged 31, Crick began studying biology and became part of an important migration of physical scientists into biology research. This migration was made possible by the newly won influence of physicists such as Sir John Randall, who had helped win the war with inventions such as radar. Crick had to adjust from the \"elegance and deep simplicity\" of physics to the \"elaborate chemical mechanisms that natural selection had evolved over billions of years.\" He described this transition as, \"almost as if one had to be born again.\" According to Crick, the experience of learning physics had taught him something important—hubris—and the conviction that since physics was already a success, great advances should also be possible in other sciences such as biology. Crick felt that this attitude encouraged him to be more daring than typical biologists who tended to concern themselves with the daunting problems of biology and not the past successes of physics.","Francis Crick\n\nFor the better part of two years, Crick worked on the physical properties of cytoplasm at Cambridge's Strangeways Research Laboratory, headed by Honor Bridget Fell, with a Medical Research Council studentship, until he joined Max Perutz and John Kendrew at the Cavendish Laboratory. The Cavendish Laboratory at Cambridge was under the general direction of Sir Lawrence Bragg, who had won the Nobel Prize in 1915 at the age of 25. Bragg was influential in the effort to beat a leading American chemist, Linus Pauling, to the discovery of DNA's structure (after having been pipped at the post by Pauling's success in determining the alpha helix structure of proteins). At the same time Bragg's Cavendish Laboratory was also effectively competing with King's College London, whose Biophysics department was under the direction of Sir John Randall. (Randall had refused Crick's application to work at King's College.) Francis Crick and Maurice Wilkins of King's College were personal friends, which influenced subsequent scientific events as much as the close friendship between Crick and James Watson. Crick and Wilkins first met at King's College and not, as erroneously recorded by two authors, at the Admiralty during World War II.","Francis Crick\n\nHe married twice, fathered three children and was the grandfather of six grandchildren; his brother Anthony (born in 1918) predeceased him in 1966.","Francis Crick\n\nSpouses:\n* Ruth Doreen Crick, Dodd (b. 1913, m. 18 February 1940 – 8 May 1947. d. 2011), became Mrs. James Stewart Potter\n*Odile Crick, Speed (b. 11 August 1920, m. 14 August 1949 – 28 July 2004, d. 5 July 2007)","Francis Crick\n\nChildren:\n* Michael Francis Compton (b. 25 November 1940) [by Doreen Crick]\n* Gabrielle Anne (b. 15 July 1951) [by Odile Crick]\n* Jacqueline Marie-Therese [later Nichols] (b. 12 March 1954, d. 28 February 2011) [by Odile Crick];","Francis Crick\n\nGrandchildren","Francis Crick\n\n* Alexander (b. March 1974)\n* Kindra (b. May 1976)\n* Camberley (b. June 1978)\n* Francis Henry Riley (b. February 1981), Michael & Barbara Crick's four children\n* Mark & Nicholas, the late Jacqueline and Christopher Nichols' children.","Francis Crick\n\nDeath","Francis Crick\n\nCrick died of colon cancer on the morning of 28 July 2004 at the University of California, San Diego (UCSD) Thornton Hospital in La Jolla; he was cremated and his ashes were scattered into the Pacific Ocean. A public memorial was held on 27 September 2004 at the Salk Institute, La Jolla, near San Diego, California; guest speakers included James Watson, Sydney Brenner, Alex Rich, Seymour Benzer, Aaron Klug, Christof Koch, Pat Churchland, Vilayanur Ramachandran, Tomaso Poggio, Leslie Orgel, Terry Sejnowski, his son Michael Crick, and his youngest daughter Jacqueline Nichols. A private memorial for family and colleagues was held on 3 August 2004.","Francis Crick\n\nResearch","Francis Crick\n\nCrick was interested in two fundamental unsolved problems of biology: how molecules make the transition from the non-living to the living, and how the brain makes a conscious mind. He realized that his background made him more qualified for research on the first topic and the field of biophysics. It was at this time of Crick’s transition from physics to biology that he was influenced by both Linus Pauling and Erwin Schrödinger.Crick (1990) p. 18 It was clear in theory that covalent bonds in biological molecules could provide the structural stability needed to hold genetic information in cells. It only remained as an exercise of experimental biology to discover exactly which molecule was the genetic molecule. In Crick’s view, Charles Darwin’s theory of evolution by natural selection, Gregor Mendel’s genetics and knowledge of the molecular basis of genetics, when combined, revealed the secret of life. Crick had the very optimistic view that life would very soon be created in a test tube. However, some people (such as fellow researcher and colleague Esther Lederberg) thought that Crick was unduly optimistic","Francis Crick\n\nIt was clear that some macromolecule such as a protein was likely to be the genetic molecule. However, it was well known that proteins are structural and functional macromolecules, some of which carry out enzymatic reactions of cells. In the 1940s, some evidence had been found pointing to another macromolecule, DNA, the other major component of chromosomes, as a candidate genetic molecule. In the 1944 Avery-MacLeod-McCarty experiment, Oswald Avery and his collaborators showed that a heritable phenotypic difference could be caused in bacteria by providing them with a particular DNA molecule.","Francis Crick\n\nHowever, other evidence was interpreted as suggesting that DNA was structurally uninteresting and possibly just a molecular scaffold for the apparently more interesting protein molecules. Crick was in the right place, in the right frame of mind, at the right time (1949), to join Max Perutz’s project at the University of Cambridge, and he began to work on the X-ray crystallography of proteins. X-ray crystallography theoretically offered the opportunity to reveal the molecular structure of large molecules like proteins and DNA, but there were serious technical problems then preventing X-ray crystallography from being applicable to such large molecules.","Francis Crick\n\n1949–1950","Francis Crick\n\nCrick taught himself the mathematical theory of X-ray crystallography.Crick (1990) p. 46: \"..there was no alternative but to teach X-ray diffraction to myself.\" During the period of Crick's study of X-ray diffraction, researchers in the Cambridge lab were attempting to determine the most stable helical conformation of amino acid chains in proteins (the Alpha helix). Linus Pauling was the first to identify the 3.6 amino acids per helix turn ratio of the Alpha helix. Crick was witness to the kinds of errors that his co-workers made in their failed attempts to make a correct molecular model of the α helix; these turned out to be important lessons that could be applied, in the future, to the helical structure of DNA. For example, he learned the importance of the structural rigidity that double bonds confer on molecular structures which is relevant both to peptide bonds in proteins and the structure of nucleotides in DNA.","Francis Crick\n\n1951–1953: DNA structure","Francis Crick\n\nIn 1951 and 1952, together with William Cochran and Vladimir Vand, Crick assisted in the development of a mathematical theory of X-ray diffraction by a helical molecule. This theoretical result matched well with X-ray data for proteins that contain sequences of amino acids in the Alpha helix conformation. Helical diffraction theory turned out to also be useful for understanding the structure of DNA.","Francis Crick\n\nLate in 1951, Crick started working with James Watson at Cavendish Laboratory at the University of Cambridge, England. Using \"Photo 51\" (the X-ray diffraction results of Rosalind Franklin and her graduate student Raymond Gosling of King's College London, given to them by Gosling and Franklin's colleague Maurice Wilkins), Watson and Crick together developed a model for a helical structure of DNA, which they published in 1953. For this and subsequent work they were jointly awarded the Nobel Prize in Physiology or Medicine in 1962 with Maurice Wilkins.","Francis Crick\n\nWhen James Watson came to Cambridge, Crick was a 35-year-old graduate student (due to his work during WWII) and Watson was only 23, but he already had a Ph.D. They shared an interest in the fundamental problem of learning how genetic information might be stored in molecular form. Watson and Crick talked endlessly about DNA and the idea that it might be possible to guess a good molecular model of its structure. A key piece of experimentally-derived information came from X-ray diffraction images that had been obtained by Maurice Wilkins, Rosalind Franklin, and their research student, Raymond Gosling. In November 1951, Wilkins came to Cambridge and shared his data with Watson and Crick. Alexander Stokes (another expert in helical diffraction theory) and Wilkins (both at King's College) had reached the conclusion that X-ray diffraction data for DNA indicated that the molecule had a helical structure—but Franklin vehemently disputed this conclusion. Stimulated by their discussions with Wilkins and what Watson learned by attending a talk given by Franklin about her work on DNA, Crick and Watson produced and showed off an erroneous first model of DNA.","Francis Crick\n\nTheir hurry to produce a model of DNA structure was driven in part by the knowledge that they were competing against Linus Pauling. Given Pauling's recent success in discovering the Alpha helix, they feared that Pauling might also be the first to determine the structure of DNA.","Francis Crick\n\nMany have speculated about what might have happened had Pauling been able to travel to Britain as planned in May 1952. As it was, his political activities caused his travel to be restricted by the U. S. government and he did not visit the UK until later, at which point he met none of the DNA researchers in England. At any rate he was preoccupied with proteins at the time, not DNA. Watson and Crick were not officially working on DNA. Crick was writing his Ph.D. thesis; Watson also had other work such as trying to obtain crystals of myoglobin for X-ray diffraction experiments. In 1952, Watson performed X-ray diffraction on tobacco mosaic virus and found results indicating that it had helical structure. Having failed once, Watson and Crick were now somewhat reluctant to try again and for a while they were forbidden to make further efforts to find a molecular model of DNA.","Francis Crick\n\nOf great importance to the model building effort of Watson and Crick was Rosalind Franklin's understanding of basic chemistry, which indicated that the hydrophilic phosphate-containing backbones of the nucleotide chains of DNA should be positioned so as to interact with water molecules on the outside of the molecule while the hydrophobic bases should be packed into the core. Franklin shared this chemical knowledge with Watson and Crick when she pointed out to them that their first model (from 1951, with the phosphates inside) was obviously wrong.","Francis Crick\n\nCrick described what he saw as the failure of Maurice Wilkins and Rosalind Franklin to cooperate and work towards finding a molecular model of DNA as a major reason why he and Watson eventually made a second attempt to do so. They asked for, and received, permission to do so from both William Lawrence Bragg and Wilkins. In order to construct their model of DNA, Watson and Crick made use of information from unpublished X-ray diffraction images of Franklin's (shown at meetings and freely shared by Wilkins), including preliminary accounts of Franklin's results/photographs of the X-ray images that were included in a written progress report for the King's College laboratory of Sir John Randall from late 1952.","Francis Crick\n\nIt is a matter of debate whether Watson and Crick should have had access to Franklin's results without her knowledge or permission, and before she had a chance to formally publish the results of her detailed analysis of her X-ray diffraction data which were included in the progress report. However, Watson and Crick found fault in her steadfast assertion that, according to her data, a helical structure was not the only possible shape for DNA—so they had a dilemma. In an effort to clarify this issue, Max Ferdinand Perutz later published what had been in the progress report, and suggested that nothing was in the report that Franklin herself had not said in her talk (attended by Watson) in late 1951. Further, Perutz explained that the report was to a Medical Research Council (MRC) committee that had been created in order to \"establish contact between the different groups of people working for the Council\". Randall's and Perutz's laboratories were both funded by the MRC.","Francis Crick\n\nIt is also not clear how important Franklin's unpublished results from the progress report actually were for the model-building done by Watson and Crick. After the first crude X-ray diffraction images of DNA were collected in the 1930s, William Astbury had talked about stacks of nucleotides spaced at 3.4 angström (0.34 nanometre) intervals in DNA. A citation to Astbury's earlier X-ray diffraction work was one of only eight references in Franklin's first paper on DNA.Franklin's citation to the earlier work of W. T. Astbury is in: Analysis of Astbury's published DNA results and the better X-ray diffraction images collected by Wilkins and Franklin revealed the helical nature of DNA. It was possible to predict the number of bases stacked within a single turn of the DNA helix (10 per turn; a full turn of the helix is 27 angströms [2.7 nm] in the compact A form, 34 angströms [3.4 nm] in the wetter B form). Wilkins shared this information about the B form of DNA with Crick and Watson. Crick did not see Franklin's B form X-ray images (Photo 51) until after the DNA double helix model was published.","Francis Crick\n\nOne of the few references cited by Watson and Crick when they published their model of DNA was to a published article that included Sven Furberg's DNA model that had the bases on the inside. Thus, the Watson and Crick model was not the first \"bases in\" model to be proposed. Furberg's results had also provided the correct orientation of the DNA sugars with respect to the bases. During their model building, Crick and Watson learned that an antiparallel orientation of the two nucleotide chain backbones worked best to orient the base pairs in the centre of a double helix. Crick's access to Franklin's progress report of late 1952 is what made Crick confident that DNA was a double helix with antiparallel chains, but there were other chains of reasoning and sources of information that also led to these conclusions.","Francis Crick\n\nAs a result of leaving King's College for Birkbeck College, Franklin was asked by John Randall to give up her work on DNA. When it became clear to Wilkins and the supervisors of Watson and Crick that Franklin was going to the new job, and that Linus Pauling was working on the structure of DNA, they were willing to share Franklin's data with Watson and Crick, in the hope that they could find a good model of DNA before Pauling was able. Franklin's X-ray diffraction data for DNA and her systematic analysis of DNA's structural features was useful to Watson and Crick in guiding them towards a correct molecular model. The key problem for Watson and Crick, which could not be resolved by the data from King's College, was to guess how the nucleotide bases pack into the core of the DNA double helix.","Francis Crick\n\nAnother key to finding the correct structure of DNA was the so-called Chargaff ratios, experimentally determined ratios of the nucleotide subunits of DNA: the amount of guanine is equal to cytosine and the amount of adenine is equal to thymine. A visit by Erwin Chargaff to England in 1952 reinforced the salience of this important fact for Watson and Crick. The significance of these ratios for the structure of DNA were not recognized until Watson, persisting in building structural models, realized that A:T and C:G pairs are structurally similar. In particular, the length of each base pair is the same. Chargaff had also pointed out to Watson that, in the aqueous, saline environment of the cell, the predominant tautomers of the pyrimidine (C and T) bases would be the amine and keto configurations of cytosine and thymine, rather than the imino and enol forms that Crick and Watson had assumed. They consulted Jerry Donohue who confirmed the most likely structures of the nucleotide bases. The base pairs are held together by hydrogen bonds, the same non-covalent interaction that stabilize the protein α-helix. The correct structures were essential for the positioning of the hydrogen bonds.","Francis Crick\n\nThese insights led Watson to deduce the true biological relationships of the A:T and C:G pairs. After the discovery of the hydrogen bonded A:T and C:G pairs, Watson and Crick soon had their anti-parallel, double helical model of DNA, with the hydrogen bonds at the core of the helix providing a way to \"unzip\" the two complementary strands for easy replication: the last key requirement for a likely model of the genetic molecule. As important as Crick's contributions to the discovery of the double helical DNA model were, he stated that without the chance to collaborate with Watson, he would not have found the structure by himself.","Francis Crick\n\nCrick did tentatively attempt to perform some experiments on nucleotide base pairing, but he was more of a theoretical biologist than an experimental biologist. There was another near-discovery of the base pairing rules in early 1952. Crick had started to think about interactions between the bases. He asked John Griffith to try to calculate attractive interactions between the DNA bases from chemical principles and quantum mechanics. Griffith's best guess was that A:T and G:C were attractive pairs. At that time, Crick was not aware of Chargaff's rules and he made little of Griffith's calculations, although it did start him thinking about complementary replication. Identification of the correct base-pairing rules (A-T, G-C) was achieved by Watson \"playing\" with cardboard cut-out models of the nucleotide bases, much in the manner that Linus Pauling had discovered the protein alpha helix a few years earlier. The Watson and Crick discovery of the DNA double helix structure was made possible by their willingness to combine theory, modeling and experimental results (albeit mostly done by others) to achieve their goal.","Francis Crick\n\nThe DNA double helix structure proposed by Watson and Crick was based upon \"Watson-Crick\" bonds between the four bases most frequently found in DNA (A, C, T, G) and RNA (A, C, U, G). However, later research showed that triple-stranded, quadruple-stranded and other more complex DNA molecular structures required Hoogsteen base pairing. The entire field of synthetic biology began with work by researchers such as Erik T. Kool, in which bases other than A, C, T and G are used in a synthetic DNA. In addition to synthetic DNA there are also attempts to construct synthetic codons, synthetic endonucleases, synthetic proteins and synthetic zinc fingers. Using synthetic DNA, instead of there being 43 codons, if there are n new bases there could be as many as n3 codons. Research is currently being done to see if codons can be expanded to more than 3 bases. These new codons can code for new amino acids. These synthetic molecules can be used not only in medicine, but in creation of new materials.","Francis Crick\n\nThe discovery was made on 28 February 1953; the first Watson/Crick paper appeared in Nature on 25 April 1953. Sir Lawrence Bragg, the director of the Cavendish Laboratory, where Watson and Crick worked, gave a talk at Guy's Hospital Medical School in London on Thursday 14 May 1953 which resulted in an article by Ritchie Calder in The News Chronicle of London, on Friday 15 May 1953, entitled \"Why You Are You. Nearer Secret of Life.\" The news reached readers of The New York Times the next day; Victor K. McElheny, in researching his biography, \"Watson and DNA: Making a Scientific Revolution\", found a clipping of a six-paragraph New York Times article written from London and dated 16 May 1953 with the headline \"Form of 'Life Unit' in Cell Is Scanned.\" The article ran in an early edition and was then pulled to make space for news deemed more important. (The New York Times subsequently ran a longer article on 12 June 1953). The university's undergraduate newspaper Varsity also ran its own short article on the discovery on Saturday 30 May 1953.","Francis Crick\n\nBragg's original announcement of the discovery at a Solvay conference on proteins in Belgium on 8 April 1953 went unreported by the British press.","Francis Crick\n\nIn a seven-page, handwritten letter to his son at a British boarding school on 19 March 1953 Crick explained his discovery, beginning the letter \"My Dear Michael, Jim Watson and I have probably made a most important discovery...\". The letter was put up for auction at Christie's New York on 10 April 2013 with an estimate of $1 to $2 million, eventually selling for $6,059,750, the largest amount ever paid for a letter at auction.","Francis Crick\n\nSydney Brenner, Jack Dunitz, Dorothy Hodgkin, Leslie Orgel, and Beryl M. Oughton, were some of the first people in April 1953 to see the model of the structure of DNA, constructed by Crick and Watson; at the time they were working at Oxford University's Chemistry Department. All were impressed by the new DNA model, especially Brenner who subsequently worked with Crick at Cambridge in the Cavendish Laboratory and the new Laboratory of Molecular Biology. According to the late Dr. Beryl Oughton, later Rimmer, they all travelled together in two cars once Dorothy Hodgkin announced to them that they were off to Cambridge to see the model of the structure of DNA. Orgel also later worked with Crick at the Salk Institute for Biological Studies.","Francis Crick\n\nIn addition, the entire field of synthetic biology began with researchers such as Erik T. Kool, where bases other than A, C, T and G are used in a synthetic DNA. In addition to synthetic DNA there are also attempts to construct synthetic codons, synthetic endonucleases, synthetic proteins and synthetic zinc fingers. Using synthetic DNA, instead of there being 43 codons, if there are n new bases there could be as many as n3 codons. Research is currently being done to see if codons can be expanded to more than 3 bases. These new codons can code for new amino acids. These synthetic molecules can be used not only in medicine, but in creation of new materials.","Francis Crick\n\nMolecular biology","Francis Crick\n\nIn 1954, at the age of 37, Crick completed his Ph.D. thesis: \"X-Ray Diffraction: Polypeptides and Proteins\" and received his degree. Crick then worked in the laboratory of David Harker at Brooklyn Polytechnic Institute, where he continued to develop his skills in the analysis of X-ray diffraction data for proteins, working primarily on ribonuclease and the mechanisms of protein synthesis. David Harker, the American X-ray crystallographer, was described as \"the John Wayne of crystallography\" by Vittorio Luzzati, a crystallographer at the Centre for Molecular Genetics in Gif-sur-Yvette near Paris, who had worked with Rosalind Franklin.","Francis Crick\n\nAfter the discovery of the double helix model of DNA, Crick's interests quickly turned to the biological implications of the structure. In 1953, Watson and Crick published another article in Nature which stated: \"it therefore seems likely that the precise sequence of the bases is the code that carries the genetical information\".","Francis Crick\n\nIn 1956, Crick and Watson speculated on the structure of small viruses. They suggested that spherical viruses such as Tomato bushy stunt virus had icosahedral symmetry and were made from 60 identical subunits.","Francis Crick\n\nAfter his short time in New York, Crick returned to Cambridge where he worked until 1976, at which time he moved to California. Crick engaged in several X-ray diffraction collaborations such as one with Alexander Rich on the structure of collagen. However, Crick was quickly drifting away from continued work related to his expertise in the interpretation of X-ray diffraction patterns of proteins.","Francis Crick\n\nGeorge Gamow established a group of scientists interested in the role of RNA as an intermediary between DNA as the genetic storage molecule in the nucleus of cells and the synthesis of proteins in the cytoplasm (the RNA Tie Club). It was clear to Crick that there had to be a code by which a short sequence of nucleotides would specify a particular amino acid in a newly synthesized protein. In 1956, Crick wrote an informal paper about the genetic coding problem for the small group of scientists in Gamow's RNA group. In this article, Crick reviewed the evidence supporting the idea that there was a common set of about 20 amino acids used to synthesize proteins. Crick proposed that there was a corresponding set of small \"adaptor molecules\" that would hydrogen bond to short sequences of a nucleic acid, and also link to one of the amino acids. He also explored the many theoretical possibilities by which short nucleic acid sequences might code for the 20 amino acids.","Francis Crick\n\nDuring the mid-to-late 1950s Crick was very much intellectually engaged in sorting out the mystery of how proteins are synthesized. By 1958, Crick's thinking had matured and he could list in an orderly way all of the key features of the protein synthesis process: \n*genetic information stored in the sequence of DNA molecules\n*a \"messenger\" RNA molecule to carry the instructions for making one protein to the cytoplasm\n*adaptor molecules (\"they might contain nucleotides\") to match short sequences of nucleotides in the RNA messenger molecules to specific amino acids\n*ribonucleic-protein complexes that catalyse the assembly of amino acids into proteins according to the messenger RNA","Francis Crick\n\nThe adaptor molecules were eventually shown to be tRNAs and the catalytic \"ribonucleic-protein complexes\" became known as ribosomes. An important step was later realization (in 1960) that the messenger RNA was not the same as the ribosomal RNA. None of this, however, answered the fundamental theoretical question of the exact nature of the genetic code. In his 1958 article, Crick speculated, as had others, that a triplet of nucleotides could code for an amino acid. Such a code might be \"degenerate\", with 4×4×4=64 possible triplets of the four nucleotide subunits while there were only 20 amino acids. Some amino acids might have multiple triplet codes. Crick also explored other codes in which, for various reasons, only some of the triplets were used, \"magically\" producing just the 20 needed combinations. Experimental results were needed; theory alone could not decide the nature of the code. Crick also used the term \"central dogma\" to summarize an idea that implies that genetic information flow between macromolecules would be essentially one-way:","Francis Crick\n\nDNA → RNA → Protein","Francis Crick\n\nSome critics thought that by using the word \"dogma\", Crick was implying that this was a rule that could not be questioned, but all he really meant was that it was a compelling idea without much solid evidence to support it. In his thinking about the biological processes linking DNA genes to proteins, Crick made explicit the distinction between the materials involved, the energy required, and the information flow. Crick was focused on this third component (information) and it became the organizing principle of what became known as molecular biology. Crick had by this time become a highly influential theoretical molecular biologist.","Francis Crick\n\nProof that the genetic code is a degenerate triplet code finally came from genetics experiments, some of which were performed by Crick. The details of the code came mostly from work by Marshall Nirenberg and others who synthesized synthetic RNA molecules and used them as templates for in vitro protein synthesis. Nirenberg first announced his results to a small audience in Moscow at a 1961 conference. Crick's reaction was to invite Nirenberg to deliver his talk to a larger audience.","Francis Crick\n\nControversy","Francis Crick\n\nAn enduring controversy has been generated by Watson and Crick's use of DNA X-ray diffraction data collected by Rosalind Franklin and her student Raymond Gosling. The controversy arose from the fact that some of Franklin's unpublished data were used without her knowledge or consent by Watson and Crick in their construction of the double helix model of DNA. Of the four DNA researchers, only Rosalind Franklin had a degree in chemistry: Wilkins and Crick had backgrounds in physics, Watson in molecular biology.","Francis Crick\n\nPrior to publication of the double helix structure, Watson and Crick had little direct interaction with Franklin herself. They were, however, aware of her work, more aware than she herself realized. Watson was present at a lecture, given in November 1951, where Franklin presented the two forms of the molecule, type A and type B, and discussed the position of the phosphate units on the external part of the molecule. She also specified the amount of water to be found in the molecule in accordance with other parts of it, data that have considerable importance in terms of the stability of the molecule. Franklin was the first to discover and formulate these facts, which in fact constituted the basis for all later attempts to build a model of the molecule. Before this both Linus Pauling and Watson and Crick had generated erroneous models with the chains inside and the bases pointing outwards. Her identification of the space group for DNA crystals revealed to Crick that the two DNA strands were antiparallel.","Francis Crick\n\nIn January 1953, James Watson was shown an X-ray photograph of B-DNA (called photograph 51), by Maurice Wilkins. Maurice Wilkins had been given photograph 51 by Rosalind Franklin's Ph.D. student Raymond Gosling. Wilkins and Gosling had worked together in the Medical Research Council's (MRC) Biophysics Unit before director John Randall appointed Franklin to take over both DNA diffraction work and guidance of Gosling's thesis. It appears that Randall did not communicate effectively with them about Franklin's appointment, contributing to confusion and friction between Wilkins and Franklin.","Francis Crick\n\nIn the middle of February 1953, Crick's thesis advisor, Max Perutz, gave Crick a copy of a report written for a Medical Research Council biophysics committee visit to King's in December 1952, containing data from the King's group, including some of Rosalind Franklin's crystallographic calculations.","Francis Crick\n\nFranklin was unaware that photograph 51 and other information had been shared with Crick and Watson. She wrote a series of three draft manuscripts, two of which included a double helical DNA backbone. Her two A form manuscripts reached Acta Crystallographica in Copenhagen on 6 March 1953, one day before Crick and Watson had completed their model.","Francis Crick\n\nThe X-ray diffraction images collected by Gosling and Franklin provided the best evidence for the helical nature of DNA. Franklin's experimental work thus proved crucial in Watson and Crick's discovery. Her experimental results provided estimates of the water content of DNA crystals, and these results were most consistent with the three sugar-phosphate backbones being on the outside of the molecule. Franklin's X-Ray photograph showed that the backbones had to be on the outside. Although she at first insisted vehemently that her data did not force one to conclude that DNA has a helical structure, in the drafts she submitted in 1953 she argues for a double helical DNA backbone. Her identification of the space group for DNA crystals revealed to Crick that the DNA strands were antiparallel, which helped Watson and Crick decide to look for DNA models with two antiparallel polynucleotide strands.","Francis Crick\n\nIn summary, Watson and Crick had three sources for Franklin's unpublished data: 1) her 1951 seminar, attended by Watson, 2) discussions with Wilkins, who worked in the same laboratory with Franklin, 3) a research progress report that was intended to promote coordination of Medical Research Council-supported laboratories. Watson, Crick, Wilkins and Franklin all worked in MRC laboratories.","Francis Crick\n\nCrick and Watson felt that they had benefited from collaborating with Wilkins. They offered him a co-authorship on the article that first described the double helix structure of DNA. Wilkins turned down the offer, a fact that may have led to the terse character of the acknowledgment of experimental work done at King's College in the eventual published paper. Rather than make any of the DNA researchers at King's College co-authors on the Watson and Crick double helix article, the solution that was arrived at was to publish two additional papers from King's College along with the helix paper. Brenda Maddox suggests that because of the importance of her experimental results in Watson and Crick's model building and theoretical analysis, Franklin should have had her name on the original Watson and Crick paper in Nature. Franklin and Gosling submitted their own joint 'second' paper to Nature at the same time as Wilkins, Stokes, and Wilson submitted theirs (i.e. the 'third' paper on DNA).","Francis Crick\n\nWatson's portrayal of Franklin in The Double Helix (written after Franklin's death when libel laws did not apply anymore) was negative and gave the appearance that she was Wilkins' assistant and was unable to interpret her own DNA data.","Francis Crick\n\nThe X-ray diffraction images collected by Franklin provided the best evidence for the helical nature of DNA. While Franklin's experimental work proved important to Crick and Watson's development of a correct model, she herself could not realize it at the time. When she left King's College, Director Sir John Randall insisted that all DNA work belonged exclusively to King's and ordered Franklin to not even think about it. Franklin subsequently did superb work in J. D. Bernal's Lab at Birkbeck College with the tobacco mosaic virus extending ideas on helical construction.","Francis Crick\n\nViews on religion","Francis Crick\n\nCrick referred to himself as a humanist, which he defined as the belief \"that human problems can and must be faced in terms of human moral and intellectual resources without invoking supernatural authority.\" He publicly called for humanism to replace religion as a guiding force for humanity, writing:","Francis Crick\n\n\"The human dilemma is hardly new. We find ourselves through no wish of our own on this slowly revolving planet in an obscure corner of a vast universe. Our questioning intelligence will not let us live in cow-like content with our lot. We have a deep need to know why we are here. What is the world made of? More important, what are we made of? In the past religion answered these questions, often in considerable detail. Now we know that almost all these answers are highly likely to be nonsense, having sprung from man's ignorance and his enormous capacity for self-deception... The simple fables of the religions of the world have come to seem like tales told to children. Even understood symbolically they are often perverse, if not rather unpleasant... Humanists, then, live in a mysterious, exciting and intellectually expanding world, which, once glimpsed, makes the old worlds of the religions seem fake-cosy and stale... \":","Francis Crick\n\nCrick was especially critical of Christianity:","Francis Crick\n\n\"I do not respect Christian beliefs. I think they are ridiculous. If we could get rid of them we could more easily get down to the serious problem of trying to find out what the world is all about.\":","Francis Crick\n\nCrick once joked, \"Christianity may be OK between consenting adults in private but should not be taught to young children.\"","Francis Crick\n\nIn his book Of Molecules and Men, Crick expressed his views on the relationship between science and religion. After suggesting that it would become possible for a computer to be programmed so as to have a soul, he wondered: at what point during biological evolution did the first organism have a soul? At what moment does a baby get a soul? Crick stated his view that the idea of a non-material soul that could enter a body and then persist after death is just that, an imagined idea. For Crick, the mind is a product of physical brain activity and the brain had evolved by natural means over millions of years. He felt that it was important that evolution by natural selection be taught in schools and that it was regrettable that English schools had compulsory religious instruction. He also considered that a new scientific world view was rapidly being established, and predicted that once the detailed workings of the brain were eventually revealed, erroneous Christian concepts about the nature of humans and the world would no longer be tenable; traditional conceptions of the \"soul\" would be replaced by a new understanding of the physical basis of mind.","Francis Crick\n\nHe was sceptical of organized religion, referring to himself as a skeptic and an agnostic with \"a strong inclination towards atheism\".","Francis Crick\n\nIn 1960, Crick accepted an honorary fellowship at Churchill College, Cambridge, one factor being that the new college did not have a chapel. Some time later a large donation was made to establish a chapel and the College Council decided to accept it. Crick resigned his fellowship in protest.","Francis Crick\n\nIn October 1969 Crick participated in a celebration of the 100th year of the journal Nature in which he attempted to make some predictions about what the next 30 years would hold for molecular biology. His speculations were later published in Nature. Near the end of the article, Crick briefly mentioned the search for life on other planets, but he held little hope that extraterrestrial life would be found by the year 2000. He also discussed what he described as a possible new direction for research, what he called \"biochemical theology\". Crick wrote \"so many people pray that one finds it hard to believe that they do not get some satisfaction from it\".","Francis Crick\n\nCrick suggested that it might be possible to find chemical changes in the brain that were molecular correlates of the act of prayer. He speculated that there might be a detectable change in the level of some neurotransmitter or neurohormone when people pray. He might have been imagining substances such as dopamine that are released by the brain under certain conditions and produce rewarding sensations. Crick's suggestion that there might someday be a new science of \"biochemical theology\" seems to have been realized under an alternative name: there is now the new field of neurotheology. Crick's view of the relationship between science and religion continued to play a role in his work as he made the transition from molecular biology research into theoretical neuroscience.","Francis Crick\n\nCrick asked in 1998 \"and if some of the Bible is manifestly wrong, why should any of the rest of it be accepted automatically? ... And what would be more important than to find our true place in the universe by removing one by one these unfortunate vestiges of earlier beliefs?\"","Francis Crick\n\nIn 2003 he was one of 22 Nobel laureates who signed the Humanist Manifesto.","Francis Crick\n\nDirected panspermia","Francis Crick\n\nDuring the 1960s, Crick became concerned with the origins of the genetic code. In 1966, Crick took the place of Leslie Orgel at a meeting where Orgel was to talk about the origin of life. Crick speculated about possible stages by which an initially simple code with a few amino acid types might have evolved into the more complex code used by existing organisms. At that time, everyone thought of proteins as the only kind of enzymes and ribozymes had not yet been found. Many molecular biologists were puzzled by the problem of the origin of a protein replicating system that is as complex as that which exists in organisms currently inhabiting Earth. In the early 1970s, Crick and Orgel further speculated about the possibility that the production of living systems from molecules may have been a very rare event in the universe, but once it had developed it could be spread by intelligent life forms using space travel technology, a process they called \"directed panspermia\".","Francis Crick\n\nIn a retrospective article, Crick and Orgel noted that they had been overly pessimistic about the chances of abiogenesis on Earth when they had assumed that some kind of self-replicating protein system was the molecular origin of life.","Francis Crick\n\nIn 1976 Crick addressed the origin of protein synthesis in a paper with Sydney Brenner, Aaron Klug, and George Pieczenik. In this paper, they speculate that code constraints on nucleotide sequences allow protein synthesis without the need for a ribosome. It, however, requires a five base binding between the mRNA and tRNA with a flip of the anti-codon creating a triplet coding, even though it is a five-base physical interaction. Thomas H. Jukes pointed out that the code constraints on the mRNA sequence required for this translation mechanism is still preserved.","Francis Crick\n\nNeuroscience and other interests","Francis Crick\n\nCrick's period at Cambridge was the pinnacle of his long scientific career, but he left Cambridge in 1977 after 30 years, having been offered (and having refused) the Mastership of Gonville & Caius. James Watson claimed at a Cambridge conference marking the 50th anniversary of the discovery of the structure of DNA in 2003: \"Now perhaps it's a pretty well kept secret that one of the most uninspiring acts of the University of Cambridge over this past century was to turn down Francis Crick when he applied to be the Professor of Genetics, in 1958. Now there may have been a series of arguments, which led them to reject Francis. It was really saying, don't push us to the frontier.\" The apparently \"pretty well kept secret\" had already been recorded in Soraya De Chadarevian's \"Designs For Life: Molecular Biology After World War II\", published by CUP in 2002. His major contribution to molecular biology in Cambridge is well documented in The History of the University of Cambridge: Volume 4 (1870 to 1990), which was published by Cambridge University Press in 1992.","Francis Crick\n\nAccording to the University of Cambridge's genetics department official website, the electors of the professorship could not reach consensus, prompting the intervention of then University Vice-Chancellor Lord Adrian. Lord Adrian first offered the professorship to a compromise candidate, Guido Pontecorvo, who refused, and is said to have offered it then to Crick, who also refused.","Francis Crick\n\nIn 1976, Crick took a sabbatical year at the Salk Institute for Biological Studies in La Jolla, California. Crick had been a nonresident fellow of the Institute since 1960. Crick wrote, \"I felt at home in Southern California.\" After the sabbatical, Crick left Cambridge in order to continue working at the Salk Institute. He was also a professor at the University of California, San Diego. He taught himself neuroanatomy and studied many other areas of neuroscience research. It took him several years to disengage from molecular biology because exciting discoveries continued to be made, including the discovery of alternative splicing and the discovery of restriction enzymes, which helped make possible genetic engineering. Eventually, in the 1980s, Crick was able to devote his full attention to his other interest, consciousness. His autobiographical book, What Mad Pursuit: A Personal View of Scientific Discovery, includes a description of why he left molecular biology and switched to neuroscience.","Francis Crick\n\nUpon taking up work in theoretical neuroscience, Crick was struck by several things:\n*there were many isolated subdisciplines within neuroscience with little contact between them\n*many people who were interested in behaviour treated the brain as a black box\n*consciousness was viewed as a taboo subject by many neurobiologists","Francis Crick\n\nCrick hoped he might aid progress in neuroscience by promoting constructive interactions between specialists from the many different subdisciplines concerned with consciousness. He even collaborated with neurophilosophers such as Patricia Churchland. In 1983, as a result of their studies of computer models of neural networks, Crick and Mitchison proposed that the function of REM sleep is to remove certain modes of interactions in networks of cells in the mammalian cerebral cortex; they called this hypothetical process 'reverse learning' or 'unlearning'. In the final phase of his career, Crick established a collaboration with Christof Koch that lead to publication of a series of articles on consciousness during the period spanning from 1990 to 2005. Crick made the strategic decision to focus his theoretical investigation of consciousness on how the brain generates visual awareness within a few hundred milliseconds of viewing a scene. Crick and Koch proposed that consciousness seems so mysterious because it involves very short-term memory processes that are as yet poorly understood. Crick also published a book describing how neurobiology had reached a mature enough stage so that consciousness could be the subject of a unified effort to study it at the molecular, cellular and behavioural levels.","Francis Crick\n\nCrick's book The Astonishing Hypothesis made the argument that neuroscience now had the tools required to begin a scientific study of how brains produce conscious experiences. Crick was skeptical about the value of computational models of mental function that are not based on details about brain structure and function.","Francis Crick\n\nReactions","Francis Crick\n\nCrick was often described as very talkative, with Watson – in The Double Helix – implying lack of modesty. His personality combined with his scientific accomplishments produced many opportunities for Crick to stimulate reactions from others, both inside and outside the scientific world, which was the centre of his intellectual and professional life.Describing Crick's influence on his scientific colleagues, Francis Crick Papers archivist Chris Beckett wrote of the importance of, \".....Crick's presence and eloquence —direct and beguiling, by all accounts in the archive— at conference after conference, through formal lectures, extempore summaries, informal meetings and individual conversations. Indeed, one has the impression that it was through these frequent persuasive moments of personal delivery and purposive conversations that Crick was most influential.\" Also described as an example of Crick's wide recognition and public profile are some of the times Crick was addressed as \"Sir Francis Crick\" with the assumption that someone so famous must have been knighted. Crick spoke rapidly, and rather loudly, and had an infectious and reverberating laugh, and a lively sense of humour. One colleague from the Salk Institute described him as \"a brainstorming intellectual powerhouse with a mischievous smile.... Francis was never mean-spirited, just incisive.","Francis Crick\n\nHe detected microscopic flaws in logic. In a room full of smart scientists, Francis continually reearned his position as the heavyweight champ.\"","Francis Crick\n\nEugenics","Francis Crick\n\nCrick occasionally expressed his views on eugenics, usually in private letters. For example, Crick advocated a form of positive eugenics in which wealthy parents would be encouraged to have more children. He once remarked, \"In the long run, it is unavoidable that society will begin to worry about the character of the next generation... It is not a subject at the moment which we can tackle easily because people have so many religious beliefs and until we have a more uniform view of ourselves I think it would be risky to try and do anything in the way of eugenics... I would be astonished if, in the next 100 or 200 years, society did not come round to the view that they would have to try to improve the next generation in some extent or one way or another.\"","Francis Crick\n\nCreationism","Francis Crick\n\nCrick was a firm critic of Young Earth creationism. In the 1987 United States Supreme Court case Edwards v. Aguillard, Crick joined a group of other Nobel laureates who advised, \"'Creation-science' simply has no place in the public-school science classroom.\" Crick was also an advocate for the establishment of Darwin Day as a British national holiday.","Francis Crick\n\nRecognition","Francis Crick\n\nIn addition to his third share of the 1962 Nobel prize for Physiology or Medicine, he received many awards and honours, including the Royal and Copley medals of the Royal Society (1972 and 1975), and also the Order of Merit (on 27 November 1991); he refused an offer of a CBE in 1963 and later refused an offer of a knighthood, but was often referred to in error as 'Sir Francis Crick' and even on occasions as 'Lord Crick.'","Francis Crick\n\nThe award of Nobel prizes to John Kendrew and Max Perutz, and to Crick, Watson, and Wilkins was satirised in a short sketch in the BBC TV programme That Was The Week That Was with the Nobel Prizes being referred to as 'The Alfred Nobel Peace Pools.'","Francis Crick\n\nFrancis Crick Medal and Lecture","Francis Crick\n\nThe Francis Crick Medal and Lecture was established in 2003 following an endowment by his former colleague, Sydney Brenner, joint winner of the 2002 Nobel Prize in Physiology and Medicine. The lecture is delivered annually in any field of biological sciences, with preference given to the areas in which Francis Crick himself worked. Importantly, the lectureship is aimed at younger scientists, ideally under 40, or whose career progression corresponds to this age. , Crick lecture have been delivered by Julie Ahringer, Dario Alessi, Ewan Birney, Simon Boulton, Jason Chin, Simon Fisher, Matthew Hurles, Gilean McVean, Duncan Odom, Geraint Rees, Sarah Teichmann and Daniel Wolpert.","Francis Crick\n\nFrancis Crick Institute","Francis Crick\n\nThe Francis Crick Institute is a £660,000,000 biomedical research centre currently under construction, located in London, United Kingdom. The Francis Crick Institute is a partnership between Cancer Research UK, Imperial College London, King's College London, the Medical Research Council, University College London (UCL) and the Wellcome Trust. Once completed in 2016, it will be the largest centre for biomedical research and innovation in Europe.","Francis Crick\n\nFrancis Crick Graduate Lectures","Francis Crick\n\nThe University of Cambridge Graduate School of Biological, Medical and Veterinary Sciences hosts The Francis Crick Graduate Lectures. The first two lectures were by John Gurdon and Tim Hunt.","Francis Crick\n\nOther honours","Francis Crick\n\n*The inscription on the helices of a DNA sculpture (which was donated by James Watson) outside Clare College's Thirkill Court, Cambridge, England reads: \"The structure of DNA was discovered in 1953 by Francis Crick and James Watson while Watson lived here at Clare.\" and on the base: \"The double helix model was supported by the work of Rosalind Franklin and Maurice Wilkins.\"\n*Another sculpture entitled Discovery, by artist Lucy Glendinning was installed on Tuesday, 13 December 2005 in Abington Street, Northampton. According to the late Lynn Wilson, chairman of the Wilson Foundation, \"The sculpture celebrates the life of a world class scientist who must surely be considered the greatest Northamptonian of all time — by discovering DNA he unlocked the whole future of genetics and the alphabet of life.\"\n*Westminster City Council unveiled a green plaque to Francis Crick on the front façade of 56 St George's Square, Pimlico, London SW1 on 20 June 2007; Crick lived in the first floor flat, together with Robert Dougall of BBC radio and later TV fame, a former Royal Navy associate.","Francis Crick\n\n* In addition, Crick was a Fellow of the Royal Society, a Fellow of the International Academy of Humanism, and a Fellow of CSICOP. * A sculpted bust of Francis Crick by John Sherrill Houser, which incorporates a single 'Golden' Helix, was cast in bronze in the artist's studio in New Mexico, US. The bronze was first displayed at the Francis Crick Memorial Conference (on Consciousness) at the University of Cambridge's Churchill College on 7 July 2012; it was bought by Mill Hill School in May 2013, and displayed at the inaugural Crick Dinner on 8 June 2013, and will be again at their Crick Centenary Dinner in 2016. * The Benjamin Franklin Medal for Distinguished Achievement in the Sciences of the American Philosophical Society (2001), together with James D. Watson. *Crick featured in the BBC Radio 4 series The New Elizabethans to mark the diamond Jubilee of Queen Elizabeth II in 2012. A panel of seven academics, journalists and historians named Crick among a group of 60 people in the UK \"whose actions during the reign of Elizabeth II have had a significant impact on lives in these islands and given the age its character\".","Francis Crick\n\nBooks by Crick","Francis Crick\n\n* Of Molecules and Men (Prometheus Books, 2004; original edition 1967) ISBN 1-59102-185-5\n* Life Itself: Its Origin and Nature (Simon & Schuster, 1981) ISBN 0-671-25562-2\n* What Mad Pursuit: A Personal View of Scientific Discovery (Basic Books reprint edition, 1990) ISBN 0-465-09138-5\n* The Astonishing Hypothesis: The Scientific Search For The Soul (Scribner reprint edition, 1995) ISBN 0-684-80158-2\n* Kreiseliana: about and around Georg Kreisel; ISBN 1-56881-061-X; 495 pages. For pages 25 – 32 \"Georg Kreisel: a Few Personal Recollections\" contributed by Francis Crick.","Francis Crick\n\nBooks referring to Crick","Francis Crick\n\n* Robert Olby, assisted by Martin Packer, \"Francis Crick: Hunter of Life's Secrets\", Cold Spring Harbor Laboratory Press, ISBN 978-0-87969-798-3, published 25 August 2009; 450 pp; [http://www.cshlpress.com/pdf/sample/Crick.pdf] and Peter Lawrence's review in \"Current Biology\" [http://www.mrc-lmb.cam.ac.uk/PAL/NewFiles/PAListFrames.html]. * John Bankston, Francis Crick and James D. Watson; Francis Crick and James Watson: Pioneers in DNA Research (Mitchell Lane Publishers, Inc., 2002) ISBN 1-58415-122-6. * Bill Bryson; A Short History of Nearly Everything (Broadway Books, 2003) ISBN 0-7679-0817-1. * Soraya De Chadarevian; Designs For Life: Molecular Biology After World War II, CUP 2002, 444 pp; ISBN 0-521-57078-6. * Roderick Braithwaite. \"\"'Strikingly Alive', The History of the Mill Hill School Foundation 1807–2007; published Phillimore & Co. ISBN 978-1-86077-330-3\n* Edwin Chargaff; Heraclitean Fire, Rockefeller Press, 1978. * S. Chomet (Ed.), \"D.N.A. Genesis of a Discovery\", 1994, Newman- Hemisphere Press, London\n* Dickerson, Richard E.; \"Present at the Flood: How Structural Molecular Biology Came About\", Sinauer, 2005; ISBN 0-87893-168-6. * Edward Edelson, \"Francis Crick And James Watson: And the Building Blocks of Life\"' Oxford University Press, 2000, ISBN 0-19-513971-2. * John Finch; 'A Nobel Fellow On Every Floor', Medical Research Council 2008, 381 pp, ISBN 978-1-84046-940-0.","Francis Crick\n\n*Hager, Thomas; \"Force of Nature: The Life of Linus Pauling\", Simon & Schuster 1995; ISBN 0-684-80909-5\n* Graeme Hunter; Light Is A Messenger, the life and science of William Lawrence Bragg (Oxford University Press, 2004) ISBN 0-19-852921-X. * Horace Freeland Judson, The Eighth Day of Creation. Makers of the Revolution in Biology; Penguin Books 1995, first published by Jonathan Cape, 1977; ISBN 0-14-017800-7. * Errol C. Friedberg; \"Sydney Brenner: A Biography\", pub. CSHL Press October 2010, ISBN 0-87969-947-7. * Torsten Krude (Ed.); DNA Changing Science and Society (ISBN 0-521-82378-1) CUP 2003. (The Darwin Lectures for 2003, including one by Sir Aaron Klug on Rosalind Franklin's involvement in the determination of the structure of DNA). * Robert Olby; The Path to The Double Helix: Discovery of DNA; first published in October 1974 by MacMillan, with foreword by Francis Crick; ISBN 0-486-68117-3; revised in 1994, with a 9-page postscript. *Robert Olby; Oxford National Dictionary article: ‘Crick, Francis Harry Compton (1916–2004)’, Oxford Dictionary of National Biography, Oxford University Press, January 2008. * Anne Sayre. 1975. Rosalind Franklin and DNA. New York: W.W. Norton and Company. ISBN 0-393-32044-8. * James D.","Francis Crick\n\nWatson; The Double Helix: A Personal Account of the Discovery of the Structure of DNA, Atheneum, 1980, ISBN 0-689-70602-2 (first published in 1968) is a very readable firsthand account of the research by Crick and Watson. The book also formed the basis of the award winning television dramatization Life Story by BBC Horizon (also broadcast as Race for the Double Helix). * James D. Watson; The Double Helix: A Personal Account of the Discovery of the Structure of DNA; The Norton Critical Edition, which was published in 1980, edited by Gunther S. Stent: ISBN 0-393-01245-X. * James D. Watson; \"Avoid boring people and other lessons from a life in science\" New York: Random House. ISBN 978-0-375-41284-4, 366pp."],"string":"[\n \"X-ray crystallography\\n\\nX-ray crystallography is a tool used for identifying the atomic and molecular structure of a crystal, in which the crystalline atoms cause a beam of incident X-rays to diffract into many specific directions. By measuring the angles and intensities of these diffracted beams, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal. From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their disorder and various other information.\",\n \"X-ray crystallography\\n\\nSince many materials can form crystals—such as salts, metals, minerals, semiconductors, as well as various inorganic, organic and biological molecules—X-ray crystallography has been fundamental in the development of many scientific fields. In its first decades of use, this method determined the size of atoms, the lengths and types of chemical bonds, and the atomic-scale differences among various materials, especially minerals and alloys. The method also revealed the structure and function of many biological molecules, including vitamins, drugs, proteins and nucleic acids such as DNA. X-ray crystallography is still the chief method for characterizing the atomic structure of new materials and in discerning materials that appear similar by other experiments. X-ray crystal structures can also account for unusual electronic or elastic properties of a material, shed light on chemical interactions and processes, or serve as the basis for designing pharmaceuticals against diseases.\",\n \"X-ray crystallography\\n\\nIn a single-crystal X-ray diffraction measurement, a crystal is mounted on a goniometer. The goniometer is used to position the crystal at selected orientations. The crystal is illuminated with a finely focused monochromatic beam of X-rays, producing a diffraction pattern of regularly spaced spots known as reflections. The two-dimensional images taken at different orientations are converted into a three-dimensional model of the density of electrons within the crystal using the mathematical method of Fourier transforms, combined with chemical data known for the sample. Poor resolution (fuzziness) or even errors may result if the crystals are too small, or not uniform enough in their internal makeup.\",\n \"X-ray crystallography\\n\\nX-ray crystallography is related to several other methods for determining atomic structures. Similar diffraction patterns can be produced by scattering electrons or neutrons, which are likewise interpreted by Fourier transformation. If single crystals of sufficient size cannot be obtained, various other X-ray methods can be applied to obtain less detailed information; such methods include fiber diffraction, powder diffraction and (if the sample is not crystallized) small-angle X-ray scattering (SAXS).\\nIf the material under investigation is only available in the form of nanocrystalline powders or suffers from poor crystallinity, the methods of electron crystallography can be applied for determining the atomic structure.\",\n \"X-ray crystallography\\n\\nFor all above mentioned X-ray diffraction methods, the scattering is elastic; the scattered X-rays have the same wavelength as the incoming X-ray. By contrast, inelastic X-ray scattering methods are useful in studying excitations of the sample, rather than the distribution of its atoms.\",\n \"X-ray crystallography\\n\\nHistory\",\n \"X-ray crystallography\\n\\nEarly scientific history of crystals and X-rays\",\n \"X-ray crystallography\\n\\nCrystals, though long admired for their regularity and symmetry, were not investigated scientifically until the 17th century. Johannes Kepler hypothesized in his work Strena seu de Nive Sexangula (A New Year's Gift of Hexagonal Snow) (1611) that the hexagonal symmetry of snowflake crystals was due to a regular packing of spherical water particles.\",\n \"X-ray crystallography\\n\\nThe Danish scientist Nicolas Steno (1669) pioneered experimental investigations of crystal symmetry. Steno showed that the angles between the faces are the same in every exemplar of a particular type of crystal, and René Just Haüy (1784) discovered that every face of a crystal can be described by simple stacking patterns of blocks of the same shape and size. Hence, William Hallowes Miller in 1839 was able to give each face a unique label of three small integers, the Miller indices which remain in use today for identifying crystal faces. Haüy's study led to the correct idea that crystals are a regular three-dimensional array (a Bravais lattice) of atoms and molecules; a single unit cell is repeated indefinitely along three principal directions that are not necessarily perpendicular. In the 19th century, a complete catalog of the possible symmetries of a crystal was worked out by Johan Hessel, Auguste Bravais, Evgraf Fedorov, Arthur Schönflies and (belatedly) William Barlow (1894). From the available data and physical reasoning, Barlow proposed several crystal structures in the 1880s that were validated later by X-ray crystallography; however, the available data were too scarce in the 1880s to accept his models as conclusive.\",\n \"X-ray crystallography\\n\\nWilhelm Röntgen discovered X-rays in 1895, just as the studies of crystal symmetry were being concluded. Physicists were initially uncertain of the nature of X-rays, but soon suspected (correctly) that they were waves of electromagnetic radiation, in other words, another form of light. At that time, the wave model of light—specifically, the Maxwell theory of electromagnetic radiation—was well accepted among scientists, and experiments by Charles Glover Barkla showed that X-rays exhibited phenomena associated with electromagnetic waves, including transverse polarization and spectral lines akin to those observed in the visible wavelengths. Single-slit experiments in the laboratory of Arnold Sommerfeld suggested that X-rays had a wavelength of about 1 angstrom. However, X-rays are composed of photons, and thus are not only waves of electromagnetic radiation but also exhibit particle-like properties. Albert Einstein introduced the photon concept in 1905, but it was not broadly accepted until 1922, when Arthur Compton confirmed it by the scattering of X-rays from electrons. Therefore, these particle-like properties of X-rays, such as their ionization of gases, caused William Henry Bragg to argue in 1907 that X-rays were not electromagnetic radiation.\",\n \"X-ray crystallography\\n\\nNevertheless, Bragg's view was not broadly accepted and the observation of X-ray diffraction by Max von Laue in 1912 confirmed for most scientists that X-rays were a form of electromagnetic radiation.\",\n \"X-ray crystallography\\n\\nX-ray diffraction\",\n \"X-ray crystallography\\n\\nCrystals are regular arrays of atoms, and X-rays can be considered waves of electromagnetic radiation. Atoms scatter X-ray waves, primarily through the atoms' electrons. Just as an ocean wave striking a lighthouse produces secondary circular waves emanating from the lighthouse, so an X-ray striking an electron produces secondary spherical waves emanating from the electron. This phenomenon is known as elastic scattering, and the electron (or lighthouse) is known as the scatterer. A regular array of scatterers produces a regular array of spherical waves. Although these waves cancel one another out in most directions through destructive interference, they add constructively in a few specific directions, determined by Bragg's law:\",\n \"X-ray crystallography\\n\\n2d \\\\sin \\\\theta = n \\\\lambda\",\n \"X-ray crystallography\\n\\nHere d is the spacing between diffracting planes, \\\\theta is the incident angle, n is any integer, and λ is the wavelength of the beam. These specific directions appear as spots on the diffraction pattern called reflections. Thus, X-ray diffraction results from an electromagnetic wave (the X-ray) impinging on a regular array of scatterers (the repeating arrangement of atoms within the crystal).\",\n \"X-ray crystallography\\n\\nX-rays are used to produce the diffraction pattern because their wavelength λ is typically the same order of magnitude (1–100 angstroms) as the spacing d between planes in the crystal. In principle, any wave impinging on a regular array of scatterers produces diffraction, as predicted first by Francesco Maria Grimaldi in 1665. To produce significant diffraction, the spacing between the scatterers and the wavelength of the impinging wave should be similar in size. For illustration, the diffraction of sunlight through a bird's feather was first reported by James Gregory in the later 17th century. The first artificial diffraction gratings for visible light were constructed by David Rittenhouse in 1787, and Joseph von Fraunhofer in 1821. However, visible light has too long a wavelength (typically, 5500 angstroms) to observe diffraction from crystals. Prior to the first X-ray diffraction experiments, the spacings between lattice planes in a crystal were not known with certainty.\",\n \"X-ray crystallography\\n\\nThe idea that crystals could be used as a diffraction grating for X-rays arose in 1912 in a conversation between Paul Peter Ewald and Max von Laue in the English Garden in Munich. Ewald had proposed a resonator model of crystals for his thesis, but this model could not be validated using visible light, since the wavelength was much larger than the spacing between the resonators. Von Laue realized that electromagnetic radiation of a shorter wavelength was needed to observe such small spacings, and suggested that X-rays might have a wavelength comparable to the unit-cell spacing in crystals. Von Laue worked with two technicians, Walter Friedrich and his assistant Paul Knipping, to shine a beam of X-rays through a copper sulfate crystal and record its diffraction on a photographic plate. After being developed, the plate showed a large number of well-defined spots arranged in a pattern of intersecting circles around the spot produced by the central beam. Von Laue developed a law that connects the scattering angles and the size and orientation of the unit-cell spacings in the crystal, for which he was awarded the Nobel Prize in Physics in 1914.\",\n \"X-ray crystallography\\n\\nScattering\",\n \"X-ray crystallography\\n\\nAs described in the mathematical derivation below, the X-ray scattering is determined by the density of electrons within the crystal. Since the energy of an X-ray is much greater than that of a valence electron, the scattering may be modeled as Thomson scattering, the interaction of an electromagnetic ray with a free electron. This model is generally adopted to describe the polarization of the scattered radiation.\",\n \"X-ray crystallography\\n\\nThe intensity of Thomson scattering for one particle with mass m and charge q is:\",\n \"X-ray crystallography\\n\\nI_o I_e \\\\left(\\\\frac{q^4}{m^2c^4}\\\\right)\\\\frac{1+\\\\cos^22\\\\theta}{2} \\n I_e7.94.10^{-26}\\\\frac{1+\\\\cos^22\\\\theta}{2} = I_ef\",\n \"X-ray crystallography\\n\\nHence the atomic nuclei, which are much heavier than an electron, contribute negligibly to the scattered X-rays.\",\n \"X-ray crystallography\\n\\nDevelopment from 1912 to 1920\",\n \"X-ray crystallography\\n\\nAfter Von Laue's pioneering research, the field developed rapidly, most notably by physicists William Lawrence Bragg and his father William Henry Bragg. In 1912–1913, the younger Bragg developed Bragg's law, which connects the observed scattering with reflections from evenly spaced planes within the crystal. The Braggs, father and son, shared the 1915 Nobel Prize in Physics for their work in crystallography. The earliest structures were generally simple and marked by one-dimensional symmetry. However, as computational and experimental methods improved over the next decades, it became feasible to deduce reliable atomic positions for more complicated two- and three-dimensional arrangements of atoms in the unit-cell.\",\n \"X-ray crystallography\\n\\nThe potential of X-ray crystallography for determining the structure of molecules and minerals—then only known vaguely from chemical and hydrodynamic experiments—was realized immediately. The earliest structures were simple inorganic crystals and minerals, but even these revealed fundamental laws of physics and chemistry. The first atomic-resolution structure to be \\\"solved\\\" (i.e., determined) in 1914 was that of table salt. The distribution of electrons in the table-salt structure showed that crystals are not necessarily composed of covalently bonded molecules, and proved the existence of ionic compounds. The structure of diamond was solved in the same year, proving the tetrahedral arrangement of its chemical bonds and showing that the length of C–C single bond was 1.52 angstroms. Other early structures included copper, calcium fluoride (CaF2, also known as fluorite), calcite (CaCO3) and pyrite (FeS2) in 1914; spinel (MgAl2O4) in 1915; the rutile and anatase forms of titanium dioxide (TiO2) in 1916; pyrochroite Mn(OH)2 and, by extension, brucite Mg(OH)2 in 1919;. Also in 1919 sodium nitrate (NaNO3) and caesium dichloroiodide (CsICl2) were determined by Ralph Walter Graystone Wyckoff, and the wurtzite (hexagonal ZnS) structure became known in 1920.\",\n \"X-ray crystallography\\n\\nThe structure of graphite was solved in 1916 by the related method of powder diffraction, which was developed by Peter Debye and Paul Scherrer and, independently, by Albert Hull in 1917. The structure of graphite was determined from single-crystal diffraction in 1924 by two groups independently. Hull also used the powder method to determine the structures of various metals, such as iron and magnesium.\",\n \"X-ray crystallography\\n\\nCultural and aesthetic importance of X-ray crystallography\",\n \"X-ray crystallography\\n\\nIn what has been called his scientific autobiography, The Development of X-ray Analysis, Sir William Lawrence Bragg mentioned that he believed the field of crystallography was particularly welcoming to women because the techno-aesthetics of the molecular structures resembled textiles and household objects. Bragg was known to compare crystal formation to \\\"curtains, wallpapers, mosaics, and roses.\\\"\",\n \"X-ray crystallography\\n\\nIn 1951, the Festival Pattern Group at the Festival of Britain hosted a collaborative group of textile manufacturers and experienced crystallographers to design lace and prints based on the X-ray crystallography of insulin, china clay, and hemoglobin. One of the leading scientists of the project was Dr. Helen Megaw (1907–2002), the Assistant Director of Research at the Cavendish Laboratory in Cambridge at the time. Megaw is credited as one of the central figures who took inspiration from crystal diagrams and saw their potential in design. In 2008, the Wellcome Collection in London curated an exhibition on the Festival Pattern Group called \\\"From Atom to Patterns.\\\"\",\n \"X-ray crystallography\\n\\nContributions to chemistry and material science\",\n \"X-ray crystallography\\n\\nX-ray crystallography has led to a better understanding of chemical bonds and non-covalent interactions. The initial studies revealed the typical radii of atoms, and confirmed many theoretical models of chemical bonding, such as the tetrahedral bonding of carbon in the diamond structure, the octahedral bonding of metals observed in ammonium hexachloroplatinate (IV), and the resonance observed in the planar carbonate group and in aromatic molecules. Kathleen Lonsdale's 1928 structure of hexamethylbenzene established the hexagonal symmetry of benzene and showed a clear difference in bond length between the aliphatic C–C bonds and aromatic C–C bonds; this finding led to the idea of resonance between chemical bonds, which had profound consequences for the development of chemistry. Her conclusions were anticipated by William Henry Bragg, who published models of naphthalene and anthracene in 1921 based on other molecules, an early form of molecular replacement.\",\n \"X-ray crystallography\\n\\nAlso in the 1920s, Victor Moritz Goldschmidt and later Linus Pauling developed rules for eliminating chemically unlikely structures and for determining the relative sizes of atoms. These rules led to the structure of brookite (1928) and an understanding of the relative stability of the rutile, brookite and anatase forms of titanium dioxide.\",\n \"X-ray crystallography\\n\\nThe distance between two bonded atoms is a sensitive measure of the bond strength and its bond order; thus, X-ray crystallographic studies have led to the discovery of even more exotic types of bonding in inorganic chemistry, such as metal-metal double bonds, metal-metal quadruple bonds, and three-center, two-electron bonds. X-ray crystallography—or, strictly speaking, an inelastic Compton scattering experiment—has also provided evidence for the partly covalent character of hydrogen bonds. In the field of organometallic chemistry, the X-ray structure of ferrocene initiated scientific studies of sandwich compounds, while that of Zeise's salt stimulated research into \\\"back bonding\\\" and metal-pi complexes. Finally, X-ray crystallography had a pioneering role in the development of supramolecular chemistry, particularly in clarifying the structures of the crown ethers and the principles of host-guest chemistry.\",\n \"X-ray crystallography\\n\\nIn material sciences, many complicated inorganic and organometallic systems have been analyzed using single-crystal methods, such as fullerenes, metalloporphyrins, and other complicated compounds. Single-crystal diffraction is also used in the pharmaceutical industry, due to recent problems with polymorphs. The major factors affecting the quality of single-crystal structures are the crystal's size and regularity; recrystallization is a commonly used technique to improve these factors in small-molecule crystals. The Cambridge Structural Database contains over 500,000 structures; over 99% of these structures were determined by X-ray diffraction.\",\n \"X-ray crystallography\\n\\nMineralogy and metallurgy\",\n \"X-ray crystallography\\n\\nSince the 1920s, X-ray diffraction has been the principal method for determining the arrangement of atoms in minerals and metals. The application of X-ray crystallography to mineralogy began with the structure of garnet, which was determined in 1924 by Menzer. A systematic X-ray crystallographic study of the silicates was undertaken in the 1920s. This study showed that, as the Si/O ratio is altered, the silicate crystals exhibit significant changes in their atomic arrangements. Machatschki extended these insights to minerals in which aluminium substitutes for the silicon atoms of the silicates. The first application of X-ray crystallography to metallurgy likewise occurred in the mid-1920s. Most notably, Linus Pauling's structure of the alloy Mg2Sn led to his theory of the stability and structure of complex ionic crystals.\",\n \"X-ray crystallography\\n\\nOn October 17, 2012, the Curiosity rover on the planet Mars at \\\"Rocknest\\\" performed the first X-ray diffraction analysis of Martian soil. The results from the rover's CheMin analyzer revealed the presence of several minerals, including feldspar, pyroxenes and olivine, and suggested that the Martian soil in the sample was similar to the \\\"weathered basaltic soils\\\" of Hawaiian volcanoes.\",\n \"X-ray crystallography\\n\\nEarly organic and small biological molecules\",\n \"X-ray crystallography\\n\\nThe first structure of an organic compound, hexamethylenetetramine, was solved in 1923. This was followed by several studies of long-chain fatty acids, which are an important component of biological membranes. In the 1930s, the structures of much larger molecules with two-dimensional complexity began to be solved. A significant advance was the structure of phthalocyanine, a large planar molecule that is closely related to porphyrin molecules important in biology, such as heme, corrin and chlorophyll.\",\n \"X-ray crystallography\\n\\nX-ray crystallography of biological molecules took off with Dorothy Crowfoot Hodgkin, who solved the structures of cholesterol (1937), penicillin (1946) and vitamin B12 (1956), for which she was awarded the Nobel Prize in Chemistry in 1964. In 1969, she succeeded in solving the structure of insulin, on which she worked for over thirty years.\",\n \"X-ray crystallography\\n\\nBiological macromolecular crystallography\",\n \"X-ray crystallography\\n\\nCrystal structures of proteins (which are irregular and hundreds of times larger than cholesterol) began to be solved in the late 1950s, beginning with the structure of sperm whale myoglobin by Sir John Cowdery Kendrew, for which he shared the Nobel Prize in Chemistry with Max Perutz in 1962. Since that success, over 86817 X-ray crystal structures of proteins, nucleic acids and other biological molecules have been determined. For comparison, the nearest competing method in terms of structures analyzed is nuclear magnetic resonance (NMR) spectroscopy, which has resolved 9561 chemical structures. Moreover, crystallography can solve structures of arbitrarily large molecules, whereas solution-state NMR is restricted to relatively small ones (less than 70 kDa). X-ray crystallography is now used routinely by scientists to determine how a pharmaceutical drug interacts with its protein target and what changes might improve it. However, intrinsic membrane proteins remain challenging to crystallize because they require detergents or other means to solubilize them in isolation, and such detergents often interfere with crystallization. Such membrane proteins are a large component of the genome, and include many proteins of great physiological importance, such as ion channels and receptors.\",\n \"X-ray crystallography\\n\\nHelium cryogenics are used to prevent radiation damage in protein crystals.Cryogenic (\",\n \"X-ray crystallography\\n\\nOn the other end of the size scale, relative small molecules are able to lure the resolving power of X-ray crystallography. The structure assigned in 1991 to the antibiotic isolated from a marina organism, diazonamide A - C40H34Cl2N6O6 with M = 765.65 - proved to be incorrect by the classical proof of structure: a synthetic sample was not identical to the natural product. The mistake was possible because of the inability of X-ray crystallography to distinguish between the correct -OH / >NH and the interchanged -NH2 / -O- groups in the incorrect structure.\",\n \"X-ray crystallography\\n\\nRelationship to other scattering techniques\",\n \"X-ray crystallography\\n\\nElastic vs. inelastic scattering\",\n \"X-ray crystallography\\n\\nX-ray crystallography is a form of elastic scattering; the outgoing X-rays have the same energy, and thus same wavelength, as the incoming X-rays, only with altered direction. By contrast, inelastic scattering occurs when energy is transferred from the incoming X-ray to the crystal, e.g., by exciting an inner-shell electron to a higher energy level. Such inelastic scattering reduces the energy (or increases the wavelength) of the outgoing beam. Inelastic scattering is useful for probing such excitations of matter, but not in determining the distribution of scatterers within the matter, which is the goal of X-ray crystallography.\",\n \"X-ray crystallography\\n\\nX-rays range in wavelength from 10 to 0.01 nanometers; a typical wavelength used for crystallography is 1 Å (0.1 nm), which is on the scale of covalent chemical bonds and the radius of a single atom. Longer-wavelength photons (such as ultraviolet radiation) would not have sufficient resolution to determine the atomic positions. At the other extreme, shorter-wavelength photons such as gamma rays are difficult to produce in large numbers, difficult to focus, and interact too strongly with matter, producing particle-antiparticle pairs. Therefore, X-rays are the \\\"sweetspot\\\" for wavelength when determining atomic-resolution structures from the scattering of electromagnetic radiation.\",\n \"X-ray crystallography\\n\\nOther X-ray techniques\",\n \"X-ray crystallography\\n\\nOther forms of elastic X-ray scattering include powder diffraction, Small-Angle X-ray Scattering (SAXS) and several types of X-ray fiber diffraction, which was used by Rosalind Franklin in determining the double-helix structure of DNA. In general, single-crystal X-ray diffraction offers more structural information than these other techniques; however, it requires a sufficiently large and regular crystal, which is not always available.\",\n \"X-ray crystallography\\n\\nThese scattering methods generally use monochromatic X-rays, which are restricted to a single wavelength with minor deviations. A broad spectrum of X-rays (that is, a blend of X-rays with different wavelengths) can also be used to carry out X-ray diffraction, a technique known as the Laue method. This is the method used in the original discovery of X-ray diffraction. Laue scattering provides much structural information with only a short exposure to the X-ray beam, and is therefore used in structural studies of very rapid events (Time resolved crystallography). However, it is not as well-suited as monochromatic scattering for determining the full atomic structure of a crystal and therefore works better with crystals with relatively simple atomic arrangements.\",\n \"X-ray crystallography\\n\\nThe Laue back reflection mode records X-rays scattered backwards from a broad spectrum source. This is useful if the sample is too thick for X-rays to transmit through it. The diffracting planes in the crystal are determined by knowing that the normal to the diffracting plane bisects the angle between the incident beam and the diffracted beam. A Greninger chart can be used to interpret the back reflection Laue photograph.\",\n \"X-ray crystallography\\n\\nElectron and neutron diffraction\",\n \"X-ray crystallography\\n\\nOther particles, such as electrons and neutrons, may be used to produce a diffraction pattern. Although electron, neutron, and X-ray scattering are based on different physical processes, the resulting diffraction patterns are analyzed using the same coherent diffraction imaging techniques.\",\n \"X-ray crystallography\\n\\nAs derived below, the electron density within the crystal and the diffraction patterns are related by a simple mathematical method, the Fourier transform, which allows the density to be calculated relatively easily from the patterns. However, this works only if the scattering is weak, i.e., if the scattered beams are much less intense than the incoming beam. Weakly scattered beams pass through the remainder of the crystal without undergoing a second scattering event. Such re-scattered waves are called \\\"secondary scattering\\\" and hinder the analysis. Any sufficiently thick crystal will produce secondary scattering, but since X-rays interact relatively weakly with the electrons, this is generally not a significant concern. By contrast, electron beams may produce strong secondary scattering even for relatively thin crystals (>100 nm). Since this thickness corresponds to the diameter of many viruses, a promising direction is the electron diffraction of isolated macromolecular assemblies, such as viral capsids and molecular machines, which may be carried out with a cryo-electron microscope. Moreover, the strong interaction of electrons with matter (about 1000 times stronger than for X-rays) allows determination of the atomic structure of extremely small volumes.\",\n \"X-ray crystallography\\n\\nThe field of applications for electron crystallography ranges from bio molecules like membrane proteins over organic thin films to the complex structures of (nanocrystalline) intermetallic compounds and zeolites.\",\n \"X-ray crystallography\\n\\nNeutron diffraction is an excellent method for structure determination, although it has been difficult to obtain intense, monochromatic beams of neutrons in sufficient quantities. Traditionally, nuclear reactors have been used, although sources producing neutrons by spallation are becoming increasingly available. Being uncharged, neutrons scatter much more readily from the atomic nuclei rather than from the electrons. Therefore, neutron scattering is very useful for observing the positions of light atoms with few electrons, especially hydrogen, which is essentially invisible in the X-ray diffraction. Neutron scattering also has the remarkable property that the solvent can be made invisible by adjusting the ratio of normal water, H2O, and heavy water, D2O.\",\n \"X-ray crystallography\\n\\nMethods\",\n \"X-ray crystallography\\n\\nOverview of single-crystal X-ray diffraction\",\n \"X-ray crystallography\\n\\nThe oldest and most precise method of X-ray crystallography is single-crystal X-ray diffraction, in which a beam of X-rays strikes a single crystal, producing scattered beams. When they land on a piece of film or other detector, these beams make a diffraction pattern of spots; the strengths and angles of these beams are recorded as the crystal is gradually rotated. Each spot is called a reflection, since it corresponds to the reflection of the X-rays from one set of evenly spaced planes within the crystal. For single crystals of sufficient purity and regularity, X-ray diffraction data can determine the mean chemical bond lengths and angles to within a few thousandths of an angstrom and to within a few tenths of a degree, respectively. The atoms in a crystal are not static, but oscillate about their mean positions, usually by less than a few tenths of an angstrom. X-ray crystallography allows measuring the size of these oscillations.\",\n \"X-ray crystallography\\n\\nProcedure\",\n \"X-ray crystallography\\n\\nThe technique of single-crystal X-ray crystallography has three basic steps. The first—and often most difficult—step is to obtain an adequate crystal of the material under study. The crystal should be sufficiently large (typically larger than 0.1 mm in all dimensions), pure in composition and regular in structure, with no significant internal imperfections such as cracks or twinning.\",\n \"X-ray crystallography\\n\\nIn the second step, the crystal is placed in an intense beam of X-rays, usually of a single wavelength (monochromatic X-rays), producing the regular pattern of reflections. As the crystal is gradually rotated, previous reflections disappear and new ones appear; the intensity of every spot is recorded at every orientation of the crystal. Multiple data sets may have to be collected, with each set covering slightly more than half a full rotation of the crystal and typically containing tens of thousands of reflections.\",\n \"X-ray crystallography\\n\\nIn the third step, these data are combined computationally with complementary chemical information to produce and refine a model of the arrangement of atoms within the crystal. The final, refined model of the atomic arrangement—now called a crystal structure—is usually stored in a public database.\",\n \"X-ray crystallography\\n\\nLimitations\",\n \"X-ray crystallography\\n\\nAs the crystal's repeating unit, its unit cell, becomes larger and more complex, the atomic-level picture provided by X-ray crystallography becomes less well-resolved (more \\\"fuzzy\\\") for a given number of observed reflections. Two limiting cases of X-ray crystallography—\\\"small-molecule\\\" and \\\"macromolecular\\\" crystallography—are often discerned. Small-molecule crystallography typically involves crystals with fewer than 100 atoms in their asymmetric unit; such crystal structures are usually so well resolved that the atoms can be discerned as isolated \\\"blobs\\\" of electron density. By contrast, macromolecular crystallography often involves tens of thousands of atoms in the unit cell. Such crystal structures are generally less well-resolved (more \\\"smeared out\\\"); the atoms and chemical bonds appear as tubes of electron density, rather than as isolated atoms. In general, small molecules are also easier to crystallize than macromolecules; however, X-ray crystallography has proven possible even for viruses with hundreds of thousands of atoms. Though normally x-ray crystallography can only be performed if the sample is in crystal form, new research has been done into sampling non-crystalline forms of samples.\",\n \"X-ray crystallography\\n\\nCrystallization\",\n \"X-ray crystallography\\n\\nAlthough crystallography can be used to characterize the disorder in an impure or irregular crystal, crystallography generally requires a pure crystal of high regularity to solve the structure of a complicated arrangement of atoms. Pure, regular crystals can sometimes be obtained from natural or synthetic materials, such as samples of metals, minerals or other macroscopic materials. The regularity of such crystals can sometimes be improved with macromolecular crystal annealing and other methods. However, in many cases, obtaining a diffraction-quality crystal is the chief barrier to solving its atomic-resolution structure.\",\n \"X-ray crystallography\\n\\nSmall-molecule and macromolecular crystallography differ in the range of possible techniques used to produce diffraction-quality crystals. Small molecules generally have few degrees of conformational freedom, and may be crystallized by a wide range of methods, such as chemical vapor deposition and recrystallization. By contrast, macromolecules generally have many degrees of freedom and their crystallization must be carried out so as to maintain a stable structure. For example, proteins and larger RNA molecules cannot be crystallized if their tertiary structure has been unfolded; therefore, the range of crystallization conditions is restricted to solution conditions in which such molecules remain folded.\",\n \"X-ray crystallography\\n\\nProtein crystals are almost always grown in solution. The most common approach is to lower the solubility of its component molecules very gradually; if this is done too quickly, the molecules will precipitate from solution, forming a useless dust or amorphous gel on the bottom of the container. Crystal growth in solution is characterized by two steps: nucleation of a microscopic crystallite (possibly having only 100 molecules), followed by growth of that crystallite, ideally to a diffraction-quality crystal. The solution conditions that favor the first step (nucleation) are not always the same conditions that favor the second step (subsequent growth). The crystallographer's goal is to identify solution conditions that favor the development of a single, large crystal, since larger crystals offer improved resolution of the molecule. Consequently, the solution conditions should disfavor the first step (nucleation) but favor the second (growth), so that only one large crystal forms per droplet. If nucleation is favored too much, a shower of small crystallites will form in the droplet, rather than one large crystal; if favored too little, no crystal will form whatsoever.\",\n \"X-ray crystallography\\n\\nOther approaches involves, crystallizing proteins under oil, where aqueous protein solutions are dispensed under liquid oil, and water evaporates through the layer of oil. Different oils have different evaporation permeabilities, therefore yielding changes in concentration rates from different percipient/protein mixture. The technique relies on bringing the protein directly into the nucleation zone by mixing protein with the appropriate amount of percipient to prevent the diffusion of water out of the drop.\",\n \"X-ray crystallography\\n\\nIt is extremely difficult to predict good conditions for nucleation or growth of well-ordered crystals. In practice, favorable conditions are identified by screening; a very large batch of the molecules is prepared, and a wide variety of crystallization solutions are tested. Hundreds, even thousands, of solution conditions are generally tried before finding the successful one. The various conditions can use one or more physical mechanisms to lower the solubility of the molecule; for example, some may change the pH, some contain salts of the Hofmeister series or chemicals that lower the dielectric constant of the solution, and still others contain large polymers such as polyethylene glycol that drive the molecule out of solution by entropic effects. It is also common to try several temperatures for encouraging crystallization, or to gradually lower the temperature so that the solution becomes supersaturated. These methods require large amounts of the target molecule, as they use high concentration of the molecule(s) to be crystallized. Due to the difficulty in obtaining such large quantities (milligrams) of crystallization-grade protein, robots have been developed that are capable of accurately dispensing crystallization trial drops that are in the order of 100 nanoliters in volume.\",\n \"X-ray crystallography\\n\\nThis means that 10-fold less protein is used per experiment when compared to crystallization trials set up by hand (in the order of 1 microliter).\",\n \"X-ray crystallography\\n\\nSeveral factors are known to inhibit or mar crystallization. The growing crystals are generally held at a constant temperature and protected from shocks or vibrations that might disturb their crystallization. Impurities in the molecules or in the crystallization solutions are often inimical to crystallization. Conformational flexibility in the molecule also tends to make crystallization less likely, due to entropy. Ironically, molecules that tend to self-assemble into regular helices are often unwilling to assemble into crystals . Crystals can be marred by twinning, which can occur when a unit cell can pack equally favorably in multiple orientations; although recent advances in computational methods may allow solving the structure of some twinned crystals. Having failed to crystallize a target molecule, a crystallographer may try again with a slightly modified version of the molecule; even small changes in molecular properties can lead to large differences in crystallization behavior.\",\n \"X-ray crystallography\\n\\nData collection\",\n \"X-ray crystallography\\n\\nMounting the crystal\",\n \"X-ray crystallography\\n\\nThe crystal is mounted for measurements so that it may be held in the X-ray beam and rotated. There are several methods of mounting. In the past, crystals were loaded into glass capillaries with the crystallization solution (the mother liquor). Nowadays, crystals of small molecules are typically attached with oil or glue to a glass fiber or a loop, which is made of nylon or plastic and attached to a solid rod. Protein crystals are scooped up by a loop, then flash-frozen with liquid nitrogen. This freezing reduces the radiation damage of the X-rays, as well as the noise in the Bragg peaks due to thermal motion (the Debye-Waller effect). However, untreated protein crystals often crack if flash-frozen; therefore, they are generally pre-soaked in a cryoprotectant solution before freezing. Unfortunately, this pre-soak may itself cause the crystal to crack, ruining it for crystallography. Generally, successful cryo-conditions are identified by trial and error.\",\n \"X-ray crystallography\\n\\nThe capillary or loop is mounted on a goniometer, which allows it to be positioned accurately within the X-ray beam and rotated. Since both the crystal and the beam are often very small, the crystal must be centered within the beam to within ~25 micrometers accuracy, which is aided by a camera focused on the crystal. The most common type of goniometer is the \\\"kappa goniometer\\\", which offers three angles of rotation: the ω angle, which rotates about an axis perpendicular to the beam; the κ angle, about an axis at ~50° to the ω axis; and, finally, the φ angle about the loop/capillary axis. When the κ angle is zero, the ω and φ axes are aligned. The κ rotation allows for convenient mounting of the crystal, since the arm in which the crystal is mounted may be swung out towards the crystallographer. The oscillations carried out during data collection (mentioned below) involve the ω axis only. An older type of goniometer is the four-circle goniometer, and its relatives such as the six-circle goniometer.\",\n \"X-ray crystallography\\n\\nX-ray Sources\",\n \"X-ray crystallography\\n\\nRotating Anode\",\n \"X-ray crystallography\\n\\nSmall scale can be done on a local X-ray tube source, typically coupled with an image plate detector. These have the advantage of being (relatively) inexpensive and easy to maintain, and allow for quick screening and collection of samples. However, the wavelength light produced is limited by anode material, typically copper. Further, intensity is limited by the power applied and cooling capacity available to avoid melting the anode. In such systems, electrons are boiled off of a cathode and accelerated through a strong electric potential of ~50 kV; having reached a high speed, the electrons collide with a metal plate, emitting bremsstrahlung and some strong spectral lines corresponding to the excitation of inner-shell electrons of the metal. The most common metal used is copper, which can be kept cool easily, due to its high thermal conductivity, and which produces strong Kα and Kβ lines. The Kβ line is sometimes suppressed with a thin (~10 µm) nickel foil. The simplest and cheapest variety of sealed X-ray tube has a stationary anode (the Crookes tube) and run with ~2 kW of electron beam power. The more expensive variety has a rotating-anode type source that run with ~14 kW of e-beam power.\",\n \"X-ray crystallography\\n\\nX-rays are generally filtered (by use of X-Ray Filters) to a single wavelength (made monochromatic) and collimated to a single direction before they are allowed to strike the crystal. The filtering not only simplifies the data analysis, but also removes radiation that degrades the crystal without contributing useful information. Collimation is done either with a collimator (basically, a long tube) or with a clever arrangement of gently curved mirrors. Mirror systems are preferred for small crystals (under 0.3 mm) or with large unit cells (over 150 Å)\",\n \"X-ray crystallography\\n\\nSynchrotron Radiation\",\n \"X-ray crystallography\\n\\nSynchrotron radiation are some of the brightest lights on earth. It is the single most powerful tool available to X-ray crystallographers. It is made of X-ray beams generated in large machines called synchrotrons. These machines accelerate electrically charged particles, often electrons, to nearly the speed of light and confine them in a (roughly) circular loop using magnetic fields.\",\n \"X-ray crystallography\\n\\nSynchrotrons are generally national facilities, each with several dedicated beamlines where data is collected without interruption. Synchrotrons were originally designed for use by high-energy physicists studying subatomic particles and cosmic phenomena. The largest component of each synchrotron is its electron storage ring. This ring is actually not a perfect circle, but a many-sided polygon. At each corner of the polygon, or sector, precisely aligned magnets bend the electron stream. As the electrons’ path is bent, they emit bursts of energy in the form of X-rays.\",\n \"X-ray crystallography\\n\\nUsing synchrotron radiation frequently has specific requirements for X-ray crystallography. The intense ionizing radiation can cause radiation damage to samples, particularly macromolecular crystals. Cryo crystallography protects the sample from radiation damage, by freezing the crystal at liquid nitrogen temperatures (~100 K). However, synchrotron radiation frequently has the advantage of user selectable wavelengths, allowing for anomalous scattering experiments which maximizes anomalous signal. This is critical in experiments such as SAD and MAD.\",\n \"X-ray crystallography\\n\\nFree Electron Laser\",\n \"X-ray crystallography\\n\\nRecently, free electron lasers have been developed for use in X-ray crystallography. These are the brightest X-ray sources currently available; with the X-rays coming in femtosecond bursts. The intensity of the source is such that atomic resolution diffraction patterns can be resolved for crystals otherwise too small for collection. However, the intense light source also destroys the sample, requiring multiple crystals to be shot. As each crystal is randomly oriented in the beam, hundreds of thousands of individual diffraction images must be collected in order to get a complete data-set. This method, serial femtosecond crystallography, has been used in solving the structure of a number of protein crystal structures, sometimes noting differences with equivalent structures collected from synchrotron sources.\",\n \"X-ray crystallography\\n\\nRecording the reflections\",\n \"X-ray crystallography\\n\\nWhen a crystal is mounted and exposed to an intense beam of X-rays, it scatters the X-rays into a pattern of spots or reflections that can be observed on a screen behind the crystal. A similar pattern may be seen by shining a laser pointer at a compact disc. The relative intensities of these spots provide the information to determine the arrangement of molecules within the crystal in atomic detail. The intensities of these reflections may be recorded with photographic film, an area detector or with a charge-coupled device (CCD) image sensor. The peaks at small angles correspond to low-resolution data, whereas those at high angles represent high-resolution data; thus, an upper limit on the eventual resolution of the structure can be determined from the first few images. Some measures of diffraction quality can be determined at this point, such as the mosaicity of the crystal and its overall disorder, as observed in the peak widths. Some pathologies of the crystal that would render it unfit for solving the structure can also be diagnosed quickly at this point.\",\n \"X-ray crystallography\\n\\nOne image of spots is insufficient to reconstruct the whole crystal; it represents only a small slice of the full Fourier transform. To collect all the necessary information, the crystal must be rotated step-by-step through 180°, with an image recorded at every step; actually, slightly more than 180° is required to cover reciprocal space, due to the curvature of the Ewald sphere. However, if the crystal has a higher symmetry, a smaller angular range such as 90° or 45° may be recorded. The rotation axis should be changed at least once, to avoid developing a \\\"blind spot\\\" in reciprocal space close to the rotation axis. It is customary to rock the crystal slightly (by 0.5–2°) to catch a broader region of reciprocal space.\",\n \"X-ray crystallography\\n\\nMultiple data sets may be necessary for certain phasing methods. For example, MAD phasing requires that the scattering be recorded at least three (and usually four, for redundancy) wavelengths of the incoming X-ray radiation. A single crystal may degrade too much during the collection of one data set, owing to radiation damage; in such cases, data sets on multiple crystals must be taken.\",\n \"X-ray crystallography\\n\\nData analysis\",\n \"X-ray crystallography\\n\\nCrystal symmetry, unit cell, and image scaling\",\n \"X-ray crystallography\\n\\nThe recorded series of two-dimensional diffraction patterns, each corresponding to a different crystal orientation, is converted into a three-dimensional model of the electron density; the conversion uses the mathematical technique of Fourier transforms, which is explained below. Each spot corresponds to a different type of variation in the electron density; the crystallographer must determine which variation corresponds to which spot (indexing), the relative strengths of the spots in different images (merging and scaling) and how the variations should be combined to yield the total electron density (phasing).\",\n \"X-ray crystallography\\n\\nData processing begins with indexing the reflections. This means identifying the dimensions of the unit cell and which image peak corresponds to which position in reciprocal space. A byproduct of indexing is to determine the symmetry of the crystal, i.e., its space group. Some space groups can be eliminated from the beginning. For example, reflection symmetries cannot be observed in chiral molecules; thus, only 65 space groups of 230 possible are allowed for protein molecules which are almost always chiral. Indexing is generally accomplished using an autoindexing routine. Having assigned symmetry, the data is then integrated. This converts the hundreds of images containing the thousands of reflections into a single file, consisting of (at the very least) records of the Miller index of each reflection, and an intensity for each reflection (at this state the file often also includes error estimates and measures of partiality (what part of a given reflection was recorded on that image)).\",\n \"X-ray crystallography\\n\\nA full data set may consist of hundreds of separate images taken at different orientations of the crystal. The first step is to merge and scale these various images, that is, to identify which peaks appear in two or more images (merging) and to scale the relative images so that they have a consistent intensity scale. Optimizing the intensity scale is critical because the relative intensity of the peaks is the key information from which the structure is determined. The repetitive technique of crystallographic data collection and the often high symmetry of crystalline materials cause the diffractometer to record many symmetry-equivalent reflections multiple times. This allows calculating the symmetry-related R-factor, a reliability index based upon how similar are the measured intensities of symmetry-equivalent reflections, thus assessing the quality of the data.\",\n \"X-ray crystallography\\n\\nInitial phasing\",\n \"X-ray crystallography\\n\\nThe data collected from a diffraction experiment is a reciprocal space representation of the crystal lattice. The position of each diffraction 'spot' is governed by the size and shape of the unit cell, and the inherent symmetry within the crystal. The intensity of each diffraction 'spot' is recorded, and this intensity is proportional to the square of the structure factor amplitude. The structure factor is a complex number containing information relating to both the amplitude and phase of a wave. In order to obtain an interpretable electron density map, both amplitude and phase must be known (an electron density map allows a crystallographer to build a starting model of the molecule). The phase cannot be directly recorded during a diffraction experiment: this is known as the phase problem. Initial phase estimates can be obtained in a variety of ways:\\n* Ab initio phasing or direct methods – This is usually the method of choice for small molecules (\\n* Anomalous X-ray scattering (MAD or SAD phasing) – the X-ray wavelength may be scanned past an absorption edge of an atom, which changes the scattering in a known way.\",\n \"X-ray crystallography\\n\\nBy recording full sets of reflections at three different wavelengths (far below, far above and in the middle of the absorption edge) one can solve for the substructure of the anomalously diffracting atoms and hence the structure of the whole molecule. The most popular method of incorporating anomalous scattering atoms into proteins is to express the protein in a methionine auxotroph (a host incapable of synthesizing methionine) in a media rich in seleno-methionine, which contains selenium atoms. A MAD experiment can then be conducted around the absorption edge, which should then yield the position of any methionine residues within the protein, providing initial phases. * Heavy atom methods (multiple isomorphous replacement) – If electron-dense metal atoms can be introduced into the crystal, direct methods or Patterson-space methods can be used to determine their location and to obtain initial phases. Such heavy atoms can be introduced either by soaking the crystal in a heavy atom-containing solution, or by co-crystallization (growing the crystals in the presence of a heavy atom). As in MAD phasing, the changes in the scattering amplitudes can be interpreted to yield the phases.\",\n \"X-ray crystallography\\n\\nAlthough this is the original method by which protein crystal structures were solved, it has largely been superseded by MAD phasing with selenomethionine.\",\n \"X-ray crystallography\\n\\nModel building and phase refinement\",\n \"X-ray crystallography\\n\\nHaving obtained initial phases, an initial model can be built. This model can be used to refine the phases, leading to an improved model, and so on. Given a model of some atomic positions, these positions and their respective Debye-Waller factors (or B-factors, accounting for the thermal motion of the atom) can be refined to fit the observed diffraction data, ideally yielding a better set of phases. A new model can then be fit to the new electron density map and a further round of refinement is carried out. This continues until the correlation between the diffraction data and the model is maximized. The agreement is measured by an R-factor defined as\",\n \"X-ray crystallography\\n\\nR = \\\\frac{\\\\sum_{\\\\mathrm{all\\\\ reflections}} \\\\left|F_{o} - F_{c} \\\\right|}{\\\\sum_{\\\\mathrm{all\\\\ reflections}} \\\\left|F_{o} \\\\right|}\",\n \"X-ray crystallography\\n\\nwhere F is the structure factor. A similar quality criterion is Rfree, which is calculated from a subset (~10%) of reflections that were not included in the structure refinement. Both R factors depend on the resolution of the data. As a rule of thumb, Rfree should be approximately the resolution in angstroms divided by 10; thus, a data-set with 2 Å resolution should yield a final Rfree ~ 0.2. Chemical bonding features such as stereochemistry, hydrogen bonding and distribution of bond lengths and angles are complementary measures of the model quality. Phase bias is a serious problem in such iterative model building. Omit maps are a common technique used to check for this.\",\n \"X-ray crystallography\\n\\nIt may not be possible to observe every atom of the crystallized molecule – it must be remembered that the resulting electron density is an average of all the molecules within the crystal. In some cases, there is too much residual disorder in those atoms, and the resulting electron density for atoms existing in many conformations is smeared to such an extent that it is no longer detectable in the electron density map. Weakly scattering atoms such as hydrogen are routinely invisible. It is also possible for a single atom to appear multiple times in an electron density map, e.g., if a protein sidechain has multiple (f(\\\\mathbf{r}) = \\\\frac{1}{\\\\left(2\\\\pi\\\\right)^{3}} \\\\int F(\\\\mathbf{q}) e^{\\\\mathrm{i}\\\\mathbf{q}\\\\cdot\\\\mathbf{r}} \\\\mathrm{d}\\\\mathbf{q}\",\n \"X-ray crystallography\\n\\nwhere the integral is taken over all values of q. The three-dimensional real vector q represents a point in reciprocal space, that is, to a particular oscillation in the electron density as one moves in the direction in which q points. The length of q corresponds to 2\\\\pi divided by the wavelength of the oscillation. The corresponding formula for a Fourier transform will be used below\\nF(\\\\mathbf{q}) = \\\\int f(\\\\mathbf{r}) \\\\mathrm{e}^{-\\\\mathrm{i}\\\\mathbf{q}\\\\cdot\\\\mathbf{r}}\\\\mathrm{d}\\\\mathbf{r}\\nwhere the integral is summed over all possible values of the position vector r within the crystal.\",\n \"X-ray crystallography\\n\\nThe Fourier transform F(q) is generally a complex number, and therefore has a magnitude |F(q)| and a phase φ(q) related by the equation\\nF(\\\\mathbf{q}) = \\\\left|F(\\\\mathbf{q}) \\\\right|\\\\mathrm{e}^{\\\\mathrm{i}\\\\phi(\\\\mathbf{q})}\\nThe intensities of the reflections observed in X-ray diffraction give us the magnitudes |F(q)| but not the phases φ(q). To obtain the phases, full sets of reflections are collected with known alterations to the scattering, either by modulating the wavelength past a certain absorption edge or by adding strongly scattering (i.e., electron-dense) metal atoms such as mercury. Combining the magnitudes and phases yields the full Fourier transform F(q), which may be inverted to obtain the electron density f(r).\",\n \"X-ray crystallography\\n\\nCrystals are often idealized as being perfectly periodic. In that ideal case, the atoms are positioned on a perfect lattice, the electron density is perfectly periodic, and the Fourier transform F(q) is zero except when q belongs to the reciprocal lattice (the so-called Bragg peaks). In reality, however, crystals are not perfectly periodic; atoms vibrate about their mean position, and there may be disorder of various types, such as mosaicity, dislocations, various point defects, and heterogeneity in the conformation of crystallized molecules. Therefore, the Bragg peaks have a finite width and there may be significant diffuse scattering, a continuum of scattered X-rays that fall between the Bragg peaks.\",\n \"X-ray crystallography\\n\\nIntuitive understanding by Bragg's law\",\n \"X-ray crystallography\\n\\nAn intuitive understanding of X-ray diffraction can be obtained from the Bragg model of diffraction. In this model, a given reflection is associated with a set of evenly spaced sheets running through the crystal, usually passing through the centers of the atoms of the crystal lattice. The orientation of a particular set of sheets is identified by its three Miller indices (h, k, l), and let their spacing be noted by d. William Lawrence Bragg proposed a model in which the incoming X-rays are scattered specularly (mirror-like) from each plane; from that assumption, X-rays scattered from adjacent planes will combine constructively (constructive interference) when the angle θ between the plane and the X-ray results in a path-length difference that is an integer multiple n of the X-ray wavelength λ. 2 d\\\\sin\\\\theta = n\\\\lambda\\\\,\\nA reflection is said to be indexed when its Miller indices (or, more correctly, its reciprocal lattice vector components) have been identified from the known wavelength and the scattering angle 2θ. Such indexing gives the unit-cell parameters, the lengths and angles of the unit-cell, as well as its space group.\",\n \"X-ray crystallography\\n\\nSince Bragg's law does not interpret the relative intensities of the reflections, however, it is generally inadequate to solve for the arrangement of atoms within the unit-cell; for that, a Fourier transform method must be carried out.\",\n \"X-ray crystallography\\n\\nScattering as a Fourier transform\",\n \"X-ray crystallography\\n\\nThe incoming X-ray beam has a polarization and should be represented as a vector wave; however, for simplicity, let it be represented here as a scalar wave. We also ignore the complication of the time dependence of the wave and just concentrate on the wave's spatial dependence. Plane waves can be represented by a wave vector kin, and so the strength of the incoming wave at time t=0 is given by\\nA \\\\mathrm{e}^{\\\\mathrm{i}\\\\mathbf{k}_{\\\\mathrm{in}} \\\\cdot \\\\mathbf{r}}\",\n \"X-ray crystallography\\n\\nAt position r within the sample, let there be a density of scatterers f(r); these scatterers should produce a scattered spherical wave of amplitude proportional to the local amplitude of the incoming wave times the number of scatterers in a small volume dV about r\\n\\\\mathrm{amplitude\\\\ of\\\\ scattered\\\\ wave} = A \\\\mathrm{e}^{\\\\mathrm{i}\\\\mathbf{k} \\\\cdot \\\\mathbf{r}} S f(\\\\mathbf{r}) \\\\mathrm{d}V\\nwhere S is the proportionality constant.\",\n \"X-ray crystallography\\n\\nLet's consider the fraction of scattered waves that leave with an outgoing wave-vector of kout and strike the screen at rscreen. Since no energy is lost (elastic, not inelastic scattering), the wavelengths are the same as are the magnitudes of the wave-vectors |kin|=|kout|. From the time that the photon is scattered at r until it is absorbed at rscreen, the photon undergoes a change in phase\\ne^{i \\\\mathbf{k}_{out} \\\\cdot \\\\left( \\\\mathbf{r}_{\\\\mathrm{screen}} - \\\\mathbf{r} \\\\right)}\",\n \"X-ray crystallography\\n\\nThe net radiation arriving at rscreen is the sum of all the scattered waves throughout the crystal\\nA S \\\\int \\\\mathrm{d}\\\\mathbf{r} f(\\\\mathbf{r}) \\\\mathrm{e}^{\\\\mathrm{i} \\\\mathbf{k}_{in} \\\\cdot \\\\mathbf{r}}\\ne^{i \\\\mathbf{k}_{out} \\\\cdot \\\\left( \\\\mathbf{r}_{\\\\mathrm{screen}} - \\\\mathbf{r} \\\\right)} =\\nA S e^{i \\\\mathbf{k}_{out} \\\\cdot \\\\mathbf{r}_{\\\\mathrm{screen}}}\\n\\\\int \\\\mathrm{d}\\\\mathbf{r} f(\\\\mathbf{r}) \\\\mathrm{e}^{\\\\mathrm{i} \\\\left( \\\\mathbf{k}_{in} - \\\\mathbf{k}_{out} \\\\right) \\\\cdot \\\\mathbf{r}}\",\n \"X-ray crystallography\\n\\nwhich may be written as a Fourier transform\\nA S \\\\mathrm{e}^{\\\\mathrm{i} \\\\mathbf{k}_{out} \\\\cdot \\\\mathbf{r}_{\\\\mathrm{screen}}}\\n\\\\int d\\\\mathbf{r} f(\\\\mathbf{r}) \\\\mathrm{e}^{-\\\\mathrm{i} \\\\mathbf{q} \\\\cdot \\\\mathbf{r}} =\\nA S \\\\mathrm{e}^{\\\\mathrm{i} \\\\mathbf{k}_{out} \\\\cdot \\\\mathbf{r}_{\\\\mathrm{screen}}} F(\\\\mathbf{q})\",\n \"X-ray crystallography\\n\\nwhere q = kout – kin. The measured intensity of the reflection will be square of this amplitude\\nA^{2} S^{2} \\\\left|F(\\\\mathbf{q}) \\\\right|^{2}\",\n \"X-ray crystallography\\n\\nFriedel and Bijvoet mates\",\n \"X-ray crystallography\\n\\nFor every reflection corresponding to a point q in the reciprocal space, there is another reflection of the same intensity at the opposite point -q. This opposite reflection is known as the Friedel mate of the original reflection. This symmetry results from the mathematical fact that the density of electrons f(r) at a position r is always a real number. As noted above, f(r) is the inverse transform of its Fourier transform F(q); however, such an inverse transform is a complex number in general. To ensure that f(r) is real, the Fourier transform F(q) must be such that the Friedel mates F(−q) and F(q) are complex conjugates of one another. Thus, F(−q) has the same magnitude as F(q) but they have the opposite phase, i.e., φ(q) = −φ(q)\\nF(-\\\\mathbf{q}) \\\\left|F(-\\\\mathbf{q}) \\\\right|\\\\mathrm{e}^{\\\\mathrm{i}\\\\phi(-\\\\mathbf{q})} \\n F^{*}(\\\\mathbf{q}) = \\\\left| F(\\\\mathbf{q}) \\\\right|\\\\mathrm{e}^{-\\\\mathrm{i}\\\\phi(\\\\mathbf{q})}\",\n \"X-ray crystallography\\n\\nThe equality of their magnitudes ensures that the Friedel mates have the same intensity |F|2. This symmetry allows one to measure the full Fourier transform from only half the reciprocal space, e.g., by rotating the crystal slightly more than 180° instead of a full 360° revolution. In crystals with significant symmetry, even more reflections may have the same intensity (Bijvoet mates); in such cases, even less of the reciprocal space may need to be measured. In favorable cases of high symmetry, sometimes only 90° or even only 45° of data are required to completely explore the reciprocal space.\",\n \"X-ray crystallography\\n\\nThe Friedel-mate constraint can be derived from the definition of the inverse Fourier transform\\nf(\\\\mathbf{r}) \\\\int \\\\frac{d\\\\mathbf{q}}{\\\\left(2\\\\pi\\\\right)^{3}} F(\\\\mathbf{q}) \\\\mathrm{e}^{\\\\mathrm{i}\\\\mathbf{q}\\\\cdot\\\\mathbf{r}}\",\n \"X-ray crystallography\\n\\n\\\\int \\\\frac{d\\\\mathbf{q}}{\\\\left(2\\\\pi\\\\right)^{3}} \\\\left|F(\\\\mathbf{q}) \\\\right|\\\\mathrm{e}^{\\\\mathrm{i}\\\\phi(\\\\mathbf{q})} \\\\mathrm{e}^{\\\\mathrm{i}\\\\mathbf{q}\\\\cdot\\\\mathbf{r}}\",\n \"X-ray crystallography\\n\\nSince Euler's formula states that eix = cos(x) + i sin(x), the inverse Fourier transform can be separated into a sum of a purely real part and a purely imaginary part\\nf(\\\\mathbf{r}) \\\\int \\\\frac{d\\\\mathbf{q}}{\\\\left(2\\\\pi\\\\right)^{3}} \\\\left|F(\\\\mathbf{q}) \\\\right|\\\\mathrm{e}^{\\\\mathrm{i}\\\\left(\\\\phi+\\\\mathbf{q}\\\\cdot\\\\mathbf{r}\\\\right)}\",\n \"X-ray crystallography\\n\\n\\\\int \\\\frac{d\\\\mathbf{q}}{\\\\left(2\\\\pi\\\\right)^{3}} \\\\left|F(\\\\mathbf{q}) \\\\right|\\n\\\\cos\\\\left(\\\\phi+\\\\mathbf{q}\\\\cdot\\\\mathbf{r}\\\\right) +\\ni \\\\int \\\\frac{d\\\\mathbf{q}}{\\\\left(2\\\\pi\\\\right)^{3}} \\\\left|F(\\\\mathbf{q}) \\\\right|\\n\\\\sin\\\\left(\\\\phi+\\\\mathbf{q}\\\\cdot\\\\mathbf{r}\\\\right) = I_{\\\\mathrm{cos}} + iI_{\\\\mathrm{sin}}\",\n \"X-ray crystallography\\n\\nThe function f(r) is real if and only if the second integral Isin is zero for all values of r. In turn, this is true if and only if the above constraint is satisfied\\nI_{\\\\mathrm{sin}} \\\\int \\\\frac{d\\\\mathbf{q}}{\\\\left(2\\\\pi\\\\right)^{3}} \\\\left|F(\\\\mathbf{q}) \\\\right|\\\\sin\\\\left(\\\\phi+\\\\mathbf{q}\\\\cdot\\\\mathbf{r}\\\\right)\",\n \"X-ray crystallography\\n\\n\\\\int \\\\frac{d\\\\mathbf{q}}{\\\\left(2\\\\pi\\\\right)^{3}} \\\\left|F(\\\\mathbf{-q}) \\\\right|\\n\\\\sin\\\\left(-\\\\phi-\\\\mathbf{q}\\\\cdot\\\\mathbf{r}\\\\right) = -I_{\\\\mathrm{sin}}\",\n \"X-ray crystallography\\n\\nsince Isin −Isin implies that Isin\\n0.\",\n \"X-ray crystallography\\n\\nEwald's sphere\",\n \"X-ray crystallography\\n\\nEach X-ray diffraction image represents only a slice, a spherical slice of reciprocal space, as may be seen by the Ewald sphere construction. Both kout and kin have the same length, due to the elastic scattering, since the wavelength has not changed. Therefore, they may be represented as two radial vectors in a sphere in reciprocal space, which shows the values of q that are sampled in a given diffraction image. Since there is a slight spread in the incoming wavelengths of the incoming X-ray beam, the values of|F(q)|can be measured only for q vectors located between the two spheres corresponding to those radii. Therefore, to obtain a full set of Fourier transform data, it is necessary to rotate the crystal through slightly more than 180°, or sometimes less if sufficient symmetry is present. A full 360° rotation is not needed because of a symmetry intrinsic to the Fourier transforms of real functions (such as the electron density), but \\\"slightly more\\\" than 180° is needed to cover all of reciprocal space within a given resolution because of the curvature of the Ewald sphere.\",\n \"X-ray crystallography\\n\\nIn practice, the crystal is rocked by a small amount (0.25-1°) to incorporate reflections near the boundaries of the spherical Ewald's shells.\",\n \"X-ray crystallography\\n\\nPatterson function\",\n \"X-ray crystallography\\n\\nA well-known result of Fourier transforms is the autocorrelation theorem, which states that the autocorrelation c(r) of a function f(r)\\nc(\\\\mathbf{r}) \\\\int d\\\\mathbf{x} f(\\\\mathbf{x}) f(\\\\mathbf{x} + \\\\mathbf{r}) \\n \\\\int \\\\frac{d\\\\mathbf{q}}{\\\\left(2\\\\pi\\\\right)^{3}} C(\\\\mathbf{q}) e^{i\\\\mathbf{q}\\\\cdot\\\\mathbf{r}}\",\n \"X-ray crystallography\\n\\nhas a Fourier transform C(q) that is the squared magnitude of F(q)\\nC(\\\\mathbf{q}) = \\\\left|F(\\\\mathbf{q}) \\\\right|^{2}\",\n \"X-ray crystallography\\n\\nTherefore, the autocorrelation function c(r) of the electron density (also known as the Patterson function ) can be computed directly from the reflection intensities, without computing the phases. In principle, this could be used to determine the crystal structure directly; however, it is difficult to realize in practice. The autocorrelation function corresponds to the distribution of vectors between atoms in the crystal; thus, a crystal of N atoms in its unit cell may have N(N-1) peaks in its Patterson function. Given the inevitable errors in measuring the intensities, and the mathematical difficulties of reconstructing atomic positions from the interatomic vectors, this technique is rarely used to solve structures, except for the simplest crystals.\",\n \"X-ray crystallography\\n\\nAdvantages of a crystal\",\n \"X-ray crystallography\\n\\nIn principle, an atomic structure could be determined from applying X-ray scattering to non-crystalline samples, even to a single molecule. However, crystals offer a much stronger signal due to their periodicity. A crystalline sample is by definition periodic; a crystal is composed of many unit cells repeated indefinitely in three independent directions. Such periodic systems have a Fourier transform that is concentrated at periodically repeating points in reciprocal space known as Bragg peaks; the Bragg peaks correspond to the reflection spots observed in the diffraction image. Since the amplitude at these reflections grows linearly with the number N of scatterers, the observed intensity of these spots should grow quadratically, like N2. In other words, using a crystal concentrates the weak scattering of the individual unit cells into a much more powerful, coherent reflection that can be observed above the noise. This is an example of constructive interference.\",\n \"X-ray crystallography\\n\\nIn a liquid, powder or amorphous sample, molecules within that sample are in random orientations. Such samples have a continuous Fourier spectrum that uniformly spreads its amplitude thereby reducing the measured signal intensity, as is observed in SAXS. More importantly, the orientational information is lost. Although theoretically possible, it is experimentally difficult to obtain atomic-resolution structures of complicated, asymmetric molecules from such rotationally averaged data. An intermediate case is fiber diffraction in which the subunits are arranged periodically in at least one dimension.\",\n \"X-ray crystallography\\n\\nNobel Prizes for X-ray Crystallography\",\n \"DNA\\n\\nDeoxyribonucleic acid (; DNA) is a molecule that carries the genetic instructions used in the growth, development, functioning and reproduction of all known living organisms and many viruses. DNA and RNA are nucleic acids; alongside proteins and complex carbohydrates (polysaccharides), they are one of the three major types of macromolecule that are essential for all known forms of life. Most DNA molecules consist of two biopolymer strands coiled around each other to form a double helix.\",\n \"DNA\\n\\nThe two DNA strands are known as polynucleotides since they are composed of simpler units called nucleotides. Each nucleotide is composed of a nitrogen-containing nucleobase—either cytosine (C), guanine (G), adenine (A), or thymine (T)—as well as a sugar called deoxyribose and a phosphate group. The nucleotides are joined to one another in a chain by covalent bonds between the sugar of one nucleotide and the phosphate of the next, resulting in an alternating sugar-phosphate backbone. According to base pairing rules (A with T, and C with G), hydrogen bonds bind the nitrogenous bases of the two separate polynucleotide strands to make double-stranded DNA. The total amount of related DNA base pairs on Earth is estimated at 5.0 x 1037, and weighs 50 billion tonnes. In comparison, the total mass of the biosphere has been estimated to be as much as 4 TtC (trillion tons of carbon).\",\n \"DNA\\n\\nDNA stores biological information. The DNA backbone is resistant to cleavage, and both strands of the double-stranded structure store the same biological information. Biological information is replicated as the two strands are separated. A significant portion of DNA (more than 98% for humans) is non-coding, meaning that these sections do not serve as patterns for protein sequences.\",\n \"DNA\\n\\nThe two strands of DNA run in opposite directions to each other and are therefore anti-parallel. Attached to each sugar is one of four types of nucleobases (informally, bases). It is the sequence of these four nucleobases along the backbone that encodes biological information. Under the genetic code, RNA strands are translated to specify the sequence of amino acids within proteins. These RNA strands are initially created using DNA strands as a template in a process called transcription.\",\n \"DNA\\n\\nWithin eukaryotic cells, DNA is organized into long structures called chromosomes. During cell division these chromosomes are duplicated in the process of DNA replication, providing each cell its own complete set of chromosomes. Eukaryotic organisms (animals, plants, fungi, and protists) store most of their DNA inside the cell nucleus and some of their DNA in organelles, such as mitochondria or chloroplasts. In contrast, prokaryotes (bacteria and archaea) store their DNA only in the cytoplasm. Within the eukaryotic chromosomes, chromatin proteins such as histones compact and organize DNA. These compact structures guide the interactions between DNA and other proteins, helping control which parts of the DNA are transcribed.\",\n \"DNA\\n\\nDNA was first isolated by Friedrich Miescher in 1869. Its molecular structure was identified by James Watson and Francis Crick in 1953, whose model-building efforts were guided by X-ray diffraction data acquired by Rosalind Franklin. DNA is used by researchers as a molecular tool to explore physical laws and theories, such as the ergodic theorem and the theory of elasticity. The unique material properties of DNA have made it an attractive molecule for material scientists and engineers interested in micro- and nano-fabrication. Among notable advances in this field are DNA origami and DNA-based hybrid materials.\",\n \"DNA\\n\\nProperties\",\n \"DNA\\n\\nDNA is a long polymer made from repeating units called nucleotides. The structure of DNA is non-static, all species comprises two helical chains each coiled round the same axis, and each with a pitch of 34 ångströms (3.4 nanometres) and a radius of 10 ångströms (1.0 nanometre). According to another study, when measured in a particular solution, the DNA chain measured 22 to 26 ångströms wide (2.2 to 2.6 nanometres), and one nucleotide unit measured 3.3 Å (0.33 nm) long. Although each individual repeating unit is very small, DNA polymers can be very large molecules containing millions of nucleotides. For instance, the DNA in the largest human chromosome, chromosome number 1, consists of approximately 220 million base pairs and would be 85 mm long if straightened.\",\n \"DNA\\n\\nIn living organisms DNA does not usually exist as a single molecule, but instead as a pair of molecules that are held tightly together.Berg J., Tymoczko J. and Stryer L. (2002) Biochemistry. W. H. Freeman and Company ISBN 0-7167-4955-6 These two long strands entwine like vines, in the shape of a double helix. The nucleotide repeats contain both the segment of the backbone of the molecule, which holds the chain together, and a nucleobase, which interacts with the other DNA strand in the helix. A nucleobase linked to a sugar is called a nucleoside and a base linked to a sugar and one or more phosphate groups is called a nucleotide. A polymer comprising multiple linked nucleotides (as in DNA) is called a polynucleotide.\",\n \"DNA\\n\\nThe backbone of the DNA strand is made from alternating phosphate and sugar residues. The sugar in DNA is 2-deoxyribose, which is a pentose (five-carbon) sugar. The sugars are joined together by phosphate groups that form phosphodiester bonds between the third and fifth carbon atoms of adjacent sugar rings. These asymmetric bonds mean a strand of DNA has a direction. In a double helix the direction of the nucleotides in one strand is opposite to their direction in the other strand: the strands are antiparallel. The asymmetric ends of DNA strands are called the 5′ (five prime) and 3′ (three prime) ends, with the 5′ end having a terminal phosphate group and the 3′ end a terminal hydroxyl group. One major difference between DNA and RNA is the sugar, with the 2-deoxyribose in DNA being replaced by the alternative pentose sugar ribose in RNA.\",\n \"DNA\\n\\nThe DNA double helix is stabilized primarily by two forces: hydrogen bonds between nucleotides and base-stacking interactions among aromatic nucleobases. In the aqueous environment of the cell, the conjugated bonds of nucleotide bases align perpendicular to the axis of the DNA molecule, minimizing their interaction with the solvation shell and therefore, the Gibbs free energy. The four bases found in DNA are adenine (abbreviated A), cytosine (C), guanine (G) and thymine (T). These four bases are attached to the sugar/phosphate to form the complete nucleotide, as shown for adenosine monophosphate. Adenine pairs with thymine and guanine pairs with cytosine. It was represented by A-T base pairs and G-C base pairs.\",\n \"DNA\\n\\nNucleobase classification\",\n \"DNA\\n\\nThe nucleobases are classified into two types: the purines, A and G, being fused five- and six-membered heterocyclic compounds, and the pyrimidines, the six-membered rings C and T. A fifth pyrimidine nucleobase, uracil (U), usually takes the place of thymine in RNA and differs from thymine by lacking a methyl group on its ring. In addition to RNA and DNA a large number of artificial nucleic acid analogues have also been created to study the properties of nucleic acids, or for use in biotechnology.\",\n \"DNA\\n\\nUracil is not usually found in DNA, occurring only as a breakdown product of cytosine. However, in a number of bacteriophages – Bacillus subtilis bacteriophages PBS1 and PBS2 and Yersinia bacteriophage piR1-37 – thymine has been replaced by uracil. Another phage - Staphylococcal phage S6 - has been identified with a genome where thymine has been replaced by uracil.\",\n \"DNA\\n\\nBase J (beta-d-glucopyranosyloxymethyluracil), a modified form of uracil, is also found in a number of organisms: the flagellates Diplonema and Euglena, and all the kinetoplastid genera. Biosynthesis of J occurs in two steps: in the first step a specific thymidine in DNA is converted into hydroxymethyldeoxyuridine; in the second HOMedU is glycosylated to form J. Proteins that bind specifically to this base have been identified. These proteins appear to be distant relatives of the Tet1 oncogene that is involved in the pathogenesis of acute myeloid leukemia. J appears to act as a termination signal for RNA polymerase II.\",\n \"DNA\\n\\nGrooves\",\n \"DNA\\n\\nTwin helical strands form the DNA backbone. Another double helix may be found tracing the spaces, or grooves, between the strands. These voids are adjacent to the base pairs and may provide a binding site. As the strands are not symmetrically located with respect to each other, the grooves are unequally sized. One groove, the major groove, is 22 Å wide and the other, the minor groove, is 12 Å wide. The width of the major groove means that the edges of the bases are more accessible in the major groove than in the minor groove. As a result, proteins such as transcription factors that can bind to specific sequences in double-stranded DNA usually make contact with the sides of the bases exposed in the major groove. This situation varies in unusual conformations of DNA within the cell (see below), but the major and minor grooves are always named to reflect the differences in size that would be seen if the DNA is twisted back into the ordinary B form.\",\n \"DNA\\n\\nBase pairing\",\n \"DNA\\n\\nIn a DNA double helix, each type of nucleobase on one strand bonds with just one type of nucleobase on the other strand. This is called complementary base pairing. Here, purines form hydrogen bonds to pyrimidines, with adenine bonding only to thymine in two hydrogen bonds, and cytosine bonding only to guanine in three hydrogen bonds. This arrangement of two nucleotides binding together across the double helix is called a base pair. As hydrogen bonds are not covalent, they can be broken and rejoined relatively easily. The two strands of DNA in a double helix can therefore be pulled apart like a zipper, either by a mechanical force or high temperature. As a result of this complementarity, all the information in the double-stranded sequence of a DNA helix is duplicated on each strand, which is vital in DNA replication. Indeed, this reversible and specific interaction between complementary base pairs is critical for all the functions of DNA in living organisms.\",\n \"DNA\\n\\nTop, a GC base pair with three hydrogen bonds. Bottom, an AT base pair with two hydrogen bonds. Non-covalent hydrogen bonds between the pairs are shown as dashed lines.\\nThe two types of base pairs form different numbers of hydrogen bonds, AT forming two hydrogen bonds, and GC forming three hydrogen bonds (see figures, right).\\nDNA with high GC-content is more stable than DNA with low GC-content.\",\n \"DNA\\n\\nAs noted above, most DNA molecules are actually two polymer strands, bound together in a helical fashion by noncovalent bonds; this double stranded structure (dsDNA) is maintained largely by the intrastrand base stacking interactions, which are strongest for G,C stacks. The two strands can come apart – a process known as melting – to form two single-stranded DNA molecules (ssDNA) molecules. Melting occurs at high temperature, low salt and high pH (low pH also melts DNA, but since DNA is unstable due to acid depurination, low pH is rarely used).\",\n \"DNA\\n\\nThe stability of the dsDNA form depends not only on the GC-content (% G,C basepairs) but also on sequence (since stacking is sequence specific) and also length (longer molecules are more stable). The stability can be measured in various ways; a common way is the \\\"melting temperature\\\", which is the temperature at which 50% of the ds molecules are converted to ss molecules; melting temperature is dependent on ionic strength and the concentration of DNA.\\nAs a result, it is both the percentage of GC base pairs and the overall length of a DNA double helix that determines the strength of the association between the two strands of DNA. Long DNA helices with a high GC-content have stronger-interacting strands, while short helices with high AT content have weaker-interacting strands. In biology, parts of the DNA double helix that need to separate easily, such as the TATAAT Pribnow box in some promoters, tend to have a high AT content, making the strands easier to pull apart.\",\n \"DNA\\n\\nIn the laboratory, the strength of this interaction can be measured by finding the temperature necessary to break the hydrogen bonds, their melting temperature (also called Tm value). When all the base pairs in a DNA double helix melt, the strands separate and exist in solution as two entirely independent molecules. These single-stranded DNA molecules (ssDNA) have no single common shape, but some conformations are more stable than others.\",\n \"DNA\\n\\nSense and antisense\",\n \"DNA\\n\\nA DNA sequence is called \\\"sense\\\" if its sequence is the same as that of a messenger RNA copy that is translated into protein. The sequence on the opposite strand is called the \\\"antisense\\\" sequence. Both sense and antisense sequences can exist on different parts of the same strand of DNA (i.e. both strands can contain both sense and antisense sequences). In both prokaryotes and eukaryotes, antisense RNA sequences are produced, but the functions of these RNAs are not entirely clear. One proposal is that antisense RNAs are involved in regulating gene expression through RNA-RNA base pairing.\",\n \"DNA\\n\\nA few DNA sequences in prokaryotes and eukaryotes, and more in plasmids and viruses, blur the distinction between sense and antisense strands by having overlapping genes. In these cases, some DNA sequences do double duty, encoding one protein when read along one strand, and a second protein when read in the opposite direction along the other strand. In bacteria, this overlap may be involved in the regulation of gene transcription, while in viruses, overlapping genes increase the amount of information that can be encoded within the small viral genome.\",\n \"DNA\\n\\nSupercoiling\",\n \"DNA\\n\\nDNA can be twisted like a rope in a process called DNA supercoiling. With DNA in its \\\"relaxed\\\" state, a strand usually circles the axis of the double helix once every 10.4 base pairs, but if the DNA is twisted the strands become more tightly or more loosely wound. If the DNA is twisted in the direction of the helix, this is positive supercoiling, and the bases are held more tightly together. If they are twisted in the opposite direction, this is negative supercoiling, and the bases come apart more easily. In nature, most DNA has slight negative supercoiling that is introduced by enzymes called topoisomerases. These enzymes are also needed to relieve the twisting stresses introduced into DNA strands during processes such as transcription and DNA replication.\",\n \"DNA\\n\\nAlternative DNA structures\",\n \"DNA\\n\\nDNA exists in many possible conformations that include A-DNA, B-DNA, and Z-DNA forms, although, only B-DNA and Z-DNA have been directly observed in functional organisms. The conformation that DNA adopts depends on the hydration level, DNA sequence, the amount and direction of supercoiling, chemical modifications of the bases, the type and concentration of metal ions, as well as the presence of polyamines in solution.\",\n \"DNA\\n\\nThe first published reports of A-DNA X-ray diffraction patterns—and also B-DNA—used analyses based on Patterson transforms that provided only a limited amount of structural information for oriented fibers of DNA. An alternative analysis was then proposed by Wilkins et al., in 1953, for the in vivo B-DNA X-ray diffraction/scattering patterns of highly hydrated DNA fibers in terms of squares of Bessel functions. In the same journal, James Watson and Francis Crick presented their molecular modeling analysis of the DNA X-ray diffraction patterns to suggest that the structure was a double-helix.\",\n \"DNA\\n\\nAlthough the \\\"B-DNA form\\\" is most common under the conditions found in cells, it is not a well-defined conformation but a family of related DNA conformations that occur at the high hydration levels present in living cells. Their corresponding X-ray diffraction and scattering patterns are characteristic of molecular paracrystals with a significant degree of disorder.\",\n \"DNA\\n\\nCompared to B-DNA, the A-DNA form is a wider right-handed spiral, with a shallow, wide minor groove and a narrower, deeper major groove. The A form occurs under non-physiological conditions in partially dehydrated samples of DNA, while in the cell it may be produced in hybrid pairings of DNA and RNA strands, as well as in enzyme-DNA complexes. Segments of DNA where the bases have been chemically modified by methylation may undergo a larger change in conformation and adopt the Z form. Here, the strands turn about the helical axis in a left-handed spiral, the opposite of the more common B form. These unusual structures can be recognized by specific Z-DNA binding proteins and may be involved in the regulation of transcription.\",\n \"DNA\\n\\nAlternative DNA chemistry\",\n \"DNA\\n\\nFor a number of years exobiologists have proposed the existence of a shadow biosphere, a postulated microbial biosphere of Earth that uses radically different biochemical and molecular processes than currently known life. One of the proposals was the existence of lifeforms that use arsenic instead of phosphorus in DNA. A report in 2010 of the possibility in the bacterium GFAJ-1, was announced, though the research was disputed, and evidence suggests the bacterium actively prevents the incorporation of arsenic into the DNA backbone and other biomolecules.\",\n \"DNA\\n\\nQuadruplex structures\",\n \"DNA\\n\\nAt the ends of the linear chromosomes are specialized regions of DNA called telomeres. The main function of these regions is to allow the cell to replicate chromosome ends using the enzyme telomerase, as the enzymes that normally replicate DNA cannot copy the extreme 3′ ends of chromosomes. These specialized chromosome caps also help protect the DNA ends, and stop the DNA repair systems in the cell from treating them as damage to be corrected. In human cells, telomeres are usually lengths of single-stranded DNA containing several thousand repeats of a simple TTAGGG sequence.\",\n \"DNA\\n\\nThese guanine-rich sequences may stabilize chromosome ends by forming structures of stacked sets of four-base units, rather than the usual base pairs found in other DNA molecules. Here, four guanine bases form a flat plate and these flat four-base units then stack on top of each other, to form a stable G-quadruplex structure. These structures are stabilized by hydrogen bonding between the edges of the bases and chelation of a metal ion in the centre of each four-base unit. Other structures can also be formed, with the central set of four bases coming from either a single strand folded around the bases, or several different parallel strands, each contributing one base to the central structure.\",\n \"DNA\\n\\nIn addition to these stacked structures, telomeres also form large loop structures called telomere loops, or T-loops. Here, the single-stranded DNA curls around in a long circle stabilized by telomere-binding proteins. At the very end of the T-loop, the single-stranded telomere DNA is held onto a region of double-stranded DNA by the telomere strand disrupting the double-helical DNA and base pairing to one of the two strands. This triple-stranded structure is called a displacement loop or D-loop.\",\n \"DNA\\n\\nBranched DNA can form networks containing multiple branches.\",\n \"DNA\\n\\nBranched DNA\",\n \"DNA\\n\\nIn DNA, fraying occurs when non-complementary regions exist at the end of an otherwise complementary double-strand of DNA. However, branched DNA can occur if a third strand of DNA is introduced and contains adjoining regions able to hybridize with the frayed regions of the pre-existing double-strand. Although the simplest example of branched DNA involves only three strands of DNA, complexes involving additional strands and multiple branches are also possible. Branched DNA can be used in nanotechnology to construct geometric shapes, see the section on uses in technology below.\",\n \"DNA\\n\\nChemical modifications and altered DNA packaging\",\n \"DNA\\n\\nStructure of cytosine with and without the 5-methyl group. Deamination converts 5-methylcytosine into thymine.\",\n \"DNA\\n\\nBase modifications and DNA packaging\",\n \"DNA\\n\\nThe expression of genes is influenced by how the DNA is packaged in chromosomes, in a structure called chromatin. Base modifications can be involved in packaging, with regions that have low or no gene expression usually containing high levels of methylation of cytosine bases. DNA packaging and its influence on gene expression can also occur by covalent modifications of the histone protein core around which DNA is wrapped in the chromatin structure or else by remodeling carried out by chromatin remodeling complexes (see Chromatin remodeling). There is, further, crosstalk between DNA methylation and histone modification, so they can coordinately affect chromatin and gene expression.\",\n \"DNA\\n\\nFor one example, cytosine methylation, produces 5-methylcytosine, which is important for X-chromosome inactivation. The average level of methylation varies between organisms – the worm Caenorhabditis elegans lacks cytosine methylation, while vertebrates have higher levels, with up to 1% of their DNA containing 5-methylcytosine. Despite the importance of 5-methylcytosine, it can deaminate to leave a thymine base, so methylated cytosines are particularly prone to mutations. Other base modifications include adenine methylation in bacteria, the presence of 5-hydroxymethylcytosine in the brain, and the glycosylation of uracil to produce the \\\"J-base\\\" in kinetoplastids.\",\n \"DNA\\n\\nDamage\",\n \"DNA\\n\\nDNA can be damaged by many sorts of mutagens, which change the DNA sequence. Mutagens include oxidizing agents, alkylating agents and also high-energy electromagnetic radiation such as ultraviolet light and X-rays. The type of DNA damage produced depends on the type of mutagen. For example, UV light can damage DNA by producing thymine dimers, which are cross-links between pyrimidine bases. On the other hand, oxidants such as free radicals or hydrogen peroxide produce multiple forms of damage, including base modifications, particularly of guanosine, and double-strand breaks. A typical human cell contains about 150,000 bases that have suffered oxidative damage. Of these oxidative lesions, the most dangerous are double-strand breaks, as these are difficult to repair and can produce point mutations, insertions and deletions from the DNA sequence, as well as chromosomal translocations. These mutations can cause cancer. Because of inherent limitations in the DNA repair mechanisms, if humans lived long enough, they would all eventually develop cancer. DNA damages that are naturally occurring, due to normal cellular processes that produce reactive oxygen species, the hydrolytic activities of cellular water, etc., also occur frequently.\",\n \"DNA\\n\\nAlthough most of these damages are repaired, in any cell some DNA damage may remain despite the action of repair processes. These remaining DNA damages accumulate with age in mammalian postmitotic tissues. This accumulation appears to be an important underlying cause of aging.\",\n \"DNA\\n\\nMany mutagens fit into the space between two adjacent base pairs, this is called intercalation. Most intercalators are aromatic and planar molecules; examples include ethidium bromide, acridines, daunomycin, and doxorubicin. For an intercalator to fit between base pairs, the bases must separate, distorting the DNA strands by unwinding of the double helix. This inhibits both transcription and DNA replication, causing toxicity and mutations. As a result, DNA intercalators may be carcinogens, and in the case of thalidomide, a teratogen. Others such as benzo(a)pyrene|benzo[a]pyrene diol epoxide and aflatoxin form DNA adducts that induce errors in replication. Nevertheless, due to their ability to inhibit DNA transcription and replication, other similar toxins are also used in chemotherapy to inhibit rapidly growing cancer cells.\",\n \"DNA\\n\\nBiological functions\",\n \"DNA\\n\\nDNA usually occurs as linear chromosomes in eukaryotes, and circular chromosomes in prokaryotes. The set of chromosomes in a cell makes up its genome; the human genome has approximately 3 billion base pairs of DNA arranged into 46 chromosomes. The information carried by DNA is held in the sequence of pieces of DNA called genes. Transmission of genetic information in genes is achieved via complementary base pairing. For example, in transcription, when a cell uses the information in a gene, the DNA sequence is copied into a complementary RNA sequence through the attraction between the DNA and the correct RNA nucleotides. Usually, this RNA copy is then used to make a matching protein sequence in a process called translation, which depends on the same interaction between RNA nucleotides. In alternative fashion, a cell may simply copy its genetic information in a process called DNA replication. The details of these functions are covered in other articles; here the focus is on the interactions between DNA and other molecules that mediate the function of the genome.\",\n \"DNA\\n\\nGenes and genomes\",\n \"DNA\\n\\nGenomic DNA is tightly and orderly packed in the process called DNA condensation to fit the small available volumes of the cell. In eukaryotes, DNA is located in the cell nucleus, as well as small amounts in mitochondria and chloroplasts. In prokaryotes, the DNA is held within an irregularly shaped body in the cytoplasm called the nucleoid. The genetic information in a genome is held within genes, and the complete set of this information in an organism is called its genotype. A gene is a unit of heredity and is a region of DNA that influences a particular characteristic in an organism. Genes contain an open reading frame that can be transcribed, as well as regulatory sequences such as promoters and enhancers, which control the transcription of the open reading frame.\",\n \"DNA\\n\\nIn many species, only a small fraction of the total sequence of the genome encodes protein. For example, only about 1.5% of the human genome consists of protein-coding exons, with over 50% of human DNA consisting of non-coding repetitive sequences. The reasons for the presence of so much noncoding DNA in eukaryotic genomes and the extraordinary differences in genome size, or C-value, among species represent a long-standing puzzle known as the \\\"C-value enigma\\\". However, some DNA sequences that do not code protein may still encode functional non-coding RNA molecules, which are involved in the regulation of gene expression.\",\n \"DNA\\n\\nSome noncoding DNA sequences play structural roles in chromosomes. Telomeres and centromeres typically contain few genes, but are important for the function and stability of chromosomes. An abundant form of noncoding DNA in humans are pseudogenes, which are copies of genes that have been disabled by mutation. These sequences are usually just molecular fossils, although they can occasionally serve as raw genetic material for the creation of new genes through the process of gene duplication and divergence.\",\n \"DNA\\n\\nTranscription and translation\",\n \"DNA\\n\\nA gene is a sequence of DNA that contains genetic information and can influence the phenotype of an organism. Within a gene, the sequence of bases along a DNA strand defines a messenger RNA sequence, which then defines one or more protein sequences. The relationship between the nucleotide sequences of genes and the amino-acid sequences of proteins is determined by the rules of translation, known collectively as the genetic code. The genetic code consists of three-letter 'words' called codons formed from a sequence of three nucleotides (e.g. ACT, CAG, TTT).\",\n \"DNA\\n\\nIn transcription, the codons of a gene are copied into messenger RNA by RNA polymerase. This RNA copy is then decoded by a ribosome that reads the RNA sequence by base-pairing the messenger RNA to transfer RNA, which carries amino acids. Since there are 4 bases in 3-letter combinations, there are 64 possible codons (43 combinations). These encode the twenty standard amino acids, giving most amino acids more than one possible codon. There are also three 'stop' or 'nonsense' codons signifying the end of the coding region; these are the TAA, TGA, and TAG codons.\",\n \"DNA\\n\\nReplication\",\n \"DNA\\n\\nCell division is essential for an organism to grow, but, when a cell divides, it must replicate the DNA in its genome so that the two daughter cells have the same genetic information as their parent. The double-stranded structure of DNA provides a simple mechanism for DNA replication. Here, the two strands are separated and then each strand's complementary DNA sequence is recreated by an enzyme called DNA polymerase. This enzyme makes the complementary strand by finding the correct base through complementary base pairing, and bonding it onto the original strand. As DNA polymerases can only extend a DNA strand in a 5′ to 3′ direction, different mechanisms are used to copy the antiparallel strands of the double helix. In this way, the base on the old strand dictates which base appears on the new strand, and the cell ends up with a perfect copy of its DNA.\",\n \"DNA\\n\\nExtracellular nucleic acids\",\n \"DNA\\n\\nNaked extracellular DNA (eDNA), most of it released by cell death, is nearly ubiquitous in the environment. Its concentration in soil may be as high as 2 μg/L, and its concentration in natural aquatic environments may be as high at 88 μg/L. Various possible functions have been proposed for eDNA: it may be involved in horizontal gene transfer; it may provide nutrients; and it may act as a buffer to recruit or titrate ions or antibiotics. Extracellular DNA acts as a functional extracellular matrix component in the biofilms of a number of bacterial species. It may act as a recognition factor to regulate the attachment and dispersal of specific cell types in the biofilm; it may contribute to biofilm formation; and it may contribute to the biofilm's physical strength and resistance to biological stress.\",\n \"DNA\\n\\nInteractions with proteins\",\n \"DNA\\n\\nAll the functions of DNA depend on interactions with proteins. These protein interactions can be non-specific, or the protein can bind specifically to a single DNA sequence. Enzymes can also bind to DNA and of these, the polymerases that copy the DNA base sequence in transcription and DNA replication are particularly important.\",\n \"DNA\\n\\nDNA-binding proteins\",\n \"DNA\\n\\nInteraction of DNA (shown in orange) with histones (shown in blue). These proteins' basic amino acids bind to the acidic phosphate groups on DNA.\",\n \"DNA\\n\\nStructural proteins that bind DNA are well-understood examples of non-specific DNA-protein interactions. Within chromosomes, DNA is held in complexes with structural proteins. These proteins organize the DNA into a compact structure called chromatin. In eukaryotes this structure involves DNA binding to a complex of small basic proteins called histones, while in prokaryotes multiple types of proteins are involved. The histones form a disk-shaped complex called a nucleosome, which contains two complete turns of double-stranded DNA wrapped around its surface. These non-specific interactions are formed through basic residues in the histones making ionic bonds to the acidic sugar-phosphate backbone of the DNA, and are therefore largely independent of the base sequence. Chemical modifications of these basic amino acid residues include methylation, phosphorylation and acetylation. These chemical changes alter the strength of the interaction between the DNA and the histones, making the DNA more or less accessible to transcription factors and changing the rate of transcription. Other non-specific DNA-binding proteins in chromatin include the high-mobility group proteins, which bind to bent or distorted DNA. These proteins are important in bending arrays of nucleosomes and arranging them into the larger structures that make up chromosomes.\",\n \"DNA\\n\\nA distinct group of DNA-binding proteins are the DNA-binding proteins that specifically bind single-stranded DNA. In humans, replication protein A is the best-understood member of this family and is used in processes where the double helix is separated, including DNA replication, recombination and DNA repair. These binding proteins seem to stabilize single-stranded DNA and protect it from forming stem-loops or being degraded by nucleases.\",\n \"DNA\\n\\nIn contrast, other proteins have evolved to bind to particular DNA sequences. The most intensively studied of these are the various transcription factors, which are proteins that regulate transcription. Each transcription factor binds to one particular set of DNA sequences and activates or inhibits the transcription of genes that have these sequences close to their promoters. The transcription factors do this in two ways. Firstly, they can bind the RNA polymerase responsible for transcription, either directly or through other mediator proteins; this locates the polymerase at the promoter and allows it to begin transcription. Alternatively, transcription factors can bind enzymes that modify the histones at the promoter. This changes the accessibility of the DNA template to the polymerase.\",\n \"DNA\\n\\nAs these DNA targets can occur throughout an organism's genome, changes in the activity of one type of transcription factor can affect thousands of genes. Consequently, these proteins are often the targets of the signal transduction processes that control responses to environmental changes or cellular differentiation and development. The specificity of these transcription factors' interactions with DNA come from the proteins making multiple contacts to the edges of the DNA bases, allowing them to \\\"read\\\" the DNA sequence. Most of these base-interactions are made in the major groove, where the bases are most accessible.\",\n \"DNA\\n\\nDNA-modifying enzymes\",\n \"DNA\\n\\nNucleases and ligases\",\n \"DNA\\n\\nNucleases are enzymes that cut DNA strands by catalyzing the hydrolysis of the phosphodiester bonds. Nucleases that hydrolyse nucleotides from the ends of DNA strands are called exonucleases, while endonucleases cut within strands. The most frequently used nucleases in molecular biology are the restriction endonucleases, which cut DNA at specific sequences. For instance, the EcoRV enzyme shown to the left recognizes the 6-base sequence 5′-GATATC-3′ and makes a cut at the vertical line. In nature, these enzymes protect bacteria against phage infection by digesting the phage DNA when it enters the bacterial cell, acting as part of the restriction modification system. In technology, these sequence-specific nucleases are used in molecular cloning and DNA fingerprinting.\",\n \"DNA\\n\\nEnzymes called DNA ligases can rejoin cut or broken DNA strands. Ligases are particularly important in lagging strand DNA replication, as they join together the short segments of DNA produced at the replication fork into a complete copy of the DNA template. They are also used in DNA repair and genetic recombination.\",\n \"DNA\\n\\nTopoisomerases and helicases\",\n \"DNA\\n\\nTopoisomerases are enzymes with both nuclease and ligase activity. These proteins change the amount of supercoiling in DNA. Some of these enzymes work by cutting the DNA helix and allowing one section to rotate, thereby reducing its level of supercoiling; the enzyme then seals the DNA break. Other types of these enzymes are capable of cutting one DNA helix and then passing a second strand of DNA through this break, before rejoining the helix. Topoisomerases are required for many processes involving DNA, such as DNA replication and transcription.\",\n \"DNA\\n\\nHelicases are proteins that are a type of molecular motor. They use the chemical energy in nucleoside triphosphates, predominantly ATP, to break hydrogen bonds between bases and unwind the DNA double helix into single strands. These enzymes are essential for most processes where enzymes need to access the DNA bases.\",\n \"DNA\\n\\nPolymerases\",\n \"DNA\\n\\nPolymerases are enzymes that synthesize polynucleotide chains from nucleoside triphosphates. The sequence of their products are created based on existing polynucleotide chains—which are called templates. These enzymes function by repeatedly adding a nucleotide to the 3′ hydroxyl group at the end of the growing polynucleotide chain. As a consequence, all polymerases work in a 5′ to 3′ direction. In the active site of these enzymes, the incoming nucleoside triphosphate base-pairs to the template: this allows polymerases to accurately synthesize the complementary strand of their template. Polymerases are classified according to the type of template that they use.\",\n \"DNA\\n\\nIn DNA replication, DNA-dependent DNA polymerases make copies of DNA polynucleotide chains. In order to preserve biological information, it is essential that the sequence of bases in each copy are precisely complementary to the sequence of bases in the template strand. Many DNA polymerases have a proofreading activity. Here, the polymerase recognizes the occasional mistakes in the synthesis reaction by the lack of base pairing between the mismatched nucleotides. If a mismatch is detected, a 3′ to 5′ exonuclease activity is activated and the incorrect base removed. In most organisms, DNA polymerases function in a large complex called the replisome that contains multiple accessory subunits, such as the DNA clamp or helicases.\",\n \"DNA\\n\\nRNA-dependent DNA polymerases are a specialized class of polymerases that copy the sequence of an RNA strand into DNA. They include reverse transcriptase, which is a viral enzyme involved in the infection of cells by retroviruses, and telomerase, which is required for the replication of telomeres. Telomerase is an unusual polymerase because it contains its own RNA template as part of its structure.\",\n \"DNA\\n\\nTranscription is carried out by a DNA-dependent RNA polymerase that copies the sequence of a DNA strand into RNA. To begin transcribing a gene, the RNA polymerase binds to a sequence of DNA called a promoter and separates the DNA strands. It then copies the gene sequence into a messenger RNA transcript until it reaches a region of DNA called the terminator, where it halts and detaches from the DNA. As with human DNA-dependent DNA polymerases, RNA polymerase II, the enzyme that transcribes most of the genes in the human genome, operates as part of a large protein complex with multiple regulatory and accessory subunits.\",\n \"DNA\\n\\nGenetic recombination\",\n \"DNA\\n\\nStructure of the Holliday junction intermediate in genetic recombination. The four separate DNA strands are coloured red, blue, green and yellow.\",\n \"DNA\\n\\nA DNA helix usually does not interact with other segments of DNA, and in human cells the different chromosomes even occupy separate areas in the nucleus called \\\"chromosome territories\\\". This physical separation of different chromosomes is important for the ability of DNA to function as a stable repository for information, as one of the few times chromosomes interact is in chromosomal crossover which occurs during sexual reproduction, when genetic recombination occurs. Chromosomal crossover is when two DNA helices break, swap a section and then rejoin.\",\n \"DNA\\n\\nRecombination allows chromosomes to exchange genetic information and produces new combinations of genes, which increases the efficiency of natural selection and can be important in the rapid evolution of new proteins. Genetic recombination can also be involved in DNA repair, particularly in the cell's response to double-strand breaks.\",\n \"DNA\\n\\nThe most common form of chromosomal crossover is homologous recombination, where the two chromosomes involved share very similar sequences. Non-homologous recombination can be damaging to cells, as it can produce chromosomal translocations and genetic abnormalities. The recombination reaction is catalyzed by enzymes known as recombinases, such as RAD51. The first step in recombination is a double-stranded break caused by either an endonuclease or damage to the DNA. A series of steps catalyzed in part by the recombinase then leads to joining of the two helices by at least one Holliday junction, in which a segment of a single strand in each helix is annealed to the complementary strand in the other helix. The Holliday junction is a tetrahedral junction structure that can be moved along the pair of chromosomes, swapping one strand for another. The recombination reaction is then halted by cleavage of the junction and re-ligation of the released DNA.\",\n \"DNA\\n\\nEvolution\",\n \"DNA\\n\\nDNA contains the genetic information that allows all modern living things to function, grow and reproduce. However, it is unclear how long in the 4-billion-year history of life DNA has performed this function, as it has been proposed that the earliest forms of life may have used RNA as their genetic material. RNA may have acted as the central part of early cell metabolism as it can both transmit genetic information and carry out catalysis as part of ribozymes. This ancient RNA world where nucleic acid would have been used for both catalysis and genetics may have influenced the evolution of the current genetic code based on four nucleotide bases. This would occur, since the number of different bases in such an organism is a trade-off between a small number of bases increasing replication accuracy and a large number of bases increasing the catalytic efficiency of ribozymes. However, there is no direct evidence of ancient genetic systems, as recovery of DNA from most fossils is impossible because DNA survives in the environment for less than one million years, and slowly degrades into short fragments in solution.\",\n \"DNA\\n\\nClaims for older DNA have been made, most notably a report of the isolation of a viable bacterium from a salt crystal 250 million years old, but these claims are controversial.\",\n \"DNA\\n\\nBuilding blocks of DNA (adenine, guanine and related organic molecules) may have been formed extraterrestrially in outer space. Complex DNA and RNA organic compounds of life, including uracil, cytosine and thymine, have also been formed in the laboratory under conditions mimicking those found in outer space, using starting chemicals, such as pyrimidine, found in meteorites. Pyrimidine, like polycyclic aromatic hydrocarbons (PAHs), the most carbon-rich chemical found in the universe, may have been formed in red giants or in interstellar dust and gas clouds.\",\n \"DNA\\n\\nUses in technology\",\n \"DNA\\n\\nGenetic engineering\",\n \"DNA\\n\\nMethods have been developed to purify DNA from organisms, such as phenol-chloroform extraction, and to manipulate it in the laboratory, such as restriction digests and the polymerase chain reaction. Modern biology and biochemistry make intensive use of these techniques in recombinant DNA technology. Recombinant DNA is a man-made DNA sequence that has been assembled from other DNA sequences. They can be transformed into organisms in the form of plasmids or in the appropriate format, by using a viral vector. The genetically modified organisms produced can be used to produce products such as recombinant proteins, used in medical research, or be grown in agriculture.\",\n \"DNA\\n\\nDNA profiling\",\n \"DNA\\n\\nForensic scientists can use DNA in blood, semen, skin, saliva or hair found at a crime scene to identify a matching DNA of an individual, such as a perpetrator. This process is formally termed DNA profiling, but may also be called \\\"genetic fingerprinting\\\". In DNA profiling, the lengths of variable sections of repetitive DNA, such as short tandem repeats and minisatellites, are compared between people. This method is usually an extremely reliable technique for identifying a matching DNA. However, identification can be complicated if the scene is contaminated with DNA from several people. DNA profiling was developed in 1984 by British geneticist Sir Alec Jeffreys, and first used in forensic science to convict Colin Pitchfork in the 1988 Enderby murders case.\",\n \"DNA\\n\\nThe development of forensic science, and the ability to now obtain genetic matching on minute samples of blood, skin, saliva or hair has led to a re-examination of a number of cases. Evidence can now be uncovered that was not scientifically possible at the time of the original examination. Combined with the removal of the double jeopardy law in some places, this can allow cases to be reopened where previous trials have failed to produce sufficient evidence to convince a jury. People charged with serious crimes may be required to provide a sample of DNA for matching purposes. The most obvious defence to DNA matches obtained forensically is to claim that cross-contamination of evidence has taken place. This has resulted in meticulous strict handling procedures with new cases of serious crime.\\nDNA profiling is also used to identify victims of mass casualty incidents. As well as positively identifying bodies or body parts in serious accidents, DNA profiling is being successfully used to identify individual victims in mass war graves – matching to family members.\",\n \"DNA\\n\\nDNA profiling is also used in DNA paternity testing in order to determine if someone is the biologicalparent or grandparent of a child with the probability of parentage is typically 99.99% when the alleged parent is biologically related to the child. Normal DNA sequencing methods happen after birth but there are new methods to test paternity while the mother is still pregnant.\",\n \"DNA\\n\\nDNA enzymes or catalytic DNA\",\n \"DNA\\n\\nDeoxyribozymes, also called DNAzymes or catalytic DNA are first discovered in 1994. They are mostly single stranded DNA sequences isolated from a large pool of random DNA sequences through a combinatorial approach called in vitro selection or SELEX. DNAzymes catalyze variety of chemical reactions including RNA/DNA cleavage, RNA/DNA ligation, amino acids phosphorylation/dephosphorylation, carbon-carbon bond formation, and etc. DNAzymes can enhance catalytic rate of chemical reactions up to 100,000,000,000-fold over the uncatalyzed reaction. The most extensively studied class of DNAzymes are RNA-cleaving DNAzymes which have been used in detection of different metal ions and designing therapeutic agents. Several metal-specific DNAzymes have been reported including the GR-5 DNAzyme (lead-specific), the CA1-3 DNAzymes (copper-specific), the 39E DNAzyme (uranyl-specific) and the NaA43 DNAzyme (sodium-specific). The NaA43 DNAzyme, which is reported to be more than 10,000-fold selective for sodium over other metal ions, was used to make a real-time sodium sensor in living cells.\",\n \"DNA\\n\\nBioinformatics\",\n \"DNA\\n\\nBioinformatics involves the development of techniques to store, data mine, search and manipulate biological data, including DNA nucleic acid sequence data. These have led to widely applied advances in computer science, especially string searching algorithms, machine learning and database theory. String searching or matching algorithms, which find an occurrence of a sequence of letters inside a larger sequence of letters, were developed to search for specific sequences of nucleotides. The DNA sequence may be aligned with other DNA sequences to identify homologous sequences and locate the specific mutations that make them distinct. These techniques, especially multiple sequence alignment, are used in studying phylogenetic relationships and protein function. Data sets representing entire genomes' worth of DNA sequences, such as those produced by the Human Genome Project, are difficult to use without the annotations that identify the locations of genes and regulatory elements on each chromosome. Regions of DNA sequence that have the characteristic patterns associated with protein- or RNA-coding genes can be identified by gene finding algorithms, which allow researchers to predict the presence of particular gene products and their possible functions in an organism even before they have been isolated experimentally.\",\n \"DNA\\n\\nEntire genomes may also be compared, which can shed light on the evolutionary history of particular organism and permit the examination of complex evolutionary events.\",\n \"DNA\\n\\nDNA nanotechnology\",\n \"DNA\\n\\nDNA nanotechnology uses the unique molecular recognition properties of DNA and other nucleic acids to create self-assembling branched DNA complexes with useful properties. DNA is thus used as a structural material rather than as a carrier of biological information. This has led to the creation of two-dimensional periodic lattices (both tile-based and using the \\\"DNA origami\\\" method) as well as three-dimensional structures in the shapes of polyhedra. Nanomechanical devices and algorithmic self-assembly have also been demonstrated, and these DNA structures have been used to template the arrangement of other molecules such as gold nanoparticles and streptavidin proteins.\",\n \"DNA\\n\\nHistory and anthropology\",\n \"DNA\\n\\nBecause DNA collects mutations over time, which are then inherited, it contains historical information, and, by comparing DNA sequences, geneticists can infer the evolutionary history of organisms, their phylogeny. This field of phylogenetics is a powerful tool in evolutionary biology. If DNA sequences within a species are compared, population geneticists can learn the history of particular populations. This can be used in studies ranging from ecological genetics to anthropology; For example, DNA evidence is being used to try to identify the Ten Lost Tribes of Israel.\",\n \"DNA\\n\\nInformation storage\",\n \"DNA\\n\\nIn a paper published in Nature in January 2013, scientists from the European Bioinformatics Institute and Agilent Technologies proposed a mechanism to use DNA's ability to code information as a means of digital data storage. The group was able to encode 739 kilobytes of data into DNA code, synthesize the actual DNA, then sequence the DNA and decode the information back to its original form, with a reported 100% accuracy. The encoded information consisted of text files and audio files. A prior experiment was published in August 2012. It was conducted by researchers at Harvard University, where the text of a 54,000-word book was encoded in DNA.\",\n \"DNA\\n\\nHistory of DNA research\",\n \"DNA\\n\\nDNA was first isolated by the Swiss physician Friedrich Miescher who, in 1869, discovered a microscopic substance in the pus of discarded surgical bandages. As it resided in the nuclei of cells, he called it \\\"nuclein\\\". In 1878, Albrecht Kossel isolated the non-protein component of \\\"nuclein\\\", nucleic acid, and later isolated its five primary nucleobases. In 1919, Phoebus Levene identified the base, sugar and phosphate nucleotide unit. Levene suggested that DNA consisted of a string of nucleotide units linked together through the phosphate groups. Levene thought the chain was short and the bases repeated in a fixed order. In 1937, William Astbury produced the first X-ray diffraction patterns that showed that DNA had a regular structure.\",\n \"DNA\\n\\nIn 1927, Nikolai Koltsov proposed that inherited traits would be inherited via a \\\"giant hereditary molecule\\\" made up of \\\"two mirror strands that would replicate in a semi-conservative fashion using each strand as a template\\\". In 1928, Frederick Griffith in his experiment discovered that traits of the \\\"smooth\\\" form of Pneumococcus could be transferred to the \\\"rough\\\" form of the same bacteria by mixing killed \\\"smooth\\\" bacteria with the live \\\"rough\\\" form. This system provided the first clear suggestion that DNA carries genetic information—the Avery–MacLeod–McCarty experiment—when Oswald Avery, along with coworkers Colin MacLeod and Maclyn McCarty, identified DNA as the transforming principle in 1943. DNA's role in heredity was confirmed in 1952, when Alfred Hershey and Martha Chase in the Hershey–Chase experiment showed that DNA is the genetic material of the T2 phage.\",\n \"DNA\\n\\nIn 1953, James Watson and Francis Crick suggested what is now accepted as the first correct double-helix model of DNA structure in the journal Nature. Their double-helix, molecular model of DNA was then based on a single X-ray diffraction image (labeled as \\\"Photo 51\\\") taken by Rosalind Franklin and Raymond Gosling in May 1952, as well as the information that the DNA bases are paired.\",\n \"DNA\\n\\nExperimental evidence supporting the Watson and Crick model was published in a series of five articles in the same issue of Nature.Nature Archives [http://www.nature.com/nature/dna50/archive.html Double Helix of DNA: 50 Years] Of these, Franklin and Gosling's paper was the first publication of their own X-ray diffraction data and original analysis method that partially supported the Watson and Crick model; this issue also contained an article on DNA structure by Maurice Wilkins and two of his colleagues, whose analysis and in vivo B-DNA X-ray patterns also supported the presence in vivo of the double-helical DNA configurations as proposed by Crick and Watson for their double-helix molecular model of DNA in the previous two pages of Nature. In 1962, after Franklin's death, Watson, Crick, and Wilkins jointly received the Nobel Prize in Physiology or Medicine. Nobel Prizes are awarded only to living recipients. A debate continues about who should receive credit for the discovery.\",\n \"DNA\\n\\nIn an influential presentation in 1957, Crick laid out the central dogma of molecular biology, which foretold the relationship between DNA, RNA, and proteins, and articulated the \\\"adaptor hypothesis\\\". Final confirmation of the replication mechanism that was implied by the double-helical structure followed in 1958 through the Meselson–Stahl experiment. Further work by Crick and coworkers showed that the genetic code was based on non-overlapping triplets of bases, called codons, allowing Har Gobind Khorana, Robert W. Holley and Marshall Warren Nirenberg to decipher the genetic code. These findings represent the birth of molecular biology.\",\n \"Francis Crick\\n\\nFrancis Harry Compton Crick (8 June 1916 – 28 July 2004) was a British molecular biologist, biophysicist, and neuroscientist, most noted for being a co-discoverer of the structure of the DNA molecule in 1953 with James Watson. Together with Watson and Maurice Wilkins, he was jointly awarded the 1962 Nobel Prize in Physiology or Medicine \\\"for their discoveries concerning the molecular structure of nucleic acids and its significance for information transfer in living material\\\".\",\n \"Francis Crick\\n\\nCrick was an important theoretical molecular biologist and played a crucial role in research related to revealing the genetic code. He is widely known for use of the term \\\"central dogma\\\" to summarize the idea that genetic information flow in cells is essentially one-way, from DNA to RNA to protein.\",\n \"Francis Crick\\n\\nDuring the remainder of his career, he held the post of J.W. Kieckhefer Distinguished Research Professor at the Salk Institute for Biological Studies in La Jolla, California. His later research centered on theoretical neurobiology and attempts to advance the scientific study of human consciousness. He remained in this post until his death; \\\"he was editing a manuscript on his death bed, a scientist until the bitter end\\\" according to Christof Koch.\",\n \"Francis Crick\\n\\nEarly life and education\",\n \"Francis Crick\\n\\nCrick was the first son of Harry Crick (1887–1948) and Annie Elizabeth Crick (née Wilkins; 1879–1955). He was born and raised in Weston Favell, then a small village near the English town of Northampton, in which Crick’s father and uncle ran the family’s boot and shoe factory. His grandfather, Walter Drawbridge Crick (1857–1903), an amateur naturalist, wrote a survey of local foraminifera (single-celled protists with shells), corresponded with Charles Darwin, and had two gastropods (snails or slugs) named after him.\",\n \"Francis Crick\\n\\nAt an early age, Francis was attracted to science and what he could learn about it from books. As a child, he was taken to church by his parents. But by about age 12, he said he did not want to go anymore, as he preferred a scientific search for answers over religious belief.\",\n \"Francis Crick\\n\\nWalter Crick, his uncle, lived in a small house on the south side of Abington Avenue; he had a shed at the bottom of his little garden where he taught Crick to blow glass, do chemical experiments and to make photographic prints. When he was eight or nine he transferred to the most junior form of the Northampton Grammar School, on the Billing Road. This was about from his home so he could walk there and back, by Park Avenue South and Abington Park Crescent, but he more often went by bus or, later, by bicycle. The teacher – a Miss Holding – was an inspired teacher and made everything interesting. The teaching in the higher forms was satisfactory, but not as stimulating. After the age of 14, he was educated at Mill Hill School in London (on scholarship), where he studied mathematics, physics, and chemistry with his best friend John Shilston. He shared the Walter Knox Prize for Chemistry on Mill Hill School's Foundation Day, Friday, 7 July 1933. He declared that his success was inspired by the quality of teaching he received whilst a pupil at Mill Hill.\",\n \"Francis Crick\\n\\nAt the age of 21, Crick earned a Bachelor of Science degree in physics from University College London. Crick had failed to gain a place at a Cambridge college, probably through failing their requirement for Latin. Crick began his PhD at UCL but was interrupted by WWII. He later became a PhD student and Honorary Fellow of Gonville and Caius College, Cambridge and mainly worked at the Cavendish Laboratory and the Medical Research Council (MRC) Laboratory of Molecular Biology in Cambridge. He was also an Honorary Fellow of Churchill College, Cambridge and of University College, London.\",\n \"Francis Crick\\n\\nCrick began a Ph.D. research project on measuring viscosity of water at high temperatures (which he later described as \\\"the dullest problem imaginable\\\" ) in the laboratory of physicist Edward Neville da Costa Andrade at University College, London, but with the outbreak of World War II (in particular, an incident during the Battle of Britain when a bomb fell through the roof of the laboratory and destroyed his experimental apparatus), Crick was deflected from a possible career in physics. During his second year as a PhD student, however, he was awarded the Carey Foster Research Prize, a great honour. He did postdoctoral work at the Polytechnic Institute of Brooklyn.\",\n \"Francis Crick\\n\\nDuring World War II, he worked for the Admiralty Research Laboratory, from which emerged a group of many notable scientists, including David Bates, Robert Boyd, George Deacon, John Gunn, Harrie Massey, and Nevill Mott; he worked on the design of magnetic and acoustic mines, and was instrumental in designing a new mine that was effective against German minesweepers.\",\n \"Francis Crick\\n\\nPost-World War II life and work\",\n \"Francis Crick\\n\\nIn 1947, aged 31, Crick began studying biology and became part of an important migration of physical scientists into biology research. This migration was made possible by the newly won influence of physicists such as Sir John Randall, who had helped win the war with inventions such as radar. Crick had to adjust from the \\\"elegance and deep simplicity\\\" of physics to the \\\"elaborate chemical mechanisms that natural selection had evolved over billions of years.\\\" He described this transition as, \\\"almost as if one had to be born again.\\\" According to Crick, the experience of learning physics had taught him something important—hubris—and the conviction that since physics was already a success, great advances should also be possible in other sciences such as biology. Crick felt that this attitude encouraged him to be more daring than typical biologists who tended to concern themselves with the daunting problems of biology and not the past successes of physics.\",\n \"Francis Crick\\n\\nFor the better part of two years, Crick worked on the physical properties of cytoplasm at Cambridge's Strangeways Research Laboratory, headed by Honor Bridget Fell, with a Medical Research Council studentship, until he joined Max Perutz and John Kendrew at the Cavendish Laboratory. The Cavendish Laboratory at Cambridge was under the general direction of Sir Lawrence Bragg, who had won the Nobel Prize in 1915 at the age of 25. Bragg was influential in the effort to beat a leading American chemist, Linus Pauling, to the discovery of DNA's structure (after having been pipped at the post by Pauling's success in determining the alpha helix structure of proteins). At the same time Bragg's Cavendish Laboratory was also effectively competing with King's College London, whose Biophysics department was under the direction of Sir John Randall. (Randall had refused Crick's application to work at King's College.) Francis Crick and Maurice Wilkins of King's College were personal friends, which influenced subsequent scientific events as much as the close friendship between Crick and James Watson. Crick and Wilkins first met at King's College and not, as erroneously recorded by two authors, at the Admiralty during World War II.\",\n \"Francis Crick\\n\\nHe married twice, fathered three children and was the grandfather of six grandchildren; his brother Anthony (born in 1918) predeceased him in 1966.\",\n \"Francis Crick\\n\\nSpouses:\\n* Ruth Doreen Crick, Dodd (b. 1913, m. 18 February 1940 – 8 May 1947. d. 2011), became Mrs. James Stewart Potter\\n*Odile Crick, Speed (b. 11 August 1920, m. 14 August 1949 – 28 July 2004, d. 5 July 2007)\",\n \"Francis Crick\\n\\nChildren:\\n* Michael Francis Compton (b. 25 November 1940) [by Doreen Crick]\\n* Gabrielle Anne (b. 15 July 1951) [by Odile Crick]\\n* Jacqueline Marie-Therese [later Nichols] (b. 12 March 1954, d. 28 February 2011) [by Odile Crick];\",\n \"Francis Crick\\n\\nGrandchildren\",\n \"Francis Crick\\n\\n* Alexander (b. March 1974)\\n* Kindra (b. May 1976)\\n* Camberley (b. June 1978)\\n* Francis Henry Riley (b. February 1981), Michael & Barbara Crick's four children\\n* Mark & Nicholas, the late Jacqueline and Christopher Nichols' children.\",\n \"Francis Crick\\n\\nDeath\",\n \"Francis Crick\\n\\nCrick died of colon cancer on the morning of 28 July 2004 at the University of California, San Diego (UCSD) Thornton Hospital in La Jolla; he was cremated and his ashes were scattered into the Pacific Ocean. A public memorial was held on 27 September 2004 at the Salk Institute, La Jolla, near San Diego, California; guest speakers included James Watson, Sydney Brenner, Alex Rich, Seymour Benzer, Aaron Klug, Christof Koch, Pat Churchland, Vilayanur Ramachandran, Tomaso Poggio, Leslie Orgel, Terry Sejnowski, his son Michael Crick, and his youngest daughter Jacqueline Nichols. A private memorial for family and colleagues was held on 3 August 2004.\",\n \"Francis Crick\\n\\nResearch\",\n \"Francis Crick\\n\\nCrick was interested in two fundamental unsolved problems of biology: how molecules make the transition from the non-living to the living, and how the brain makes a conscious mind. He realized that his background made him more qualified for research on the first topic and the field of biophysics. It was at this time of Crick’s transition from physics to biology that he was influenced by both Linus Pauling and Erwin Schrödinger.Crick (1990) p. 18 It was clear in theory that covalent bonds in biological molecules could provide the structural stability needed to hold genetic information in cells. It only remained as an exercise of experimental biology to discover exactly which molecule was the genetic molecule. In Crick’s view, Charles Darwin’s theory of evolution by natural selection, Gregor Mendel’s genetics and knowledge of the molecular basis of genetics, when combined, revealed the secret of life. Crick had the very optimistic view that life would very soon be created in a test tube. However, some people (such as fellow researcher and colleague Esther Lederberg) thought that Crick was unduly optimistic\",\n \"Francis Crick\\n\\nIt was clear that some macromolecule such as a protein was likely to be the genetic molecule. However, it was well known that proteins are structural and functional macromolecules, some of which carry out enzymatic reactions of cells. In the 1940s, some evidence had been found pointing to another macromolecule, DNA, the other major component of chromosomes, as a candidate genetic molecule. In the 1944 Avery-MacLeod-McCarty experiment, Oswald Avery and his collaborators showed that a heritable phenotypic difference could be caused in bacteria by providing them with a particular DNA molecule.\",\n \"Francis Crick\\n\\nHowever, other evidence was interpreted as suggesting that DNA was structurally uninteresting and possibly just a molecular scaffold for the apparently more interesting protein molecules. Crick was in the right place, in the right frame of mind, at the right time (1949), to join Max Perutz’s project at the University of Cambridge, and he began to work on the X-ray crystallography of proteins. X-ray crystallography theoretically offered the opportunity to reveal the molecular structure of large molecules like proteins and DNA, but there were serious technical problems then preventing X-ray crystallography from being applicable to such large molecules.\",\n \"Francis Crick\\n\\n1949–1950\",\n \"Francis Crick\\n\\nCrick taught himself the mathematical theory of X-ray crystallography.Crick (1990) p. 46: \\\"..there was no alternative but to teach X-ray diffraction to myself.\\\" During the period of Crick's study of X-ray diffraction, researchers in the Cambridge lab were attempting to determine the most stable helical conformation of amino acid chains in proteins (the Alpha helix). Linus Pauling was the first to identify the 3.6 amino acids per helix turn ratio of the Alpha helix. Crick was witness to the kinds of errors that his co-workers made in their failed attempts to make a correct molecular model of the α helix; these turned out to be important lessons that could be applied, in the future, to the helical structure of DNA. For example, he learned the importance of the structural rigidity that double bonds confer on molecular structures which is relevant both to peptide bonds in proteins and the structure of nucleotides in DNA.\",\n \"Francis Crick\\n\\n1951–1953: DNA structure\",\n \"Francis Crick\\n\\nIn 1951 and 1952, together with William Cochran and Vladimir Vand, Crick assisted in the development of a mathematical theory of X-ray diffraction by a helical molecule. This theoretical result matched well with X-ray data for proteins that contain sequences of amino acids in the Alpha helix conformation. Helical diffraction theory turned out to also be useful for understanding the structure of DNA.\",\n \"Francis Crick\\n\\nLate in 1951, Crick started working with James Watson at Cavendish Laboratory at the University of Cambridge, England. Using \\\"Photo 51\\\" (the X-ray diffraction results of Rosalind Franklin and her graduate student Raymond Gosling of King's College London, given to them by Gosling and Franklin's colleague Maurice Wilkins), Watson and Crick together developed a model for a helical structure of DNA, which they published in 1953. For this and subsequent work they were jointly awarded the Nobel Prize in Physiology or Medicine in 1962 with Maurice Wilkins.\",\n \"Francis Crick\\n\\nWhen James Watson came to Cambridge, Crick was a 35-year-old graduate student (due to his work during WWII) and Watson was only 23, but he already had a Ph.D. They shared an interest in the fundamental problem of learning how genetic information might be stored in molecular form. Watson and Crick talked endlessly about DNA and the idea that it might be possible to guess a good molecular model of its structure. A key piece of experimentally-derived information came from X-ray diffraction images that had been obtained by Maurice Wilkins, Rosalind Franklin, and their research student, Raymond Gosling. In November 1951, Wilkins came to Cambridge and shared his data with Watson and Crick. Alexander Stokes (another expert in helical diffraction theory) and Wilkins (both at King's College) had reached the conclusion that X-ray diffraction data for DNA indicated that the molecule had a helical structure—but Franklin vehemently disputed this conclusion. Stimulated by their discussions with Wilkins and what Watson learned by attending a talk given by Franklin about her work on DNA, Crick and Watson produced and showed off an erroneous first model of DNA.\",\n \"Francis Crick\\n\\nTheir hurry to produce a model of DNA structure was driven in part by the knowledge that they were competing against Linus Pauling. Given Pauling's recent success in discovering the Alpha helix, they feared that Pauling might also be the first to determine the structure of DNA.\",\n \"Francis Crick\\n\\nMany have speculated about what might have happened had Pauling been able to travel to Britain as planned in May 1952. As it was, his political activities caused his travel to be restricted by the U. S. government and he did not visit the UK until later, at which point he met none of the DNA researchers in England. At any rate he was preoccupied with proteins at the time, not DNA. Watson and Crick were not officially working on DNA. Crick was writing his Ph.D. thesis; Watson also had other work such as trying to obtain crystals of myoglobin for X-ray diffraction experiments. In 1952, Watson performed X-ray diffraction on tobacco mosaic virus and found results indicating that it had helical structure. Having failed once, Watson and Crick were now somewhat reluctant to try again and for a while they were forbidden to make further efforts to find a molecular model of DNA.\",\n \"Francis Crick\\n\\nOf great importance to the model building effort of Watson and Crick was Rosalind Franklin's understanding of basic chemistry, which indicated that the hydrophilic phosphate-containing backbones of the nucleotide chains of DNA should be positioned so as to interact with water molecules on the outside of the molecule while the hydrophobic bases should be packed into the core. Franklin shared this chemical knowledge with Watson and Crick when she pointed out to them that their first model (from 1951, with the phosphates inside) was obviously wrong.\",\n \"Francis Crick\\n\\nCrick described what he saw as the failure of Maurice Wilkins and Rosalind Franklin to cooperate and work towards finding a molecular model of DNA as a major reason why he and Watson eventually made a second attempt to do so. They asked for, and received, permission to do so from both William Lawrence Bragg and Wilkins. In order to construct their model of DNA, Watson and Crick made use of information from unpublished X-ray diffraction images of Franklin's (shown at meetings and freely shared by Wilkins), including preliminary accounts of Franklin's results/photographs of the X-ray images that were included in a written progress report for the King's College laboratory of Sir John Randall from late 1952.\",\n \"Francis Crick\\n\\nIt is a matter of debate whether Watson and Crick should have had access to Franklin's results without her knowledge or permission, and before she had a chance to formally publish the results of her detailed analysis of her X-ray diffraction data which were included in the progress report. However, Watson and Crick found fault in her steadfast assertion that, according to her data, a helical structure was not the only possible shape for DNA—so they had a dilemma. In an effort to clarify this issue, Max Ferdinand Perutz later published what had been in the progress report, and suggested that nothing was in the report that Franklin herself had not said in her talk (attended by Watson) in late 1951. Further, Perutz explained that the report was to a Medical Research Council (MRC) committee that had been created in order to \\\"establish contact between the different groups of people working for the Council\\\". Randall's and Perutz's laboratories were both funded by the MRC.\",\n \"Francis Crick\\n\\nIt is also not clear how important Franklin's unpublished results from the progress report actually were for the model-building done by Watson and Crick. After the first crude X-ray diffraction images of DNA were collected in the 1930s, William Astbury had talked about stacks of nucleotides spaced at 3.4 angström (0.34 nanometre) intervals in DNA. A citation to Astbury's earlier X-ray diffraction work was one of only eight references in Franklin's first paper on DNA.Franklin's citation to the earlier work of W. T. Astbury is in: Analysis of Astbury's published DNA results and the better X-ray diffraction images collected by Wilkins and Franklin revealed the helical nature of DNA. It was possible to predict the number of bases stacked within a single turn of the DNA helix (10 per turn; a full turn of the helix is 27 angströms [2.7 nm] in the compact A form, 34 angströms [3.4 nm] in the wetter B form). Wilkins shared this information about the B form of DNA with Crick and Watson. Crick did not see Franklin's B form X-ray images (Photo 51) until after the DNA double helix model was published.\",\n \"Francis Crick\\n\\nOne of the few references cited by Watson and Crick when they published their model of DNA was to a published article that included Sven Furberg's DNA model that had the bases on the inside. Thus, the Watson and Crick model was not the first \\\"bases in\\\" model to be proposed. Furberg's results had also provided the correct orientation of the DNA sugars with respect to the bases. During their model building, Crick and Watson learned that an antiparallel orientation of the two nucleotide chain backbones worked best to orient the base pairs in the centre of a double helix. Crick's access to Franklin's progress report of late 1952 is what made Crick confident that DNA was a double helix with antiparallel chains, but there were other chains of reasoning and sources of information that also led to these conclusions.\",\n \"Francis Crick\\n\\nAs a result of leaving King's College for Birkbeck College, Franklin was asked by John Randall to give up her work on DNA. When it became clear to Wilkins and the supervisors of Watson and Crick that Franklin was going to the new job, and that Linus Pauling was working on the structure of DNA, they were willing to share Franklin's data with Watson and Crick, in the hope that they could find a good model of DNA before Pauling was able. Franklin's X-ray diffraction data for DNA and her systematic analysis of DNA's structural features was useful to Watson and Crick in guiding them towards a correct molecular model. The key problem for Watson and Crick, which could not be resolved by the data from King's College, was to guess how the nucleotide bases pack into the core of the DNA double helix.\",\n \"Francis Crick\\n\\nAnother key to finding the correct structure of DNA was the so-called Chargaff ratios, experimentally determined ratios of the nucleotide subunits of DNA: the amount of guanine is equal to cytosine and the amount of adenine is equal to thymine. A visit by Erwin Chargaff to England in 1952 reinforced the salience of this important fact for Watson and Crick. The significance of these ratios for the structure of DNA were not recognized until Watson, persisting in building structural models, realized that A:T and C:G pairs are structurally similar. In particular, the length of each base pair is the same. Chargaff had also pointed out to Watson that, in the aqueous, saline environment of the cell, the predominant tautomers of the pyrimidine (C and T) bases would be the amine and keto configurations of cytosine and thymine, rather than the imino and enol forms that Crick and Watson had assumed. They consulted Jerry Donohue who confirmed the most likely structures of the nucleotide bases. The base pairs are held together by hydrogen bonds, the same non-covalent interaction that stabilize the protein α-helix. The correct structures were essential for the positioning of the hydrogen bonds.\",\n \"Francis Crick\\n\\nThese insights led Watson to deduce the true biological relationships of the A:T and C:G pairs. After the discovery of the hydrogen bonded A:T and C:G pairs, Watson and Crick soon had their anti-parallel, double helical model of DNA, with the hydrogen bonds at the core of the helix providing a way to \\\"unzip\\\" the two complementary strands for easy replication: the last key requirement for a likely model of the genetic molecule. As important as Crick's contributions to the discovery of the double helical DNA model were, he stated that without the chance to collaborate with Watson, he would not have found the structure by himself.\",\n \"Francis Crick\\n\\nCrick did tentatively attempt to perform some experiments on nucleotide base pairing, but he was more of a theoretical biologist than an experimental biologist. There was another near-discovery of the base pairing rules in early 1952. Crick had started to think about interactions between the bases. He asked John Griffith to try to calculate attractive interactions between the DNA bases from chemical principles and quantum mechanics. Griffith's best guess was that A:T and G:C were attractive pairs. At that time, Crick was not aware of Chargaff's rules and he made little of Griffith's calculations, although it did start him thinking about complementary replication. Identification of the correct base-pairing rules (A-T, G-C) was achieved by Watson \\\"playing\\\" with cardboard cut-out models of the nucleotide bases, much in the manner that Linus Pauling had discovered the protein alpha helix a few years earlier. The Watson and Crick discovery of the DNA double helix structure was made possible by their willingness to combine theory, modeling and experimental results (albeit mostly done by others) to achieve their goal.\",\n \"Francis Crick\\n\\nThe DNA double helix structure proposed by Watson and Crick was based upon \\\"Watson-Crick\\\" bonds between the four bases most frequently found in DNA (A, C, T, G) and RNA (A, C, U, G). However, later research showed that triple-stranded, quadruple-stranded and other more complex DNA molecular structures required Hoogsteen base pairing. The entire field of synthetic biology began with work by researchers such as Erik T. Kool, in which bases other than A, C, T and G are used in a synthetic DNA. In addition to synthetic DNA there are also attempts to construct synthetic codons, synthetic endonucleases, synthetic proteins and synthetic zinc fingers. Using synthetic DNA, instead of there being 43 codons, if there are n new bases there could be as many as n3 codons. Research is currently being done to see if codons can be expanded to more than 3 bases. These new codons can code for new amino acids. These synthetic molecules can be used not only in medicine, but in creation of new materials.\",\n \"Francis Crick\\n\\nThe discovery was made on 28 February 1953; the first Watson/Crick paper appeared in Nature on 25 April 1953. Sir Lawrence Bragg, the director of the Cavendish Laboratory, where Watson and Crick worked, gave a talk at Guy's Hospital Medical School in London on Thursday 14 May 1953 which resulted in an article by Ritchie Calder in The News Chronicle of London, on Friday 15 May 1953, entitled \\\"Why You Are You. Nearer Secret of Life.\\\" The news reached readers of The New York Times the next day; Victor K. McElheny, in researching his biography, \\\"Watson and DNA: Making a Scientific Revolution\\\", found a clipping of a six-paragraph New York Times article written from London and dated 16 May 1953 with the headline \\\"Form of 'Life Unit' in Cell Is Scanned.\\\" The article ran in an early edition and was then pulled to make space for news deemed more important. (The New York Times subsequently ran a longer article on 12 June 1953). The university's undergraduate newspaper Varsity also ran its own short article on the discovery on Saturday 30 May 1953.\",\n \"Francis Crick\\n\\nBragg's original announcement of the discovery at a Solvay conference on proteins in Belgium on 8 April 1953 went unreported by the British press.\",\n \"Francis Crick\\n\\nIn a seven-page, handwritten letter to his son at a British boarding school on 19 March 1953 Crick explained his discovery, beginning the letter \\\"My Dear Michael, Jim Watson and I have probably made a most important discovery...\\\". The letter was put up for auction at Christie's New York on 10 April 2013 with an estimate of $1 to $2 million, eventually selling for $6,059,750, the largest amount ever paid for a letter at auction.\",\n \"Francis Crick\\n\\nSydney Brenner, Jack Dunitz, Dorothy Hodgkin, Leslie Orgel, and Beryl M. Oughton, were some of the first people in April 1953 to see the model of the structure of DNA, constructed by Crick and Watson; at the time they were working at Oxford University's Chemistry Department. All were impressed by the new DNA model, especially Brenner who subsequently worked with Crick at Cambridge in the Cavendish Laboratory and the new Laboratory of Molecular Biology. According to the late Dr. Beryl Oughton, later Rimmer, they all travelled together in two cars once Dorothy Hodgkin announced to them that they were off to Cambridge to see the model of the structure of DNA. Orgel also later worked with Crick at the Salk Institute for Biological Studies.\",\n \"Francis Crick\\n\\nIn addition, the entire field of synthetic biology began with researchers such as Erik T. Kool, where bases other than A, C, T and G are used in a synthetic DNA. In addition to synthetic DNA there are also attempts to construct synthetic codons, synthetic endonucleases, synthetic proteins and synthetic zinc fingers. Using synthetic DNA, instead of there being 43 codons, if there are n new bases there could be as many as n3 codons. Research is currently being done to see if codons can be expanded to more than 3 bases. These new codons can code for new amino acids. These synthetic molecules can be used not only in medicine, but in creation of new materials.\",\n \"Francis Crick\\n\\nMolecular biology\",\n \"Francis Crick\\n\\nIn 1954, at the age of 37, Crick completed his Ph.D. thesis: \\\"X-Ray Diffraction: Polypeptides and Proteins\\\" and received his degree. Crick then worked in the laboratory of David Harker at Brooklyn Polytechnic Institute, where he continued to develop his skills in the analysis of X-ray diffraction data for proteins, working primarily on ribonuclease and the mechanisms of protein synthesis. David Harker, the American X-ray crystallographer, was described as \\\"the John Wayne of crystallography\\\" by Vittorio Luzzati, a crystallographer at the Centre for Molecular Genetics in Gif-sur-Yvette near Paris, who had worked with Rosalind Franklin.\",\n \"Francis Crick\\n\\nAfter the discovery of the double helix model of DNA, Crick's interests quickly turned to the biological implications of the structure. In 1953, Watson and Crick published another article in Nature which stated: \\\"it therefore seems likely that the precise sequence of the bases is the code that carries the genetical information\\\".\",\n \"Francis Crick\\n\\nIn 1956, Crick and Watson speculated on the structure of small viruses. They suggested that spherical viruses such as Tomato bushy stunt virus had icosahedral symmetry and were made from 60 identical subunits.\",\n \"Francis Crick\\n\\nAfter his short time in New York, Crick returned to Cambridge where he worked until 1976, at which time he moved to California. Crick engaged in several X-ray diffraction collaborations such as one with Alexander Rich on the structure of collagen. However, Crick was quickly drifting away from continued work related to his expertise in the interpretation of X-ray diffraction patterns of proteins.\",\n \"Francis Crick\\n\\nGeorge Gamow established a group of scientists interested in the role of RNA as an intermediary between DNA as the genetic storage molecule in the nucleus of cells and the synthesis of proteins in the cytoplasm (the RNA Tie Club). It was clear to Crick that there had to be a code by which a short sequence of nucleotides would specify a particular amino acid in a newly synthesized protein. In 1956, Crick wrote an informal paper about the genetic coding problem for the small group of scientists in Gamow's RNA group. In this article, Crick reviewed the evidence supporting the idea that there was a common set of about 20 amino acids used to synthesize proteins. Crick proposed that there was a corresponding set of small \\\"adaptor molecules\\\" that would hydrogen bond to short sequences of a nucleic acid, and also link to one of the amino acids. He also explored the many theoretical possibilities by which short nucleic acid sequences might code for the 20 amino acids.\",\n \"Francis Crick\\n\\nDuring the mid-to-late 1950s Crick was very much intellectually engaged in sorting out the mystery of how proteins are synthesized. By 1958, Crick's thinking had matured and he could list in an orderly way all of the key features of the protein synthesis process: \\n*genetic information stored in the sequence of DNA molecules\\n*a \\\"messenger\\\" RNA molecule to carry the instructions for making one protein to the cytoplasm\\n*adaptor molecules (\\\"they might contain nucleotides\\\") to match short sequences of nucleotides in the RNA messenger molecules to specific amino acids\\n*ribonucleic-protein complexes that catalyse the assembly of amino acids into proteins according to the messenger RNA\",\n \"Francis Crick\\n\\nThe adaptor molecules were eventually shown to be tRNAs and the catalytic \\\"ribonucleic-protein complexes\\\" became known as ribosomes. An important step was later realization (in 1960) that the messenger RNA was not the same as the ribosomal RNA. None of this, however, answered the fundamental theoretical question of the exact nature of the genetic code. In his 1958 article, Crick speculated, as had others, that a triplet of nucleotides could code for an amino acid. Such a code might be \\\"degenerate\\\", with 4×4×4=64 possible triplets of the four nucleotide subunits while there were only 20 amino acids. Some amino acids might have multiple triplet codes. Crick also explored other codes in which, for various reasons, only some of the triplets were used, \\\"magically\\\" producing just the 20 needed combinations. Experimental results were needed; theory alone could not decide the nature of the code. Crick also used the term \\\"central dogma\\\" to summarize an idea that implies that genetic information flow between macromolecules would be essentially one-way:\",\n \"Francis Crick\\n\\nDNA → RNA → Protein\",\n \"Francis Crick\\n\\nSome critics thought that by using the word \\\"dogma\\\", Crick was implying that this was a rule that could not be questioned, but all he really meant was that it was a compelling idea without much solid evidence to support it. In his thinking about the biological processes linking DNA genes to proteins, Crick made explicit the distinction between the materials involved, the energy required, and the information flow. Crick was focused on this third component (information) and it became the organizing principle of what became known as molecular biology. Crick had by this time become a highly influential theoretical molecular biologist.\",\n \"Francis Crick\\n\\nProof that the genetic code is a degenerate triplet code finally came from genetics experiments, some of which were performed by Crick. The details of the code came mostly from work by Marshall Nirenberg and others who synthesized synthetic RNA molecules and used them as templates for in vitro protein synthesis. Nirenberg first announced his results to a small audience in Moscow at a 1961 conference. Crick's reaction was to invite Nirenberg to deliver his talk to a larger audience.\",\n \"Francis Crick\\n\\nControversy\",\n \"Francis Crick\\n\\nAn enduring controversy has been generated by Watson and Crick's use of DNA X-ray diffraction data collected by Rosalind Franklin and her student Raymond Gosling. The controversy arose from the fact that some of Franklin's unpublished data were used without her knowledge or consent by Watson and Crick in their construction of the double helix model of DNA. Of the four DNA researchers, only Rosalind Franklin had a degree in chemistry: Wilkins and Crick had backgrounds in physics, Watson in molecular biology.\",\n \"Francis Crick\\n\\nPrior to publication of the double helix structure, Watson and Crick had little direct interaction with Franklin herself. They were, however, aware of her work, more aware than she herself realized. Watson was present at a lecture, given in November 1951, where Franklin presented the two forms of the molecule, type A and type B, and discussed the position of the phosphate units on the external part of the molecule. She also specified the amount of water to be found in the molecule in accordance with other parts of it, data that have considerable importance in terms of the stability of the molecule. Franklin was the first to discover and formulate these facts, which in fact constituted the basis for all later attempts to build a model of the molecule. Before this both Linus Pauling and Watson and Crick had generated erroneous models with the chains inside and the bases pointing outwards. Her identification of the space group for DNA crystals revealed to Crick that the two DNA strands were antiparallel.\",\n \"Francis Crick\\n\\nIn January 1953, James Watson was shown an X-ray photograph of B-DNA (called photograph 51), by Maurice Wilkins. Maurice Wilkins had been given photograph 51 by Rosalind Franklin's Ph.D. student Raymond Gosling. Wilkins and Gosling had worked together in the Medical Research Council's (MRC) Biophysics Unit before director John Randall appointed Franklin to take over both DNA diffraction work and guidance of Gosling's thesis. It appears that Randall did not communicate effectively with them about Franklin's appointment, contributing to confusion and friction between Wilkins and Franklin.\",\n \"Francis Crick\\n\\nIn the middle of February 1953, Crick's thesis advisor, Max Perutz, gave Crick a copy of a report written for a Medical Research Council biophysics committee visit to King's in December 1952, containing data from the King's group, including some of Rosalind Franklin's crystallographic calculations.\",\n \"Francis Crick\\n\\nFranklin was unaware that photograph 51 and other information had been shared with Crick and Watson. She wrote a series of three draft manuscripts, two of which included a double helical DNA backbone. Her two A form manuscripts reached Acta Crystallographica in Copenhagen on 6 March 1953, one day before Crick and Watson had completed their model.\",\n \"Francis Crick\\n\\nThe X-ray diffraction images collected by Gosling and Franklin provided the best evidence for the helical nature of DNA. Franklin's experimental work thus proved crucial in Watson and Crick's discovery. Her experimental results provided estimates of the water content of DNA crystals, and these results were most consistent with the three sugar-phosphate backbones being on the outside of the molecule. Franklin's X-Ray photograph showed that the backbones had to be on the outside. Although she at first insisted vehemently that her data did not force one to conclude that DNA has a helical structure, in the drafts she submitted in 1953 she argues for a double helical DNA backbone. Her identification of the space group for DNA crystals revealed to Crick that the DNA strands were antiparallel, which helped Watson and Crick decide to look for DNA models with two antiparallel polynucleotide strands.\",\n \"Francis Crick\\n\\nIn summary, Watson and Crick had three sources for Franklin's unpublished data: 1) her 1951 seminar, attended by Watson, 2) discussions with Wilkins, who worked in the same laboratory with Franklin, 3) a research progress report that was intended to promote coordination of Medical Research Council-supported laboratories. Watson, Crick, Wilkins and Franklin all worked in MRC laboratories.\",\n \"Francis Crick\\n\\nCrick and Watson felt that they had benefited from collaborating with Wilkins. They offered him a co-authorship on the article that first described the double helix structure of DNA. Wilkins turned down the offer, a fact that may have led to the terse character of the acknowledgment of experimental work done at King's College in the eventual published paper. Rather than make any of the DNA researchers at King's College co-authors on the Watson and Crick double helix article, the solution that was arrived at was to publish two additional papers from King's College along with the helix paper. Brenda Maddox suggests that because of the importance of her experimental results in Watson and Crick's model building and theoretical analysis, Franklin should have had her name on the original Watson and Crick paper in Nature. Franklin and Gosling submitted their own joint 'second' paper to Nature at the same time as Wilkins, Stokes, and Wilson submitted theirs (i.e. the 'third' paper on DNA).\",\n \"Francis Crick\\n\\nWatson's portrayal of Franklin in The Double Helix (written after Franklin's death when libel laws did not apply anymore) was negative and gave the appearance that she was Wilkins' assistant and was unable to interpret her own DNA data.\",\n \"Francis Crick\\n\\nThe X-ray diffraction images collected by Franklin provided the best evidence for the helical nature of DNA. While Franklin's experimental work proved important to Crick and Watson's development of a correct model, she herself could not realize it at the time. When she left King's College, Director Sir John Randall insisted that all DNA work belonged exclusively to King's and ordered Franklin to not even think about it. Franklin subsequently did superb work in J. D. Bernal's Lab at Birkbeck College with the tobacco mosaic virus extending ideas on helical construction.\",\n \"Francis Crick\\n\\nViews on religion\",\n \"Francis Crick\\n\\nCrick referred to himself as a humanist, which he defined as the belief \\\"that human problems can and must be faced in terms of human moral and intellectual resources without invoking supernatural authority.\\\" He publicly called for humanism to replace religion as a guiding force for humanity, writing:\",\n \"Francis Crick\\n\\n\\\"The human dilemma is hardly new. We find ourselves through no wish of our own on this slowly revolving planet in an obscure corner of a vast universe. Our questioning intelligence will not let us live in cow-like content with our lot. We have a deep need to know why we are here. What is the world made of? More important, what are we made of? In the past religion answered these questions, often in considerable detail. Now we know that almost all these answers are highly likely to be nonsense, having sprung from man's ignorance and his enormous capacity for self-deception... The simple fables of the religions of the world have come to seem like tales told to children. Even understood symbolically they are often perverse, if not rather unpleasant... Humanists, then, live in a mysterious, exciting and intellectually expanding world, which, once glimpsed, makes the old worlds of the religions seem fake-cosy and stale... \\\":\",\n \"Francis Crick\\n\\nCrick was especially critical of Christianity:\",\n \"Francis Crick\\n\\n\\\"I do not respect Christian beliefs. I think they are ridiculous. If we could get rid of them we could more easily get down to the serious problem of trying to find out what the world is all about.\\\":\",\n \"Francis Crick\\n\\nCrick once joked, \\\"Christianity may be OK between consenting adults in private but should not be taught to young children.\\\"\",\n \"Francis Crick\\n\\nIn his book Of Molecules and Men, Crick expressed his views on the relationship between science and religion. After suggesting that it would become possible for a computer to be programmed so as to have a soul, he wondered: at what point during biological evolution did the first organism have a soul? At what moment does a baby get a soul? Crick stated his view that the idea of a non-material soul that could enter a body and then persist after death is just that, an imagined idea. For Crick, the mind is a product of physical brain activity and the brain had evolved by natural means over millions of years. He felt that it was important that evolution by natural selection be taught in schools and that it was regrettable that English schools had compulsory religious instruction. He also considered that a new scientific world view was rapidly being established, and predicted that once the detailed workings of the brain were eventually revealed, erroneous Christian concepts about the nature of humans and the world would no longer be tenable; traditional conceptions of the \\\"soul\\\" would be replaced by a new understanding of the physical basis of mind.\",\n \"Francis Crick\\n\\nHe was sceptical of organized religion, referring to himself as a skeptic and an agnostic with \\\"a strong inclination towards atheism\\\".\",\n \"Francis Crick\\n\\nIn 1960, Crick accepted an honorary fellowship at Churchill College, Cambridge, one factor being that the new college did not have a chapel. Some time later a large donation was made to establish a chapel and the College Council decided to accept it. Crick resigned his fellowship in protest.\",\n \"Francis Crick\\n\\nIn October 1969 Crick participated in a celebration of the 100th year of the journal Nature in which he attempted to make some predictions about what the next 30 years would hold for molecular biology. His speculations were later published in Nature. Near the end of the article, Crick briefly mentioned the search for life on other planets, but he held little hope that extraterrestrial life would be found by the year 2000. He also discussed what he described as a possible new direction for research, what he called \\\"biochemical theology\\\". Crick wrote \\\"so many people pray that one finds it hard to believe that they do not get some satisfaction from it\\\".\",\n \"Francis Crick\\n\\nCrick suggested that it might be possible to find chemical changes in the brain that were molecular correlates of the act of prayer. He speculated that there might be a detectable change in the level of some neurotransmitter or neurohormone when people pray. He might have been imagining substances such as dopamine that are released by the brain under certain conditions and produce rewarding sensations. Crick's suggestion that there might someday be a new science of \\\"biochemical theology\\\" seems to have been realized under an alternative name: there is now the new field of neurotheology. Crick's view of the relationship between science and religion continued to play a role in his work as he made the transition from molecular biology research into theoretical neuroscience.\",\n \"Francis Crick\\n\\nCrick asked in 1998 \\\"and if some of the Bible is manifestly wrong, why should any of the rest of it be accepted automatically? ... And what would be more important than to find our true place in the universe by removing one by one these unfortunate vestiges of earlier beliefs?\\\"\",\n \"Francis Crick\\n\\nIn 2003 he was one of 22 Nobel laureates who signed the Humanist Manifesto.\",\n \"Francis Crick\\n\\nDirected panspermia\",\n \"Francis Crick\\n\\nDuring the 1960s, Crick became concerned with the origins of the genetic code. In 1966, Crick took the place of Leslie Orgel at a meeting where Orgel was to talk about the origin of life. Crick speculated about possible stages by which an initially simple code with a few amino acid types might have evolved into the more complex code used by existing organisms. At that time, everyone thought of proteins as the only kind of enzymes and ribozymes had not yet been found. Many molecular biologists were puzzled by the problem of the origin of a protein replicating system that is as complex as that which exists in organisms currently inhabiting Earth. In the early 1970s, Crick and Orgel further speculated about the possibility that the production of living systems from molecules may have been a very rare event in the universe, but once it had developed it could be spread by intelligent life forms using space travel technology, a process they called \\\"directed panspermia\\\".\",\n \"Francis Crick\\n\\nIn a retrospective article, Crick and Orgel noted that they had been overly pessimistic about the chances of abiogenesis on Earth when they had assumed that some kind of self-replicating protein system was the molecular origin of life.\",\n \"Francis Crick\\n\\nIn 1976 Crick addressed the origin of protein synthesis in a paper with Sydney Brenner, Aaron Klug, and George Pieczenik. In this paper, they speculate that code constraints on nucleotide sequences allow protein synthesis without the need for a ribosome. It, however, requires a five base binding between the mRNA and tRNA with a flip of the anti-codon creating a triplet coding, even though it is a five-base physical interaction. Thomas H. Jukes pointed out that the code constraints on the mRNA sequence required for this translation mechanism is still preserved.\",\n \"Francis Crick\\n\\nNeuroscience and other interests\",\n \"Francis Crick\\n\\nCrick's period at Cambridge was the pinnacle of his long scientific career, but he left Cambridge in 1977 after 30 years, having been offered (and having refused) the Mastership of Gonville & Caius. James Watson claimed at a Cambridge conference marking the 50th anniversary of the discovery of the structure of DNA in 2003: \\\"Now perhaps it's a pretty well kept secret that one of the most uninspiring acts of the University of Cambridge over this past century was to turn down Francis Crick when he applied to be the Professor of Genetics, in 1958. Now there may have been a series of arguments, which led them to reject Francis. It was really saying, don't push us to the frontier.\\\" The apparently \\\"pretty well kept secret\\\" had already been recorded in Soraya De Chadarevian's \\\"Designs For Life: Molecular Biology After World War II\\\", published by CUP in 2002. His major contribution to molecular biology in Cambridge is well documented in The History of the University of Cambridge: Volume 4 (1870 to 1990), which was published by Cambridge University Press in 1992.\",\n \"Francis Crick\\n\\nAccording to the University of Cambridge's genetics department official website, the electors of the professorship could not reach consensus, prompting the intervention of then University Vice-Chancellor Lord Adrian. Lord Adrian first offered the professorship to a compromise candidate, Guido Pontecorvo, who refused, and is said to have offered it then to Crick, who also refused.\",\n \"Francis Crick\\n\\nIn 1976, Crick took a sabbatical year at the Salk Institute for Biological Studies in La Jolla, California. Crick had been a nonresident fellow of the Institute since 1960. Crick wrote, \\\"I felt at home in Southern California.\\\" After the sabbatical, Crick left Cambridge in order to continue working at the Salk Institute. He was also a professor at the University of California, San Diego. He taught himself neuroanatomy and studied many other areas of neuroscience research. It took him several years to disengage from molecular biology because exciting discoveries continued to be made, including the discovery of alternative splicing and the discovery of restriction enzymes, which helped make possible genetic engineering. Eventually, in the 1980s, Crick was able to devote his full attention to his other interest, consciousness. His autobiographical book, What Mad Pursuit: A Personal View of Scientific Discovery, includes a description of why he left molecular biology and switched to neuroscience.\",\n \"Francis Crick\\n\\nUpon taking up work in theoretical neuroscience, Crick was struck by several things:\\n*there were many isolated subdisciplines within neuroscience with little contact between them\\n*many people who were interested in behaviour treated the brain as a black box\\n*consciousness was viewed as a taboo subject by many neurobiologists\",\n \"Francis Crick\\n\\nCrick hoped he might aid progress in neuroscience by promoting constructive interactions between specialists from the many different subdisciplines concerned with consciousness. He even collaborated with neurophilosophers such as Patricia Churchland. In 1983, as a result of their studies of computer models of neural networks, Crick and Mitchison proposed that the function of REM sleep is to remove certain modes of interactions in networks of cells in the mammalian cerebral cortex; they called this hypothetical process 'reverse learning' or 'unlearning'. In the final phase of his career, Crick established a collaboration with Christof Koch that lead to publication of a series of articles on consciousness during the period spanning from 1990 to 2005. Crick made the strategic decision to focus his theoretical investigation of consciousness on how the brain generates visual awareness within a few hundred milliseconds of viewing a scene. Crick and Koch proposed that consciousness seems so mysterious because it involves very short-term memory processes that are as yet poorly understood. Crick also published a book describing how neurobiology had reached a mature enough stage so that consciousness could be the subject of a unified effort to study it at the molecular, cellular and behavioural levels.\",\n \"Francis Crick\\n\\nCrick's book The Astonishing Hypothesis made the argument that neuroscience now had the tools required to begin a scientific study of how brains produce conscious experiences. Crick was skeptical about the value of computational models of mental function that are not based on details about brain structure and function.\",\n \"Francis Crick\\n\\nReactions\",\n \"Francis Crick\\n\\nCrick was often described as very talkative, with Watson – in The Double Helix – implying lack of modesty. His personality combined with his scientific accomplishments produced many opportunities for Crick to stimulate reactions from others, both inside and outside the scientific world, which was the centre of his intellectual and professional life.Describing Crick's influence on his scientific colleagues, Francis Crick Papers archivist Chris Beckett wrote of the importance of, \\\".....Crick's presence and eloquence —direct and beguiling, by all accounts in the archive— at conference after conference, through formal lectures, extempore summaries, informal meetings and individual conversations. Indeed, one has the impression that it was through these frequent persuasive moments of personal delivery and purposive conversations that Crick was most influential.\\\" Also described as an example of Crick's wide recognition and public profile are some of the times Crick was addressed as \\\"Sir Francis Crick\\\" with the assumption that someone so famous must have been knighted. Crick spoke rapidly, and rather loudly, and had an infectious and reverberating laugh, and a lively sense of humour. One colleague from the Salk Institute described him as \\\"a brainstorming intellectual powerhouse with a mischievous smile.... Francis was never mean-spirited, just incisive.\",\n \"Francis Crick\\n\\nHe detected microscopic flaws in logic. In a room full of smart scientists, Francis continually reearned his position as the heavyweight champ.\\\"\",\n \"Francis Crick\\n\\nEugenics\",\n \"Francis Crick\\n\\nCrick occasionally expressed his views on eugenics, usually in private letters. For example, Crick advocated a form of positive eugenics in which wealthy parents would be encouraged to have more children. He once remarked, \\\"In the long run, it is unavoidable that society will begin to worry about the character of the next generation... It is not a subject at the moment which we can tackle easily because people have so many religious beliefs and until we have a more uniform view of ourselves I think it would be risky to try and do anything in the way of eugenics... I would be astonished if, in the next 100 or 200 years, society did not come round to the view that they would have to try to improve the next generation in some extent or one way or another.\\\"\",\n \"Francis Crick\\n\\nCreationism\",\n \"Francis Crick\\n\\nCrick was a firm critic of Young Earth creationism. In the 1987 United States Supreme Court case Edwards v. Aguillard, Crick joined a group of other Nobel laureates who advised, \\\"'Creation-science' simply has no place in the public-school science classroom.\\\" Crick was also an advocate for the establishment of Darwin Day as a British national holiday.\",\n \"Francis Crick\\n\\nRecognition\",\n \"Francis Crick\\n\\nIn addition to his third share of the 1962 Nobel prize for Physiology or Medicine, he received many awards and honours, including the Royal and Copley medals of the Royal Society (1972 and 1975), and also the Order of Merit (on 27 November 1991); he refused an offer of a CBE in 1963 and later refused an offer of a knighthood, but was often referred to in error as 'Sir Francis Crick' and even on occasions as 'Lord Crick.'\",\n \"Francis Crick\\n\\nThe award of Nobel prizes to John Kendrew and Max Perutz, and to Crick, Watson, and Wilkins was satirised in a short sketch in the BBC TV programme That Was The Week That Was with the Nobel Prizes being referred to as 'The Alfred Nobel Peace Pools.'\",\n \"Francis Crick\\n\\nFrancis Crick Medal and Lecture\",\n \"Francis Crick\\n\\nThe Francis Crick Medal and Lecture was established in 2003 following an endowment by his former colleague, Sydney Brenner, joint winner of the 2002 Nobel Prize in Physiology and Medicine. The lecture is delivered annually in any field of biological sciences, with preference given to the areas in which Francis Crick himself worked. Importantly, the lectureship is aimed at younger scientists, ideally under 40, or whose career progression corresponds to this age. , Crick lecture have been delivered by Julie Ahringer, Dario Alessi, Ewan Birney, Simon Boulton, Jason Chin, Simon Fisher, Matthew Hurles, Gilean McVean, Duncan Odom, Geraint Rees, Sarah Teichmann and Daniel Wolpert.\",\n \"Francis Crick\\n\\nFrancis Crick Institute\",\n \"Francis Crick\\n\\nThe Francis Crick Institute is a £660,000,000 biomedical research centre currently under construction, located in London, United Kingdom. The Francis Crick Institute is a partnership between Cancer Research UK, Imperial College London, King's College London, the Medical Research Council, University College London (UCL) and the Wellcome Trust. Once completed in 2016, it will be the largest centre for biomedical research and innovation in Europe.\",\n \"Francis Crick\\n\\nFrancis Crick Graduate Lectures\",\n \"Francis Crick\\n\\nThe University of Cambridge Graduate School of Biological, Medical and Veterinary Sciences hosts The Francis Crick Graduate Lectures. The first two lectures were by John Gurdon and Tim Hunt.\",\n \"Francis Crick\\n\\nOther honours\",\n \"Francis Crick\\n\\n*The inscription on the helices of a DNA sculpture (which was donated by James Watson) outside Clare College's Thirkill Court, Cambridge, England reads: \\\"The structure of DNA was discovered in 1953 by Francis Crick and James Watson while Watson lived here at Clare.\\\" and on the base: \\\"The double helix model was supported by the work of Rosalind Franklin and Maurice Wilkins.\\\"\\n*Another sculpture entitled Discovery, by artist Lucy Glendinning was installed on Tuesday, 13 December 2005 in Abington Street, Northampton. According to the late Lynn Wilson, chairman of the Wilson Foundation, \\\"The sculpture celebrates the life of a world class scientist who must surely be considered the greatest Northamptonian of all time — by discovering DNA he unlocked the whole future of genetics and the alphabet of life.\\\"\\n*Westminster City Council unveiled a green plaque to Francis Crick on the front façade of 56 St George's Square, Pimlico, London SW1 on 20 June 2007; Crick lived in the first floor flat, together with Robert Dougall of BBC radio and later TV fame, a former Royal Navy associate.\",\n \"Francis Crick\\n\\n* In addition, Crick was a Fellow of the Royal Society, a Fellow of the International Academy of Humanism, and a Fellow of CSICOP. * A sculpted bust of Francis Crick by John Sherrill Houser, which incorporates a single 'Golden' Helix, was cast in bronze in the artist's studio in New Mexico, US. The bronze was first displayed at the Francis Crick Memorial Conference (on Consciousness) at the University of Cambridge's Churchill College on 7 July 2012; it was bought by Mill Hill School in May 2013, and displayed at the inaugural Crick Dinner on 8 June 2013, and will be again at their Crick Centenary Dinner in 2016. * The Benjamin Franklin Medal for Distinguished Achievement in the Sciences of the American Philosophical Society (2001), together with James D. Watson. *Crick featured in the BBC Radio 4 series The New Elizabethans to mark the diamond Jubilee of Queen Elizabeth II in 2012. A panel of seven academics, journalists and historians named Crick among a group of 60 people in the UK \\\"whose actions during the reign of Elizabeth II have had a significant impact on lives in these islands and given the age its character\\\".\",\n \"Francis Crick\\n\\nBooks by Crick\",\n \"Francis Crick\\n\\n* Of Molecules and Men (Prometheus Books, 2004; original edition 1967) ISBN 1-59102-185-5\\n* Life Itself: Its Origin and Nature (Simon & Schuster, 1981) ISBN 0-671-25562-2\\n* What Mad Pursuit: A Personal View of Scientific Discovery (Basic Books reprint edition, 1990) ISBN 0-465-09138-5\\n* The Astonishing Hypothesis: The Scientific Search For The Soul (Scribner reprint edition, 1995) ISBN 0-684-80158-2\\n* Kreiseliana: about and around Georg Kreisel; ISBN 1-56881-061-X; 495 pages. For pages 25 – 32 \\\"Georg Kreisel: a Few Personal Recollections\\\" contributed by Francis Crick.\",\n \"Francis Crick\\n\\nBooks referring to Crick\",\n \"Francis Crick\\n\\n* Robert Olby, assisted by Martin Packer, \\\"Francis Crick: Hunter of Life's Secrets\\\", Cold Spring Harbor Laboratory Press, ISBN 978-0-87969-798-3, published 25 August 2009; 450 pp; [http://www.cshlpress.com/pdf/sample/Crick.pdf] and Peter Lawrence's review in \\\"Current Biology\\\" [http://www.mrc-lmb.cam.ac.uk/PAL/NewFiles/PAListFrames.html]. * John Bankston, Francis Crick and James D. Watson; Francis Crick and James Watson: Pioneers in DNA Research (Mitchell Lane Publishers, Inc., 2002) ISBN 1-58415-122-6. * Bill Bryson; A Short History of Nearly Everything (Broadway Books, 2003) ISBN 0-7679-0817-1. * Soraya De Chadarevian; Designs For Life: Molecular Biology After World War II, CUP 2002, 444 pp; ISBN 0-521-57078-6. * Roderick Braithwaite. \\\"\\\"'Strikingly Alive', The History of the Mill Hill School Foundation 1807–2007; published Phillimore & Co. ISBN 978-1-86077-330-3\\n* Edwin Chargaff; Heraclitean Fire, Rockefeller Press, 1978. * S. Chomet (Ed.), \\\"D.N.A. Genesis of a Discovery\\\", 1994, Newman- Hemisphere Press, London\\n* Dickerson, Richard E.; \\\"Present at the Flood: How Structural Molecular Biology Came About\\\", Sinauer, 2005; ISBN 0-87893-168-6. * Edward Edelson, \\\"Francis Crick And James Watson: And the Building Blocks of Life\\\"' Oxford University Press, 2000, ISBN 0-19-513971-2. * John Finch; 'A Nobel Fellow On Every Floor', Medical Research Council 2008, 381 pp, ISBN 978-1-84046-940-0.\",\n \"Francis Crick\\n\\n*Hager, Thomas; \\\"Force of Nature: The Life of Linus Pauling\\\", Simon & Schuster 1995; ISBN 0-684-80909-5\\n* Graeme Hunter; Light Is A Messenger, the life and science of William Lawrence Bragg (Oxford University Press, 2004) ISBN 0-19-852921-X. * Horace Freeland Judson, The Eighth Day of Creation. Makers of the Revolution in Biology; Penguin Books 1995, first published by Jonathan Cape, 1977; ISBN 0-14-017800-7. * Errol C. Friedberg; \\\"Sydney Brenner: A Biography\\\", pub. CSHL Press October 2010, ISBN 0-87969-947-7. * Torsten Krude (Ed.); DNA Changing Science and Society (ISBN 0-521-82378-1) CUP 2003. (The Darwin Lectures for 2003, including one by Sir Aaron Klug on Rosalind Franklin's involvement in the determination of the structure of DNA). * Robert Olby; The Path to The Double Helix: Discovery of DNA; first published in October 1974 by MacMillan, with foreword by Francis Crick; ISBN 0-486-68117-3; revised in 1994, with a 9-page postscript. *Robert Olby; Oxford National Dictionary article: ‘Crick, Francis Harry Compton (1916–2004)’, Oxford Dictionary of National Biography, Oxford University Press, January 2008. * Anne Sayre. 1975. Rosalind Franklin and DNA. New York: W.W. Norton and Company. ISBN 0-393-32044-8. * James D.\",\n \"Francis Crick\\n\\nWatson; The Double Helix: A Personal Account of the Discovery of the Structure of DNA, Atheneum, 1980, ISBN 0-689-70602-2 (first published in 1968) is a very readable firsthand account of the research by Crick and Watson. The book also formed the basis of the award winning television dramatization Life Story by BBC Horizon (also broadcast as Race for the Double Helix). * James D. Watson; The Double Helix: A Personal Account of the Discovery of the Structure of DNA; The Norton Critical Edition, which was published in 1980, edited by Gunther S. Stent: ISBN 0-393-01245-X. * James D. Watson; \\\"Avoid boring people and other lessons from a life in science\\\" New York: Random House. ISBN 978-0-375-41284-4, 366pp.\"\n]","isConversational":false}}},{"rowIdx":1783,"cells":{"id":{"kind":"string","value":"tc_2755"},"question":{"kind":"string","value":"Heisenberg is most associated with which branch of physics?"},"answer":{"kind":"string","value":"Quantum Mechanics"},"answer_aliases":{"kind":"list like","value":["quantum physical","quantam physics","quantum mechenics","quantum theory","quantum physicist","quantum dislocation","quantum effects","quantum mechanical laws","quantum hypothesis","nonrelativistic quantum theory","quantum mechanical","quantum mechanic","classical quantum mechanics","quantum mechanics","quantum mechanical physics","modern quantum mechanical","quantum laws","quantum physics","quantum mechanical model","quantic mechanics","quantum mechanical properties","quantum theory of matter"],"string":"[\n \"quantum physical\",\n \"quantam physics\",\n \"quantum mechenics\",\n \"quantum theory\",\n \"quantum physicist\",\n \"quantum dislocation\",\n \"quantum effects\",\n \"quantum mechanical laws\",\n \"quantum hypothesis\",\n \"nonrelativistic quantum theory\",\n \"quantum mechanical\",\n \"quantum mechanic\",\n \"classical quantum mechanics\",\n \"quantum mechanics\",\n \"quantum mechanical physics\",\n \"modern quantum mechanical\",\n \"quantum laws\",\n \"quantum physics\",\n \"quantum mechanical model\",\n \"quantic mechanics\",\n \"quantum mechanical properties\",\n \"quantum theory of matter\"\n]","isConversational":false},"documents":{"kind":"list like","value":["Werner Heisenberg\n\nWerner Karl Heisenberg (; 5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the key pioneers of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent series of papers with Max Born and Pascual Jordan, during the same year, this matrix formulation of quantum mechanics was substantially elaborated. In 1927 he published his uncertainty principle, upon which he built his philosophy and for which he is best known. Heisenberg was awarded the Nobel Prize in Physics for 1932 \"for the creation of quantum mechanics\". He also made important contributions to the theories of the hydrodynamics of turbulent flows, the atomic nucleus, ferromagnetism, cosmic rays, and subatomic particles, and he was instrumental in planning the first West German nuclear reactor at Karlsruhe, together with a research reactor in Munich, in 1957. Considerable controversy surrounds his work on atomic research during World War II.","Werner Heisenberg\n\nFollowing World War II, he was appointed director of the Kaiser Wilhelm Institute for Physics, which soon thereafter was renamed the Max Planck Institute for Physics. He was director of the institute until it was moved to Munich in 1958, when it was expanded and renamed the Max Planck Institute for Physics and Astrophysics.","Werner Heisenberg\n\nHeisenberg was also president of the German Research Council, chairman of the Commission for Atomic Physics, chairman of the Nuclear Physics Working Group, and president of the Alexander von Humboldt Foundation.","Werner Heisenberg\n\nLife and career","Werner Heisenberg\n\nEarly years","Werner Heisenberg\n\nWerner Karl Heisenberg was born in Würzburg, Germany, to Kaspar Ernst August Heisenberg, a secondary school teacher of classical languages who became Germany's only ordentlicher Professor (ordinarius professor) of medieval and modern Greek studies in the university system, and his wife, Annie Wecklein.","Werner Heisenberg\n\nHe studied physics and mathematics from 1920 to 1923 at the Ludwig-Maximilians-Universität München and the Georg-August-Universität Göttingen. At Munich, he studied under Arnold Sommerfeld and Wilhelm Wien. At Göttingen, he studied physics with Max Born and James Franck, and he studied mathematics with David Hilbert. He received his doctorate in 1923, at Munich under Sommerfeld. He completed his Habilitation in 1924, at Göttingen under Born.","Werner Heisenberg\n\nBecause Sommerfeld had a sincere interest in his students and knew of Heisenberg's interest in Niels Bohr's theories on atomic physics, Sommerfeld took Heisenberg to Göttingen to the Bohr-Festspiele (Bohr Festival) in June 1922. At the event, Bohr was a guest lecturer and gave a series of comprehensive lectures on quantum atomic physics. There, Heisenberg met Bohr for the first time, and it had a significant and continuing effect on him.","Werner Heisenberg\n\nHeisenberg's doctoral thesis, the topic of which was suggested by Sommerfeld, was on turbulence; the thesis discussed both the stability of laminar flow and the nature of turbulent flow. The problem of stability was investigated by the use of the Orr–Sommerfeld equation, a fourth order linear differential equation for small disturbances from laminar flow. He briefly returned to this topic after World War II.","Werner Heisenberg\n\nHeisenberg's paper on the anomalous Zeeman effect was accepted as his Habilitationsschrift (Habilitation thesis) under Max Born at Göttingen.","Werner Heisenberg\n\nIn his youth he was a member and Scoutleader of the Neupfadfinder, a German Scout association and part of the German Youth Movement. In August 1923 Robert Honsell and Heisenberg organized a trip (Großfahrt) to Finland with a Scout group of this association from Munich. \nHeisenberg arrived at Munich in 1919 as a member of Freikorps to fight the Bavarian Soviet Republic established a year earlier. Five decades later he recalled those days as youthful fun, like \"playing cops and robbers and so on; it was nothing serious at all.\"","Werner Heisenberg\n\nCareer","Werner Heisenberg\n\nGöttingen, Copenhagen, and Leipzig","Werner Heisenberg\n\nFrom 1924 to 1927, Heisenberg was a Privatdozent at Göttingen. From 17 September 1924 to 1 May 1925, under an International Education Board Rockefeller Foundation fellowship, Heisenberg went to do research with Niels Bohr, director of the Institute of Theoretical Physics at the University of Copenhagen. His seminal paper, Über quantentheoretischer Umdeutung was published in September 1925. He returned to Göttingen and with Max Born and Pascual Jordan, over a period of about six months, developed the matrix mechanics formulation of quantum mechanics. On 1 May 1926, Heisenberg began his appointment as a university lecturer and assistant to Bohr in Copenhagen. It was in Copenhagen, in 1927, that Heisenberg developed his uncertainty principle, while working on the mathematical foundations of quantum mechanics. On 23 February, Heisenberg wrote a letter to fellow physicist Wolfgang Pauli, in which he first described his new principle. In his paper on the uncertainty principle, Heisenberg used the word \"Ungenauigkeit\" (imprecision).","Werner Heisenberg\n\nIn 1927, Heisenberg was appointed ordentlicher Professor (ordinarius professor) of theoretical physics and head of the department of physics at the Universität Leipzig; he gave his inaugural lecture on 1 February 1928. In his first paper published from Leipzig, Heisenberg used the Pauli exclusion principle to solve the mystery of ferromagnetism.","Werner Heisenberg\n\nIn Heisenberg's tenure at Leipzig, the quality of doctoral students, post-graduate and research associates who studied and worked with Heisenberg there is attested to by the acclaim later earned by these people; at various times, they included: Erich Bagge, Felix Bloch, Ugo Fano, Siegfried Flügge, William Vermillion Houston, Friedrich Hund, Robert S. Mulliken, Rudolf Peierls, George Placzek, Isidor Isaac Rabi, Fritz Sauter, John C. Slater, Edward Teller, John Hasbrouck van Vleck, Victor Frederick Weisskopf, Carl Friedrich von Weizsäcker, Gregor Wentzel and Clarence Zener.","Werner Heisenberg\n\nIn early 1929, Heisenberg and Pauli submitted the first of two papers laying the foundation for relativistic quantum field theory. Also in 1929, Heisenberg went on a lecture tour in China, Japan, India, and the United States.","Werner Heisenberg\n\nShortly after the discovery of the neutron by James Chadwick in 1932, Heisenberg submitted the first of three papers on his neutron-proton model of the nucleus. He was awarded the 1932 Nobel Prize in Physics.","Werner Heisenberg\n\nIn 1928, the British mathematical physicist P. A. M. Dirac had derived the relativistic wave equation of quantum mechanics, which implied the existence of positive electrons, later to be named positrons. In 1932, from a cloud chamber photograph of cosmic rays, the American physicist Carl David Anderson identified a track as having been made by a positron. In mid-1933, Heisenberg presented his theory of the positron. His thinking on Dirac's theory and further development of the theory were set forth in two papers. The first, Bemerkungen zur Diracschen Theorie des Positrons (Remarks on Dirac's theory of the positron) was published in 1934, and the second, Folgerungen aus der Diracschen Theorie des Positrons (Consequences of Dirac's Theory of the Positron), was published in 1936. In these papers Heisenberg was the first to reinterpret the Dirac equation as a \"classical\" field equation for any point particle of spin ħ/2, itself subject to quantization conditions involving anti-commutators. Thus reinterpreting it as a (quantum) field equation accurately describing electrons, Heisenberg put matter on the same footing as electromagnetism: as being described by relativistic quantum field equations which allowed the possibility of particle creation and destruction.","Werner Heisenberg\n\n(Hermann Weyl had already described this in a 1929 letter to Einstein.)","Werner Heisenberg\n\nIn the early 1930s in Germany, the Deutsche Physik movement was anti-Semitic and anti-theoretical physics, especially including quantum mechanics and the theory of relativity. As applied in the university environment, political factors took priority over the historically applied concept of scholarly ability, even though its two most prominent supporters were the Nobel Laureates in Physics Philipp Lenard and Johannes Stark.","Werner Heisenberg\n\nAfter Adolf Hitler came to power in 1933, Heisenberg was attacked in the press as a \"White Jew\" by elements of the Deutsche Physik (German Physics) movement for his insistence on teaching about the roles of Jewish scientists. As a result, he came under investigation by the SS. This was over an attempt to appoint Heisenberg as successor to Arnold Sommerfeld at the University of Munich. The issue was resolved in 1938 by Heinrich Himmler, head of the SS. While Heisenberg was not chosen as Sommerfeld's successor, he was rehabilitated to the physics community during the Third Reich. Nevertheless, supporters of Deutsche Physik launched vicious attacks against leading theoretical physicists, including Arnold Sommerfeld and Heisenberg. On 29 June 1936, a National Socialist Party newspaper published a column attacking Heisenberg. On 15 July 1937, he was attacked in a journal of the SS. This was the beginning of what is called the Heisenberg Affair.","Werner Heisenberg\n\nIn mid-1936, Heisenberg presented his theory of cosmic-ray showers in two papers. Four more papers appeared in the next two years.","Werner Heisenberg\n\nIn June 1939, Heisenberg bought a summer home for his family in Urfeld am Walchensee, in southern Germany. He also traveled to the United States in June and July, visiting Samuel Abraham Goudsmit, at the University of Michigan in Ann Arbor. However, Heisenberg refused an invitation to emigrate to the United States. He did not see Goudsmit again until six years later, when Goudsmit was the chief scientific advisor to the American Operation Alsos at the close of World War II. Ironically, Heisenberg was arrested under Operation Alsos and detained in England under Operation Epsilon.","Werner Heisenberg\n\nMatrix mechanics and the Nobel Prize","Werner Heisenberg\n\nHeisenberg’s paper establishing quantum mechanics has puzzled physicists and historians. His methods assume that the reader is familiar with Kramers-Heisenberg transition probability calculations. The main new idea, noncommuting matrices, is justified only by a rejection of unobservable quantities. It introduces the non-commutative multiplication of matrices by physical reasoning, based on the correspondence principle, despite the fact that Heisenberg was not then familiar with the mathematical theory of matrices. The path leading to these results has been reconstructed in MacKinnon, 1977, and the detailed calculations are worked out in Aitchison et al.","Werner Heisenberg\n\nIn Copenhagen, Heisenberg and Hans Kramers collaborated on a paper on dispersion, or the scattering from atoms of radiation whose wavelength is larger than the atoms. They showed that the successful formula Kramers had developed earlier could not be based on Bohr orbits, because the transition frequencies are based on level spacings which are not constant. The frequencies which occur in the Fourier transform of sharp classical orbits, by contrast, are equally spaced. But these results could be explained by a semi-classical Virtual State model: the incoming radiation excites the valence, or outer, electron to a virtual state from which it decays. In a subsequent paper Heisenberg showed that this virtual oscillator model could also explain the polarization of fluorescent radiation.","Werner Heisenberg\n\nThese two successes, and the continuing failure of the Bohr-Sommerfeld model to explain the outstanding problem of the anomalous Zeeman effect, led Heisenberg to use the virtual oscillator model to try to calculate spectral frequencies. The method proved too difficult to immediately apply to realistic problems, so Heisenberg turned to a simpler example, the anharmonic oscillator.","Werner Heisenberg\n\nThe dipole oscillator consists of a simple harmonic oscillator, which is thought of as a charged particle on a spring, perturbed by an external force, like an external charge. The motion of the oscillating charge can be expressed as a Fourier series in the frequency of the oscillator. Heisenberg solved for the quantum behavior by two different methods. First, he treated the system with the virtual oscillator method, calculating the transitions between the levels that would be produced by the external source.","Werner Heisenberg\n\nHe then solved the same problem by treating the anharmonic potential term as a perturbation to the harmonic oscillator and using the perturbation methods that he and Born had developed. Both methods led to the same results for the first and the very complicated second order correction terms. This suggested that behind the very complicated calculations lay a consistent scheme.","Werner Heisenberg\n\nSo Heisenberg set out to formulate these results without any explicit dependence on the virtual oscillator model. To do this, he replaced the Fourier expansions for the spatial coordinates by matrices, matrices which corresponded to the transition coefficients in the virtual oscillator method. He justified this replacement by an appeal to Bohr’s correspondence principle and the Pauli doctrine that quantum mechanics must be limited to observables.","Werner Heisenberg\n\nOn 9 July, Heisenberg gave Born this paper to review and submit for publication. When Born read the paper, he recognized the formulation as one which could be transcribed and extended to the systematic language of matrices, which he had learned from his study under Jakob Rosanes at Breslau University. Born, with the help of his assistant and former student Pascual Jordan, began immediately to make the transcription and extension, and they submitted their results for publication; the paper was received for publication just 60 days after Heisenberg's paper. A follow-on paper was submitted for publication before the end of the year by all three authors.","Werner Heisenberg\n\nUp until this time, matrices were seldom used by physicists; they were considered to belong to the realm of pure mathematics. Gustav Mie had used them in a paper on electrodynamics in 1912 and Born had used them in his work on the lattice theory of crystals in 1921. While matrices were used in these cases, the algebra of matrices with their multiplication did not enter the picture as they did in the matrix formulation of quantum mechanics.","Werner Heisenberg\n\nIn 1928, Albert Einstein nominated Heisenberg, Born, and Jordan for the Nobel Prize in Physics, but it was not to be. The announcement of the Nobel Prize in Physics for 1932 was delayed until November 1933. It was at that time that it was announced Heisenberg had won the Prize for 1932 \"for the creation of quantum mechanics, the application of which has, inter alia, led to the discovery of the allotropic forms of hydrogen\".","Werner Heisenberg\n\nThe Deutsche Physik movement","Werner Heisenberg\n\nOn 1 April 1935, the eminent theoretical physicist Arnold Sommerfeld, Heisenberg's doctoral advisor at the University of Munich, achieved emeritus status. However, Sommerfeld stayed in his chair during the selection process for his successor, which took until 1 December 1939. The process was lengthy due to academic and political differences between the Munich Faculty's selection and that of the Reichserziehungsministerium (REM, Reich Education Ministry) and the supporters of Deutsche Physik, which was anti-Semitic and had a bias against theoretical physics, especially quantum mechanics and the theory of relativity.","Werner Heisenberg\n\nIn 1935, the Munich Faculty drew up a list of candidates to replace Sommerfeld as ordinarius professor of theoretical physics and head of the Institute for Theoretical Physics at the University of Munich. There were three names on the list: Werner Heisenberg, who received the Nobel Prize in Physics for 1932, Peter Debye, who received the Nobel Prize in Chemistry in 1936, and Richard Becker – all former students of Sommerfeld. The Munich Faculty was firmly behind these candidates, with Heisenberg as their first choice. However, supporters of Deutsche Physik and elements in the REM had their own list of candidates, and the battle dragged on for over four years. During this time, Heisenberg came under vicious attack by the Deutsche Physik supporters. One attack was published in Das Schwarze Korps, the newspaper of the Schutzstaffel (SS), headed by Heinrich Himmler. In this, Heisenberg was called a \"White Jew\" (i.e. an Aryan who acts like a Jew) who should be made to \"disappear\". These attacks were taken seriously, as Jews were violently attacked and incarcerated. Heisenberg fought back with an editorial and a letter to Himmler, in an attempt to resolve this matter and regain his honour.","Werner Heisenberg\n\nAt one point, Heisenberg's mother visited Himmler's mother. The two women knew each other, as Heisenberg's maternal grandfather and Himmler's father were rectors and members of a Bavarian hiking club. Eventually, Himmler settled the Heisenberg affair by sending two letters, one to SS Gruppenführer Reinhard Heydrich and one to Heisenberg, both on 21 July 1938. In the letter to Heydrich, Himmler said Germany could not afford to lose or silence Heisenberg, as he would be useful for teaching a generation of scientists. To Heisenberg, Himmler said the letter came on recommendation of his family and he cautioned Heisenberg to make a distinction between professional physics research results and the personal and political attitudes of the involved scientists. The letter to Heisenberg was signed under the closing \"Mit freundlichem Gruß und, Heil Hitler!\" (With friendly greetings, Heil Hitler!\") Overall, the Heisenberg affair was a victory for academic standards and professionalism. However, the appointment of Wilhelm Müller to replace Sommerfeld was a political victory over academic standards. Müller was not a theoretical physicist, had not published in a physics journal, and was not a member of the Deutsche Physikalische Gesellschaft; his appointment was considered a travesty and detrimental to educating theoretical physicists.","Werner Heisenberg\n\nDocument #55 [https://books.google.com/books?id\nsl69XGiohsoC&pgPA152 ’White Jews’ in Science [15 July 1937]]pp. 175–6 Document #63 [https://books.google.com/books?id\nsl69XGiohsoC&pgPA175 Heinrich Himmler: Letter to Reinhard Heydrich [21 July 1938]]pp. 176–7 Document #64 [https://books.google.com/books?id\nsl69XGiohsoC&pg=PA176 Heinrich Himmler: Letter to Werner Heisenberg [21 July 1938]]pp. 261–6 Document #85 Ludwig Prandtl: Attachment to the letter to Reich Marschal (sic) Hermann Göring [28 April 1941] pp. 290–2 Document #93 Carl Ramsauer: The Munich Conciliation and Pacification Attempt [20 January 1942]","Werner Heisenberg\n\nDuring the SS investigation of Heisenberg, the three investigators had training in physics. Heisenberg had participated in the doctoral examination of one of them at the Universität Leipzig. The most influential of the three, however, was Johannes Juilfs. During their investigation, they had become supporters of Heisenberg as well as his position against the ideological policies of the Deutsche Physik movement in theoretical physics and academia.","Werner Heisenberg\n\nWorld War II","Werner Heisenberg\n\nIn 1939, shortly after the discovery of nuclear fission, the German nuclear energy project, also known as the Uranverein (Uranium Club), had begun. Heisenberg was one of the principal scientists leading research and development in the project.","Werner Heisenberg\n\nFrom 15 to 22 September 1941, Heisenberg traveled to German-occupied Copenhagen to lecture and discuss nuclear research and theoretical physics with Niels Bohr. The meeting, and specifically what it might reveal about Heisenberg's intentions concerning developing nuclear weapons for the Nazi regime, is the subject of the award-winning Michael Frayn play titled Copenhagen. A television film version of the play was made by the BBC in 2002, with Stephen Rea as Bohr, and Daniel Craig as Heisenberg. The same meeting had previously been dramatised by the BBC's Horizon science documentary series in 1992, with Anthony Bate as Bohr, and Philip Anthony as Heisenberg. Documents relating to the Bohr-Heisenberg meeting were released in 2002 by the Niels Bohr Archive and by the Heisenberg family. A dramatized account of Heisenberg's work during the war is featured in the 2015 TV series The Heavy Water War.","Werner Heisenberg\n\nOn 26 February 1942, Heisenberg presented a lecture to Reich officials on energy acquisition from nuclear fission, after the army withdrew most of its funding. The Uranium Club was transferred to the Reich Research Council (RFR) in July 1942. On 4 June 1942, Heisenberg was summoned to report to Albert Speer, Germany's Minister of Armaments, on the prospects for converting the Uranium Club's research toward developing nuclear weapons. During the meeting, Heisenberg told Speer that a bomb could not be built before 1945, and would require significant monetary and manpower resources. Five days later, on 9 June 1942, Adolf Hitler issued a decree for the reorganization of the RFR as a separate legal entity under the Reich Ministry for Armament and Ammunition; the decree appointed Reich Marshall Hermann Göring as the president.","Werner Heisenberg\n\nIn September 1942, Heisenberg submitted his first paper of a three-part series on the scattering matrix, or S-matrix, in elementary particle physics. The first two papers were published in 1943 and the third in 1944. The S-matrix described only observables, i.e., the states of incident particles in a collision process, the states of those emerging from the collision, and stable bound states; there would be no reference to the intervening states. This was the same precedent as he followed in 1925 in what turned out to be the foundation of the matrix formulation of quantum mechanics through only the use of observables.","Werner Heisenberg\n\nIn February 1943, Heisenberg was appointed to the Chair for Theoretical Physics at the Friedrich-Wilhelms-Universität (today, the Humboldt-Universität zu Berlin). In April, his election to the Preußische Akademie der Wissenschaften (Prussian Academy of Sciences) was approved. That same month, he moved his family to their retreat in Urfeld as Allied bombing increased in Berlin. In the summer, he dispatched the first of his staff at the Kaiser-Wilhelm Institut für Physik to Hechingen and its neighboring town of Haigerloch, on the edge of the Black Forest, for the same reasons. From 18–26 October, he traveled to German-occupied Netherlands. In December 1943, Heisenberg visited German-occupied Poland.","Werner Heisenberg\n\nFrom 24 January to 4 February 1944, Heisenberg traveled to occupied Copenhagen, after the German army confiscated Bohr's Institute of Theoretical Physics. He made a short return trip in April. In December, Heisenberg lectured in neutral Switzerland. The United States Office of Strategic Services sent former major league baseball catcher and OSS agent Moe Berg to attend the lecture carrying a pistol, with orders to shoot Heisenberg if his lecture indicated that Germany was close to completing an atomic bomb. Heisenberg did not give such an indication, so Berg decided not to shoot him, a decision Berg later described as his own \"uncertainty principle\".","Werner Heisenberg\n\nIn January 1945, Heisenberg, with most of the rest of his staff, moved from the Kaiser-Wilhelm Institut für Physik to the facilities in the Black Forest.","Werner Heisenberg\n\nUranium Club","Werner Heisenberg\n\nIn December 1938, the German chemists Otto Hahn and Fritz Strassmann sent a manuscript to Naturwissenschaften reporting they had detected the element barium after bombarding uranium with neutrons and Otto Hahn concluded a bursting of the uranium nucleus; simultaneously, Hahn communicated these results to his friend Lise Meitner, who had in July of that year fled to the Netherlands and then went to Sweden.","Werner Heisenberg\n\nMeitner, and her nephew Otto Robert Frisch, correctly interpreted Hahn's and Strassmann's results as being nuclear fission. Frisch confirmed this experimentally on 13 January 1939. Frisch along with Rudolf Peierls, by then both in Britain, subsequently wrote the Frisch–Peierls memorandum and joined the British Tube Alloys project.","Werner Heisenberg\n\nPaul Harteck was director of the physical chemistry department at the University of Hamburg and an advisor to the Heereswaffenamt (HWA, Army Ordnance Office). On 24 April 1939, along with his teaching assistant Wilhelm Groth, Harteck made contact with the Reichskriegsministerium (RKM, Reich Ministry of War) to alert them to the potential of military applications of nuclear chain reactions. Two days earlier, on 22 April 1939, after hearing a colloquium paper by Wilhelm Hanle on the use of uranium fission in a Uranmaschine (uranium machine, i.e., nuclear reactor), Georg Joos, along with Hanle, notified Wilhelm Dames, at the Reichserziehungsministerium (REM, Reich Ministry of Education), of potential military applications of nuclear energy. The communication was given to Abraham Esau, head of the physics section of the Reichsforschungsrat (RFR, Reich Research Council) at the REM. On 29 April, a group, organized by Esau, met at the REM to discuss the potential of a sustained nuclear chain reaction.","Werner Heisenberg\n\nThe group included the physicists Walther Bothe, Robert Döpel, Hans Geiger, Wolfgang Gentner (probably sent by Walther Bothe), Wilhelm Hanle, Gerhard Hoffmann and Georg Joos; Peter Debye was invited, but he did not attend. After this, informal work began at the Georg-August University of Göttingen by Joos, Hanle and their colleague Reinhold Mannfopff; the group of physicists was known informally as the first Uranverein (Uranium Club) and formally as Arbeitsgemeinschaft für Kernphysik. The group's work was discontinued in August 1939, when the three were called to military training.","Werner Heisenberg\n\nThe second Uranverein began after the Heereswaffenamt (HWA, Army Ordnance Office) squeezed the Reichsforschungsrat (RFR, Reich Research Council) out of the Reichserziehungsministerium (REM, Reich Ministry of Education) and started the formal German nuclear energy project under military auspices. The second Uranverein was formed on 1 September 1939, the day World War II began, and it had its first meeting on 16 September 1939. The meeting was organized by Kurt Diebner, advisor to the HWA, and held in Berlin. The invitees included Walther Bothe, Siegfried Flügge, Hans Geiger, Otto Hahn, Paul Harteck, Gerhard Hoffmann, Josef Mattauch and Georg Stetter. A second meeting was held soon thereafter and included Klaus Clusius, Robert Döpel, Werner Heisenberg and Carl Friedrich von Weizsäcker. Also at this time, the Kaiser-Wilhelm Institut für Physik (KWIP, Kaiser Wilhelm Institute for Physics, after World War II the Max Planck Institute for Physics), in Berlin-Dahlem, was placed under HWA authority, with Diebner as the administrative director, and the military control of the nuclear research commenced.","Werner Heisenberg\n\nWhen it was apparent that the nuclear energy project would not make a decisive contribution to ending the war effort in the near term, control of the KWIP was returned in January 1942 to its umbrella organization, the Kaiser-Wilhelm Gesellschaft (KWG, Kaiser Wilhelm Society, after World War II the Max-Planck Gesellschaft), and HWA control of the project was relinquished to the RFR in July 1942. The nuclear energy project thereafter maintained its kriegswichtig (important for the war) designation and funding continued from the military. However, the German nuclear power project was then broken down into the following main areas: uranium and heavy water production, uranium isotope separation and the Uranmaschine (uranium machine, i.e., nuclear reactor). Also, the project was then essentially split up between a number of institutes, where the directors dominated the research and set their own research agendas.","Werner Heisenberg\n\nThe dominant personnel and facilities were the following: \n* Institut für Physik (Walther Bothe) of the Kaiser-Wilhelm Institut für medizinische Forschung (KWImF, Kaiser Wilhelm Institute for Medical Research),\n* Institute for Physical Chemistry (Klaus Clusius) at the Ludwig Maximilian University of Munich,\n* HWA Versuchsstelle (testing station) in Gottow (Kurt Diebner),\n* Kaiser-Wilhelm-Institut für Chemie (Otto Hahn),\n* Physical Chemistry Department (Paul Harteck) of the University of Hamburg,\n* Kaiser-Wilhelm-Institut für Physik (Werner Heisenberg),\n* Second Experimental Physics Institute (Hans Kopfermann) at the Georg-August University of Göttingen,\n* Auergesellschaft (Nikolaus Riehl), and\n* II. Physikalisches Institut (Georg Stetter) at the University of Vienna.","Werner Heisenberg\n\nHeisenberg was appointed director-in-residence of the KWIP on 1 July 1942, as Peter Debye was still officially the director and on leave in the United States; Debye had gone on leave as he was a citizen of The Netherlands and had refused to become a German citizen when the HWA took administrative control of the KWIP. Heisenberg still also had his department of physics at the University of Leipzig where work was done for the Uranverein by Robert Döpel and his wife Klara Döpel. During the period Kurt Diebner administered the KWIP under the HWA program, considerable personal and professional animosity developed between Diebner and the Heisenberg inner circle – Heisenberg, Karl Wirtz, and Carl Friedrich von Weizsäcker.","Werner Heisenberg\n\nThe point in 1942, when the army relinquished its control of the German nuclear energy project, was the zenith of the project relative to the number of personnel devoting time to the effort. There were only about 70 scientists working on the project, with about 40 devoting more than half their time to nuclear fission research. After this, the number of scientists working on applied nuclear fission diminished dramatically. Many of the scientists not working with the main institutes stopped working on nuclear fission and devoted their efforts to more pressing war related work.","Werner Heisenberg\n\nOver time, the HWA and then the RFR controlled the German nuclear energy project. The most influential people in the project were Kurt Diebner, Abraham Esau, Walther Gerlach and Erich Schumann. Schumann was one of the most powerful and influential physicists in Germany. Schumann was director of the Physics Department II at the Frederick William University (later, University of Berlin), which was commissioned and funded by the Oberkommando des Heeres (OKH, Army High Command) to conduct physics research projects. He was also head of the research department of the HWA, assistant secretary of the Science Department of the OKH and Bevollmächtiger (plenipotentiary) for high explosives. Diebner, throughout the life of the nuclear energy project, had more control over nuclear fission research than did Walther Bothe, Klaus Clusius, Otto Hahn, Paul Harteck or Werner Heisenberg.","Werner Heisenberg\n\n1945: Alsos Mission and Operation Epsilon","Werner Heisenberg\n\nAlsos Mission was an Allied effort commanded by the Russian-American Colonel Boris T. Pash. He reported directly to General Leslie Groves, commander of the Manhattan Engineer District, which was developing atomic weapons for the United States. The chief scientific advisor to Alsos Mission was the physicist Samuel Goudsmit. Goudsmit was selected for this task because of his knowledge of physics, he spoke German, and he personally knew a number of the German scientists working on the German nuclear energy project. He also knew little of the Manhattan Project, so, if he were captured, he would have little intelligence value to the Germans.","Werner Heisenberg\n\nThe objectives of the Alsos Mission were to determine if the Germans had an atomic bomb program and to exploit German atomic related facilities, intellectual materials, materiel resources, and scientific personnel for the benefit of the US. Personnel on this operation generally swept into areas which had just come under control of the Allied military forces, but sometimes they operated in areas still under control by German forces.","Werner Heisenberg\n\nBerlin had been a location of many German scientific research facilities. To limit casualties and loss of equipment, many of these facilities were dispersed to other locations in the latter years of the war. The Kaiser-Wilhelm-Institut für Physik (KWIP, Kaiser Wilhelm Institute for Physics) had mostly been moved in 1943 and 1944 to Hechingen and its neighboring town of Haigerloch, on the edge of the Black Forest, which eventually became the French occupation zone. This move, some scheming, and a fast-moving American task force allowed them to take into custody a large number of German scientists associated with nuclear research. The only section of the institute which remained in Berlin was the low-temperature physics section, headed by Ludwig Bewilogua (1906–83), who was in charge of the exponential uranium pile.","Werner Heisenberg\n\nNine of the prominent German scientists who published reports in Kernphysikalische Forschungsberichte as members of the Uranverein were picked up by Operation Alsos and incarcerated in England under Operation Epsilon: Erich Bagge, Kurt Diebner, Walther Gerlach, Otto Hahn, Paul Harteck, Werner Heisenberg, Horst Korsching, Carl Friedrich von Weizsäcker and Karl Wirtz. Also incarcerated was Max von Laue, although he had nothing to do with the nuclear energy project. Goudsmit, the chief scientific advisor to Operation Alsos, thought von Laue might be beneficial to the postwar rebuilding of Germany and would benefit from the high level contacts he would have in England.","Werner Heisenberg\n\nHeisenberg had been captured and arrested by Colonel Pash at Heisenberg's retreat in Urfeld, on 3 May 1945, in an alpine operation in territory still under control by German forces. He was taken to Heidelberg, where, on 5 May, he met Goudsmit for the first time since the Ann Arbor visit in 1939. Germany surrendered just two days later. Heisenberg did not see his family again for eight months. Heisenberg was moved across France and Belgium and flown to England on 3 July 1945.","Werner Heisenberg\n\nThe 10 German scientists were held at Farm Hall in England. The facility had been a safe house of the British foreign intelligence MI6. During their detention, their conversations were recorded. Conversations thought to be of intelligence value were transcribed and translated into English. The transcripts were released in 1992. Bernstein has published an annotated version of the transcripts in his book Hitler's Uranium Club: The Secret Recordings at Farm Hall, along with an introduction to put them in perspective. A complete, unedited publication of the British version of the reports appeared as Operation Epsilon: The Farm Hall Transcripts, which was published in 1993 by the Institute of Physics in Bristol and by the University of California Press in the US.","Werner Heisenberg\n\nPost 1945","Werner Heisenberg\n\nOn 3 January 1946, the 10 Operation Epsilon detainees were transported to Alswede in Germany, which was in the British occupation zone. Heisenberg settled in Göttingen, also in the British zone. In July, he was named director of the Kaiser-Wilhelm-Institut für Physik (KWIP, Kaiser Wilhelm Institute for Physics), then located in Göttingen. Shortly thereafter, it was renamed the Max-Planck-Institut für Physik, in honor of Max Planck and to assuage political objections to the continuation of the institute. Heisenberg was its director until 1958. In 1958, the institute was moved to Munich, expanded, and renamed Max-Planck-Institut für Physik und Astrophysik (MPIFA). Heisenberg was its director from 1960 to 1970; in the interim, Heisenberg and the astrophysicist Ludwig Biermann were co-directors. Heisenberg resigned his directorship of the MPIFA on 31 December 1970. Upon the move to Munich, Heisenberg also became an ordentlicher Professor (ordinarius professor) at the University of Munich.","Werner Heisenberg\n\nJust as the Americans did with Operation Alsos, the Soviets inserted special search teams into Germany and Austria in the wake of their troops. Their objective, under the Russian Alsos, was also the exploitation of German atomic related facilities, intellectual materials, materiel resources and scientific personnel for the benefit of the Soviet Union. One of the German scientists recruited under this Soviet operation was the nuclear physicist Heinz Pose, who was made head of Laboratory V in Obninsk. When he returned to Germany on a recruiting trip for his laboratory, Pose wrote a letter to Werner Heisenberg inviting him to work in the USSR. The letter lauded the working conditions in the USSR and the available resources, as well as the favorable attitude of the Soviets towards German scientists. A courier hand delivered the recruitment letter, dated 18 July 1946, to Heisenberg; Heisenberg politely declined in a return letter to Pose.","Werner Heisenberg\n\nIn 1947, Heisenberg presented lectures in Cambridge, Edinburgh and Bristol. Heisenberg also contributed to the understanding of the phenomenon of superconductivity with a paper in 1947 and two papers in 1948, one of them with Max von Laue.","Werner Heisenberg\n\nIn the period shortly after World War II, Heisenberg briefly returned to the subject of his doctoral thesis, turbulence. Three papers were published in 1948 and one in 1950.","Werner Heisenberg\n\nIn the post-war period, Heisenberg continued his interests in cosmic-ray showers with considerations on multiple production of mesons. He published three papers in 1949, two in 1952, and one in 1955.","Werner Heisenberg\n\nOn 9 March 1949, the Deutsche Forschungsrat (German Research Council) was established by the Max-Planck Gesellschaft (MPG, Max Planck Society, successor organization to the Kaiser-Wilhelm Gesellschaft). Heisenberg was appointed president of the Deutsche Forschungsrat. In 1951, the organization was fused with the Notgemeinschaft der Deutschen Wissenschaft (NG, Emergency Association of German Science) and that same year renamed the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation). With the merger, Heisenberg was appointed to the presidium.","Werner Heisenberg\n\nIn 1952, Heisenberg served as the chairman of the Commission for Atomic Physics of the DFG. Also that year, he headed the German delegation to the European Council for Nuclear Research.","Werner Heisenberg\n\nIn 1953, Heisenberg was appointed president of the Alexander von Humboldt-Stiftung by Konrad Adenauer. Heisenberg served until 1975. Also, from 1953, Heisenberg's theoretical work concentrated on the unified field theory of elementary particles.","Werner Heisenberg\n\nIn late 1955 to early 1956, Heisenberg gave the Gifford Lectures at St Andrews University, in Scotland, on the intellectual history of physics. The lectures were later published as Physics and Philosophy: The Revolution in Modern Science.","Werner Heisenberg\n\nDuring 1956 and 1957, Heisenberg was the chairman of the Arbeitskreis Kernphysik (Nuclear Physics Working Group) of the Fachkommission II \"Forschung und Nachwuchs\" (Commission II \"Research and Growth\") of the Deutschen Atomkommission (DAtK, German Atomic Energy Commission). Other members of the Nuclear Physics Working Group in both 1956 and 1957 were: Walther Bothe, Hans Kopfermann (vice-chairman), Fritz Bopp, Wolfgang Gentner, Otto Haxel, Willibald Jentschke, Heinz Maier-Leibnitz, Josef Mattauch, Wolfgang Riezler, Wilhelm Walcher and Carl Friedrich von Weizsäcker. Wolfgang Paul was also a member of the group during 1957.","Werner Heisenberg\n\nIn 1957, Heisenberg was a signatory of the manifesto of the Göttinger Achtzehn (Göttingen Eighteen).","Werner Heisenberg\n\nFrom 1957, Heisenberg was interested in plasma physics and the process of nuclear fusion. He also collaborated with the International Institute of Atomic Physics in Geneva. He was a member of the Institute's Scientific Policy Committee, and for several years was the Committee's chairman.","Werner Heisenberg\n\nIn 1973, Heisenberg gave a lecture at Harvard University on the historical development of the concepts of quantum theory.","Werner Heisenberg\n\nOn 24 March 1973, Heisenberg gave a speech before the Catholic Academy of Bavaria, accepting the Romano Guardini Prize. An English translation of its title is \"Scientific and Religious Truth.\" And its stated goal was \"In what follows, then, we shall first of all deal with the unassailability and value of scientific truth, and then with the much wider field of religion, of which – so far as the Christian religion is concerned – Guardini himself has so persuasively written; finally – and this will be the hardest part to formulate – we shall speak of the relationship of the two truths.\"Chapter 16 \"Scientific and Religious Truth\" in Across the Frontiers, 1974, Harper & Row, p.213-229 A more detailed insight into Heisenberg's view on religion has been discussed by Wilfried Schröder in \"Natural science and religion\" (Bremen 1999, Science edition) and Wilfried Schröder \"Naturerkenntnis und Religion\" (Bremen, science edition 2008).","Werner Heisenberg\n\nPersonal life","Werner Heisenberg\n\nIn January 1937 Heisenberg met Elisabeth Schumacher (1914–1998) at a private music recital. Elisabeth was the daughter of a well-known Berlin economics professor, and her brother was the economist E. F. Schumacher, author of Small is Beautiful. Heisenberg married her on 29 April. Fraternal twins Maria and Wolfgang were born in January 1938, whereupon Wolfgang Pauli congratulated Heisenberg on his \"pair creation\" – a word play on a process from elementary particle physics, pair production. They had five more children over the next 12 years: Barbara, Christine, Jochen, Martin and Verena. Jochen became a physics professor at the University of New Hampshire.","Werner Heisenberg\n\nHeisenberg enjoyed classical music and was an accomplished pianist.","Werner Heisenberg\n\nHeisenberg was raised and lived as a Lutheran Christian, publishing and giving several talks reconciling science with his faith.","Werner Heisenberg\n\nIn his speech Scientific and Religious Truth (1974) while accepting the Romano Guardini Prize, Heisenberg affirmed:“In the history of science, ever since the famous trial of Galileo, it has repeatedly been claimed that scientific truth cannot be reconciled with the religious interpretation of the world. Although I am now convinced that scientific truth is unassailable in its own field, I have never found it possible to dismiss the content of religious thinking as simply part of an outmoded phase in the consciousness of mankind, a part we shall have to give up from now on. Thus in the course of my life I have repeatedly been compelled to ponder on the relationship of these two regions of thought, for I have never been able to doubt the reality of that to which they point.” (Heisenberg 1974, 213) “Where no guiding ideals are left to point the way, the scale of values disappears and with it the meaning of our deeds and sufferings, and at the end can lie only negation and despair. Religion is therefore the foundation of ethics, and ethics the presupposition of life.” (Heisenberg 1974, 219).","Werner Heisenberg\n\nIn his autobiographical article in the journal Truth, Henry Margenau (Professor Emeritus of Physics and Natural Philosophy at Yale University) pointed out: “I have said nothing about the years between 1936 and 1950. There were, however, a few experiences I cannot forget. One was my first meeting with Heisenberg, who came to America soon after the end of the Second World War. Our conversation was intimate and he impressed me by his deep religious conviction. He was a true Christian in every sense of that word.”","Werner Heisenberg\n\nHeisenberg also enjoyed mountaineering. In his autobiography, he included photographs from this activity.","Werner Heisenberg\n\nHeisenberg died of cancer of the kidneys and gall bladder at his home, on 1 February 1976. The next evening, his colleagues and friends walked in remembrance from the Institute of Physics to his home and each put a candle near the front door. He is buried at Munich Waldfriedhof.","Werner Heisenberg\n\nHonors and awards","Werner Heisenberg\n\nHeisenberg was awarded a number of honors:\n* Honorary doctorates from the University of Bruxelles, the Technological University of Karlsruhe, and the University of Budapest.\n* Order of Merit of Bavaria\n* Romano Guardini Prize\n* Grand Cross for Federal Service with Star\n* Knight of the Order of Merit (Civil Class)\n* Elected a Foreign Member of the Royal Society (ForMemRS) in 1955\n* Member of the Academies of Sciences of Göttingen, Bavaria, Saxony, Prussia, Sweden, Romania, Norway, Spain, The Netherlands (1939), Rome (Pontifical), the Deutsche Akademie der Naturforscher Leopoldina (Halle), the Accademia dei Lincei (Rome), and the American Academy of Sciences.\n* 1932–Nobel Prize in Physics \"for the creation of quantum mechanics, the application of which has, inter alia, led to the discovery of the allotropic forms of hydrogen\".\n* 1933–Max-Planck-Medaille of the Deutsche Physikalische Gesellschaft","Werner Heisenberg\n\nResearch Reports in Nuclear Physics","Werner Heisenberg\n\nThe following reports were published in Kernphysikalische Forschungsberichte (Research Reports in Nuclear Physics), an internal publication of the German Uranverein. The reports were classified Top Secret, they had very limited distribution, and the authors were not allowed to keep copies. The reports were confiscated under the Allied Operation Alsos and sent to the United States Atomic Energy Commission for evaluation. In 1971, the reports were declassified and returned to Germany. The reports are available at the Karlsruhe Nuclear Research Center and the American Institute of Physics. * Robert Döpel, K. Döpel, and Werner Heisenberg Bestimmung der Diffusionslänge thermischer Neutronen in Präparat 38 G-22 (5 December 1940)\n* Robert Döpel, K. Döpel, and Werner Heisenberg Bestimmung der Diffusionslänge thermischer Neutronen in schwerem Wasser G-23 (7 August 1940)\n* Werner Heisenberg Die Möglichkeit der technischer Energiegewinnung aus der Uranspaltung G-39 (6 December 1939)\n* Werner Heisenberg Bericht über die Möglichkeit technischer Energiegewinnung aus der Uranspaltung (II) G-40 (29 February 1940)\n* Robert Döpel, K.","Werner Heisenberg\n\nDöpel, and Werner Heisenberg Versuche mit Schichtenanordnungen von D2O und 38 G-75 (28 October 1941)\n* Werner Heisenberg Über die Möglichkeit der Energieerzeugung mit Hilfe des Isotops 238 G-92 (1941)\n* Werner Heisenberg Bericht über Versuche mit Schichtenanordnungen von Präparat 38 und Paraffin am Kaiser Wilhelm Institut für Physik in Berlin-Dahlem G-93 (May 1941)\n* Fritz Bopp, Erich Fischer, Werner Heisenberg, Carl-Friedrich von Weizsäcker, and Karl Wirtz Untersuchungen mit neuen Schichtenanordnungen aus U-metall und Paraffin G-127 (March 1942)\n* Robert Döpel Bericht über Unfälle beim Umgang mit Uranmetall G-135 (9 July 1942)\n* Werner Heisenberg Bemerkungen zu dem geplanten halbtechnischen Versuch mit 1,5 to D2O und 3 to 38-Metall G-161 (31 July 1942)\n* Werner Heisenberg, Fritz Bopp, Erich Fischer, Carl-Friedrich von Weizsäcker, and Karl Wirtz Messungen an Schichtenanordnungen aus 38-Metall und Paraffin G-162 (30 October 1942)\n* Robert Döpel, K. Döpel, and Werner Heisenberg Der experimentelle Nachweis der effektiven Neutronenvermehrung in einem Kugel-Schichten-System aus D2O und Uran-Metall G-136 (July 1942)\n* Werner Heisenberg Die Energiegewinnung aus der Atomkernspaltung G-217 (6 May 1943)\n* Fritz Bopp, Walther Bothe, Erich Fischer, Erwin Fünfer, Werner Heisenberg, O.","Werner Heisenberg\n\nRitter, and Karl Wirtz Bericht über einen Versuch mit 1.5 to D2O und U und 40 cm Kohlerückstreumantel (B7) G-300 (3 January 1945)\n* Robert Döpel, K. Döpel, and Werner Heisenberg Die Neutronenvermehrung in einem D2O-38-Metallschichtensystem G-373 (March 1942)","Werner Heisenberg\n\nPublications","Werner Heisenberg\n\n; Collected bibliographies\n*\n* \n*\n*\n*\n; Selected articles:","Werner Heisenberg\n\n*\n*\n*\n*\n*\n*\n*\n*\n* The paper was received on 29 July 1925. [English translation in: ] This is the first paper in the famous trilogy which launched the matrix mechanics formulation of quantum mechanics. * The paper was received on 27 September 1925. [English translation in: ] This is the second paper in the famous trilogy which launched the matrix mechanics formulation of quantum mechanics. * The paper was received on 16 November 1925. [English translation in: ] This is the third paper in the famous trilogy which launched the matrix mechanics formulation of quantum mechanics. *\n*\n*\n*\n*\n*\n*\n* The author was cited as being at Leipzig. The paper was received on 21 June 1934. *\n* The authors were cited as being at Leipzig. The paper was received on 22 December 1935. A translation of this paper has been done by W. Korolevski and H. Kleinert: [http://arxiv.org/abs/physics/0605038v1 arXiv:physics/0605038v1]. *\n*W. Heisenberg Der Durchgang sehr energiereicher Korpuskeln durch den Atomkern, Ber. Sächs, Akad. Wiss. Volume 89, 369; Die Naturwissenschaften Volume 25, 749–750 (1937)\n*\n*\n*W. Heisenberg Der Durchgang sehr energiereicher Korpuskeln durch den Atomkern, Nuovo Cimento Volume 15, 31–34; Verh. Dtsch. physik. Ges.","Werner Heisenberg\n\nVolume 19, 2 (1938)\n*\n*\n*\n*W. Heisenberg Zur Theorie der Supraleitung, Forsch. Fortschr. Volumes 21/23, 243–244 (1947); Z. Naturforsch. Volume 2a, 185–201 (1947)\n*\n*\n*\n*\n*\n*\n*\n*\n*W. Heisenberg On the stability of laminar flow, Proc. International Congress Mathematicians Volume II, 292–296 (1950)\n*\n*\n*\n* The substance of this article was presented by Heisenberg in a lecture at Harvard University.","Werner Heisenberg\n\nBooks","Werner Heisenberg\n\n*\n*\n*\n* Werner Heisenberg Physics and Beyond: Encounters and Conversations (Harper & Row, 1971)\n*\n*\n* Werner Heisenberg Physik und Philosophie: Weltperspektiven. (Ullstein Taschenbuchvlg., 1988)\n*\n* Werner Heisenberg and F. S. C. Northrop Physics and Philosophy: The Revolution in Modern Science (Great Minds Series) (Prometheus, 1999)\n*\n*\n* Werner Heisenberg Physik und Philosophie (Hirzel, 2007)\n* ([https://archive.org/details/PhysicsPhilosophy full text of 1958 version])","Uncertainty principle\n\nIn quantum mechanics, the uncertainty principle, also known as Heisenberg's uncertainty principle, is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known.","Uncertainty principle\n\nIntroduced first in 1927, by the German physicist Werner Heisenberg, it states that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa. The formal inequality relating the standard deviation of position σx and the standard deviation of momentum σp was derived by Earle Hesse Kennard later that year and by Hermann Weyl in 1928:","Uncertainty principle\n\n( is the reduced Planck constant, / ).","Uncertainty principle\n\nHistorically, the uncertainty principle has been confused with a somewhat similar effect in physics, called the observer effect, which notes that measurements of certain systems cannot be made without affecting the systems. Heisenberg offered such an observer effect at the quantum level (see below) as a physical \"explanation\" of quantum uncertainty. It has since become clear, however, that the uncertainty principle is inherent in the properties of all wave-like systems, and that it arises in quantum mechanics simply due to the matter wave nature of all quantum objects. Thus, the uncertainty principle actually states a fundamental property of quantum systems, and is not a statement about the observational success of current technology. It must be emphasized that measurement does not mean only a process in which a physicist-observer takes part, but rather any interaction between classical and quantum objects regardless of any observer. (N.B.","Uncertainty principle\n\non precision: If δx and δp are the precisions of position and momentum obtained in an individual measurement and \\sigma_{x}, \\sigma_{p} their standard deviations in an ensemble of individual measurements on similarly prepared systems, then \"There are, in principle, no restrictions on the precisions of individual measurements \\delta x and \\delta p, but the standard deviations will always satisfy \\sigma_{x}\\sigma_{p} \\ge \\hbar/2\". )","Uncertainty principle\n\nSince the uncertainty principle is such a basic result in quantum mechanics, typical experiments in quantum mechanics routinely observe aspects of it. Certain experiments, however, may deliberately test a particular form of the uncertainty principle as part of their main research program. These include, for example, tests of number–phase uncertainty relations in superconducting or quantum optics systems. Applications dependent on the uncertainty principle for their operation include extremely low noise technology such as that required in gravitational-wave interferometers.","Uncertainty principle\n\nIntroduction","Uncertainty principle\n\nThe uncertainty principle is not readily apparent on the macroscopic scales of everyday experience. So it is helpful to demonstrate how it applies to more easily understood physical situations. Two alternative frameworks for quantum physics offer different explanations for the uncertainty principle. The wave mechanics picture of the uncertainty principle is more visually intuitive, but the more abstract matrix mechanics picture formulates it in a way that generalizes more easily.","Uncertainty principle\n\nMathematically, in wave mechanics, the uncertainty relation between position and momentum arises because the expressions of the wavefunction in the two corresponding orthonormal bases in Hilbert space are Fourier transforms of one another (i.e., position and momentum are conjugate variables). A nonzero function and its Fourier transform cannot both be sharply localized. A similar tradeoff between the variances of Fourier conjugates arises in all systems underlain by Fourier analysis, for example in sound waves: A pure tone is a sharp spike at a single frequency, while its Fourier transform gives the shape of the sound wave in the time domain, which is a completely delocalized sine wave. In quantum mechanics, the two key points are that the position of the particle takes the form of a matter wave, and momentum is its Fourier conjugate, assured by the de Broglie relation , where is the wavenumber.","Uncertainty principle\n\nIn matrix mechanics, the mathematical formulation of quantum mechanics, any pair of non-commuting self-adjoint operators representing observables are subject to similar uncertainty limits. An eigenstate of an observable represents the state of the wavefunction for a certain measurement value (the eigenvalue). For example, if a measurement of an observable is performed, then the system is in a particular eigenstate of that observable. However, the particular eigenstate of the observable need not be an eigenstate of another observable : If so, then it does not have a unique associated measurement for it, as the system is not in an eigenstate of that observable.","Uncertainty principle\n\nWave mechanics interpretation","Uncertainty principle\n\n(Ref )","Uncertainty principle\n\nAccording to the de Broglie hypothesis, every object in the universe is a wave, a situation which gives rise to this phenomenon. The position of the particle is described by a wave function \\Psi(x,t). The time-independent wave function of a single-moded plane wave of wavenumber k0 or momentum p0 is","Uncertainty principle\n\n\\psi(x) \\propto e^{ik_0 x} = e^{ip_0 x/\\hbar} ~.","Uncertainty principle\n\nThe Born rule states that this should be interpreted as a probability density amplitude function in the sense that the probability of finding the particle between a and b is","Uncertainty principle\n\n\\operatorname P [a \\leq X \\leq b] = \\int_a^b |\\psi(x)|^2 \\, \\mathrm{d}x ~.","Uncertainty principle\n\nIn the case of the single-moded plane wave, |\\psi(x)|^2 is a uniform distribution. In other words, the particle position is extremely uncertain in the sense that it could be essentially anywhere along the wave packet. Consider a wave function that is a sum of many waves, however, we may write this as","Uncertainty principle\n\n\\psi(x) \\propto \\sum_{n} A_n e^{i p_n x/\\hbar}~, \nwhere An represents the relative contribution of the mode pn to the overall total. The figures to the right show how with the addition of many plane waves, the wave packet can become more localized. We may take this a step further to the continuum limit, where the wave function is an integral over all possible modes","Uncertainty principle\n\n\\psi(x) = \\frac{1}{\\sqrt{2 \\pi \\hbar}} \\int_{-\\infty}^{\\infty} \\phi(p) \\cdot e^{i p x/\\hbar}\\, dp ~,","Uncertainty principle\n\nwith \\phi(p) representing the amplitude of these modes and is called the wave function in momentum space. In mathematical terms, we say that \\phi(p) is the Fourier transform of \\psi(x) and that x and p are conjugate variables. Adding together all of these plane waves comes at a cost, namely the momentum has become less precise, having become a mixture of waves of many different momenta.","Uncertainty principle\n\nOne way to quantify the precision of the position and momentum is the standard deviation σ. Since |\\psi(x)|^2 is a probability density function for position, we calculate its standard deviation.","Uncertainty principle\n\nThe precision of the position is improved, i.e. reduced σx, by using many plane waves, thereby weakening the precision of the momentum, i.e. increased σp. Another way of stating this is that σx and σp have an inverse relationship or are at least bounded from below. This is the uncertainty principle, the exact limit of which is the Kennard bound. Click the show button below to see a semi-formal derivation of the Kennard inequality using wave mechanics.","Uncertainty principle\n\nMatrix mechanics interpretation","Uncertainty principle\n\n(Ref )","Uncertainty principle\n\nIn matrix mechanics, observables such as position and momentum are represented by self-adjoint operators. When considering pairs of observables, an important quantity is the commutator. For a pair of operators and , one defines their commutator as\n[\\hat{A},\\hat{B}]=\\hat{A}\\hat{B}-\\hat{B}\\hat{A}.\nIn the case of position and momentum, the commutator is the canonical commutation relation\n[\\hat{x},\\hat{p}]=i \\hbar.","Uncertainty principle\n\nThe physical meaning of the non-commutativity can be understood by considering the effect of the commutator on position and momentum eigenstates. Let |\\psi\\rangle be a right eigenstate of position with a constant eigenvalue . By definition, this means that \\hat{x}|\\psi\\rangle = x_0 |\\psi\\rangle. Applying the commutator to |\\psi\\rangle yields\n[\\hat{x},\\hat{p}] | \\psi \\rangle (\\hat{x}\\hat{p}-\\hat{p}\\hat{x}) | \\psi \\rangle \n (\\hat{x} - x_0 \\hat{I}) \\cdot \\hat{p} \\, | \\psi \\rangle = i \\hbar | \\psi \\rangle,\nwhere is the identity operator.","Uncertainty principle\n\nSuppose, for the sake of proof by contradiction, that |\\psi\\rangle is also a right eigenstate of momentum, with constant eigenvalue . If this were true, then one could write\n(\\hat{x} - x_0 \\hat{I}) \\cdot \\hat{p} \\, | \\psi \\rangle (\\hat{x} - x_0 \\hat{I}) \\cdot p_0 \\, | \\psi \\rangle \n (x_0 \\hat{I} - x_0 \\hat{I}) \\cdot p_0 \\, | \\psi \\rangle=0.\nOn the other hand, the above canonical commutation relation requires that\n[\\hat{x},\\hat{p}] | \\psi \\rangle=i \\hbar | \\psi \\rangle \\ne 0.\nThis implies that no quantum state can simultaneously be both a position and a momentum eigenstate.","Uncertainty principle\n\nWhen a state is measured, it is projected onto an eigenstate in the basis of the relevant observable. For example, if a particle's position is measured, then the state amounts to a position eigenstate. This means that the state is not a momentum eigenstate, however, but rather it can be represented as a sum of multiple momentum basis eigenstates. In other words, the momentum must be less precise. This precision may be quantified by the standard deviations, \n\\sigma_{x}=\\sqrt{\\langle \\hat{x}^{2} \\rangle-\\langle \\hat{x}\\rangle ^{2}}\n\\sigma_{p}=\\sqrt{\\langle \\hat{p}^{2} \\rangle-\\langle \\hat{p}\\rangle ^{2}}.","Uncertainty principle\n\nAs in the wave mechanics interpretation above, one sees a tradeoff between the respective precisions of the two, quantified by the uncertainty principle.","Uncertainty principle\n\nRobertson–Schrödinger uncertainty relations","Uncertainty principle\n\nThe most common general form of the uncertainty principle is the Robertson uncertainty relation.","Uncertainty principle\n\nFor an arbitrary Hermitian operator \\hat{\\mathcal{O}} we can associate a standard deviation","Uncertainty principle\n\n::\\sigma_{\\mathcal{O}}=\\sqrt{\\langle \\hat{\\mathcal{O}}^2 \\rangle-\\langle \\hat{\\mathcal{O}}\\rangle^2},","Uncertainty principle\n\nwhere the brackets \\langle\\mathcal{O}\\rangle indicate an expectation value. For a pair of operators and , we may define their commutator as","Uncertainty principle\n\n::[\\hat{A},\\hat{B}]=\\hat{A}\\hat{B}-\\hat{B}\\hat{A},","Uncertainty principle\n\nIn this notation, the Robertson uncertainty relation is given by","Uncertainty principle\n\n:: \\sigma_{A}\\sigma_{B} \\geq \\left| \\frac{1}{2i}\\langle[\\hat{A},\\hat{B}]\\rangle \\right| = \\frac{1}{2}\\left|\\langle[\\hat{A},\\hat{B}]\\rangle \\right|,","Uncertainty principle\n\nThe Robertson uncertainty relation immediately follows from a slightly stronger inequality, the Schrödinger uncertainty relation,","Uncertainty principle\n\nwhere we have introduced the anticommutator,\n::\\{\\hat{A},\\hat{B}\\}=\\hat{A}\\hat{B}+\\hat{B}\\hat{A}.","Uncertainty principle\n\nSince the Robertson and Schrödinger relations are for general operators, the relations can be applied to any two observables to obtain specific uncertainty relations. A few of the most common relations found in the literature are given below.\n* For position and linear momentum, the canonical commutation relation [\\hat{x},\\hat{p}]=i\\hbar implies the Kennard inequality from above:","Uncertainty principle\n\n: \\sigma_{x}\\sigma_{p} \\geq \\frac{\\hbar}{2}\n* For two orthogonal components of the total angular momentum operator of an object:","Uncertainty principle\n\n: \\sigma_{J_i} \\sigma_{J_j} \\geq \\tfrac{\\hbar}{2} \\left|\\left\\langle J_k\\right\\rangle\\right|, ~\n: where i, j, k are distinct and Ji denotes angular momentum along the xi axis. This relation implies that unless all three components vanish together, only a single component of a system's angular momentum can be defined with arbitrary precision, normally the component parallel to an external (magnetic or electric) field. Moreover, for [{J_x}, {J_y}] i \\hbar \\epsilon_{xyz} {J_z} , a choice \\hat{A}\n J_x, ~~\\hat{B}J_y, in angular momentum multiplets, ψ \n |j, m 〉, bounds the Casimir invariant (angular momentum squared, \\langle J_x^2+ J_y^2 + J_z^2 \\rangle ) from below and thus yields useful constraints such as j (j + 1) ≥ m (m + 1), and hence j ≥ m, among others.\n* In non-relativistic mechanics, time is privileged as an independent variable. Nevertheless, in 1945, L. I. Mandelshtam and I. E. Tamm derived a non-relativistic time–energy uncertainty relation, as follows. For a quantum system in a non-stationary state and an observable B represented by a self-adjoint operator \\hat B, the following formula holds:","Uncertainty principle\n\n: \\sigma_E ~ \\frac{\\sigma_B}{\\left| \\frac{\\mathrm{d}\\langle \\hat B \\rangle}{\\mathrm{d}t}\\right |} \\ge \\frac{\\hbar}{2}.","Uncertainty principle\n\nwhere σE is the standard deviation of the energy operator (Hamiltonian) in the state , σB stands for the standard deviation of B. Although the second factor in the left-hand side has dimension of time, it is different from the time parameter that enters the Schrödinger equation. It is a lifetime of the state with respect to the observable B: In other words, this is the time interval (Δt) after which the expectation value \\langle\\hat B\\rangle changes appreciably. An informal, heuristic meaning of the principle is the following: A state that only exists for a short time cannot have a definite energy. To have a definite energy, the frequency of the state must be defined accurately, and this requires the state to hang around for many cycles, the reciprocal of the required accuracy. For example, in spectroscopy, excited states have a finite lifetime. By the time–energy uncertainty principle, they do not have a definite energy, and, each time they decay, the energy they release is slightly different. The average energy of the outgoing photon has a peak at the theoretical energy of the state, but the distribution has a finite width called the natural linewidth.","Uncertainty principle\n\nFast-decaying states have a broad linewidth, while slow decaying states have a narrow linewidth. The same linewidth effect also makes it difficult to specify the rest mass of unstable, fast-decaying particles in particle physics. The faster the particle decays (the shorter its lifetime), the less certain is its mass (the larger the particle's width). * For the number of electrons in a superconductor and the phase of its Ginzburg–Landau order parameter","Uncertainty principle\n\n: \\Delta N \\Delta \\phi \\geq 1. ~","Uncertainty principle\n\nExamples","Uncertainty principle\n\n(Refs )","Uncertainty principle\n\nQuantum harmonic oscillator stationary states","Uncertainty principle\n\nConsider a one-dimensional quantum harmonic oscillator (QHO). It is possible to express the position and momentum operators in terms of the creation and annihilation operators:\n\\hat x = \\sqrt{\\frac{\\hbar}{2m\\omega}}(a+a^{\\dagger})\n\\hat p = i\\sqrt{\\frac{m \\omega\\hbar}{2}}(a^{\\dagger}-a).","Uncertainty principle\n\nUsing the standard rules for creation and annihilation operators on the eigenstates of the QHO,\na^{\\dagger}|n\\rangle=\\sqrt{n+1}|n+1\\rangle\na|n\\rangle=\\sqrt{n}|n-1\\rangle ~ , \nthe variances may be computed directly,\n\\sigma_x^2 = \\frac{\\hbar}{m\\omega} \\left( n+\\frac{1}{2}\\right)\n\\sigma_p^2 = \\hbar m\\omega \\left( n+\\frac{1}{2}\\right)\\, .\nThe product of these standard deviations is then\n\\sigma_x \\sigma_p = \\hbar \\left(n+\\frac{1}{2}\\right) \\ge \\frac{\\hbar}{2}.~","Uncertainty principle\n\nIn particular, the above Kennard bound is saturated for the ground state , for which the probability density is just the normal distribution.","Uncertainty principle\n\nQuantum harmonic oscillator with Gaussian initial condition","Uncertainty principle\n\nIn a quantum harmonic oscillator of characteristic angular frequency ω, place a state that is offset from the bottom of the potential by some displacement x0 as\n\\psi(x)=\\left(\\frac{m \\Omega}{\\pi \\hbar}\\right)^{1/4} \\exp{\\left( -\\frac{m \\Omega (x-x_0)^2}{2\\hbar}\\right)},\nwhere Ω describes the width of the initial state but need not be the same as ω. Through integration over the propagator, we can solve for the -dependent solution. After many cancelations, the probability densities reduce to\n|\\Psi(x,t)|^2 \\sim \\mathcal{N}\\left( x_0 \\cos{(\\omega t)} , \\frac{\\hbar}{2 m \\Omega} \\left( \\cos^2{(\\omega t)} + \\frac{\\Omega^2}{\\omega^2} \\sin^2{(\\omega t)} \\right)\\right)\n|\\Phi(p,t)|^2 \\sim \\mathcal{N}\\left( -m x_0 \\omega \\sin{(\\omega t)} , \\frac{\\hbar m \\Omega}{2} \\left( \\cos^2{(\\omega t)} + \\frac{\\omega^2}{\\Omega^2} \\sin^2{(\\omega t)} \\right)\\right),\nwhere we have used the notation \\mathcal{N}(\\mu, \\sigma^2) to denote a normal distribution of mean μ and variance σ2. Copying the variances above and applying trigonometric identities, we can write the product of the standard deviations as\n\\begin{align}\\sigma_x \\sigma_p&=\\frac{\\hbar}{2}\\sqrt{\\left( \\cos^2{(\\omega t)} + \\frac{\\Omega^2}{\\omega^2} \\sin^2{(\\omega t)} \\right)\\left( \\cos^2{(\\omega t)} + \\frac{\\omega^2}{\\Omega^2} \\sin^2{(\\omega t)} \\right)} \\\\\n&= \\frac{\\hbar}{4}\\sqrt{3+\\frac{1}{2}\\left(\\frac{\\Omega^2}{\\omega^2}+\\frac{\\omega^2}{\\Omega^2}\\right)-\\left(\\frac{1}{2}\\left(\\frac{\\Omega^2}{\\omega^2}+\\frac{\\omega^2}{\\Omega^2}\\right)-1\\right) \\cos{(4 \\omega t)}}\\end{align}\nFrom the relations\n\\frac{\\Omega^2}{\\omega^2}+\\frac{\\omega^2}{\\Omega^2} \\ge 2, \\, \\, \\, |\\cos{(4 \\omega t)}| \\le 1,\nwe can conclude\n\\sigma_x \\sigma_p \\ge \\frac{\\hbar}{4}\\sqrt{3+\\frac{1}{2}\\left(\\frac{\\Omega^2}{\\omega^2}+\\frac{\\omega^2}{\\Omega^2}\\right)-\\left(\\frac{1}{2}\\left(\\frac{\\Omega^2}{\\omega^2}+\\frac{\\omega^2}{\\Omega^2}\\right)-1\\right)} = \\frac{\\hbar}{2}.","Uncertainty principle\n\nCoherent states","Uncertainty principle\n\nA coherent state is a right eigenstate of the annihilation operator,\n\\hat{a}|\\alpha\\rangle=\\alpha|\\alpha\\rangle,\nwhich may be represented in terms of Fock states as\n|\\alpha\\rangle e^{- \\bigl(\\|f\\|_{L^2(S^c)} + \\| \\hat{f} \\|_{L^2(\\Sigma^c)} \\bigr) ~.","Uncertainty principle\n\nOne expects that the factor may be replaced by , \nwhich is only known if either or is convex.","Uncertainty principle\n\nHardy's uncertainty principle","Uncertainty principle\n\nThe mathematician G. H. Hardy formulated the following uncertainty principle: it is not possible for and to both be \"very rapidly decreasing.\" Specifically, if in is such that\n|f(x)|\\leq C(1+|x|)^Ne^{-a\\pi x^2}\nand\n|\\hat{f}(\\xi)|\\leq C(1+|\\xi|)^Ne^{-b\\pi \\xi^2} (C>0,N an integer),","Uncertainty principle\n\nthen, if , while if , then there is a polynomial of degree such that","Uncertainty principle\n\n:f(x)=P(x)e^{-a\\pi x^2}. \\,","Uncertainty principle\n\nThis was later improved as follows: if is such that","Uncertainty principle\n\n\\int_{\\mathbf{R}^d}\\int_{\\mathbf{R}^d}|f(x)||\\hat{f}(\\xi)|\\frac{e^{\\pi|\\langle x,\\xi\\rangle|}}{(1+|x|+|\\xi|)^N} \\, dx \\, d\\xi \nthen\n:f(x)=P(x)e^{-\\pi\\langle Ax,x\\rangle} ~,\nwhere is a polynomial of degree and is a real positive definite matrix.","Uncertainty principle\n\nThis result was stated in Beurling's complete works without proof and proved in Hörmander (the case d1,N\n0) and Bonami, Demange, and Jaming for the general case. Note that Hörmander–Beurling's version implies the case in Hardy's Theorem while the version by Bonami–Demange–Jaming covers the full strength of Hardy's Theorem. A different proof of Beurling's theorem based on Liouville's theorem appeared in\nref.","Uncertainty principle\n\nA full description of the case as well as the following extension to Schwartz class distributions appears in ref.","Uncertainty principle\n\nTheorem. If a tempered distribution f\\in\\mathcal{S}'(\\R^d) is such that","Uncertainty principle\n\ne^{\\pi|x|^2}f\\in\\mathcal{S} '(\\R^d)\nand\ne^{\\pi|\\xi|^2}\\hat f\\in\\mathcal{S}'(\\R^d) ~,\nthen\n:f(x)=P(x)e^{-\\pi\\langle Ax,x\\rangle} ~,\nfor some convenient polynomial and real positive definite matrix of type .","Uncertainty principle\n\nHistory","Uncertainty principle\n\nWerner Heisenberg formulated the Uncertainty Principle at Niels Bohr's institute in Copenhagen, while working on the mathematical foundations of quantum mechanics.","Uncertainty principle\n\nIn 1925, following pioneering work with Hendrik Kramers, Heisenberg developed matrix mechanics, which replaced the ad hoc old quantum theory with modern quantum mechanics. The central premise was that the classical concept of motion does not fit at the quantum level, as electrons in an atom do not travel on sharply defined orbits. Rather, their motion is smeared out in a strange way: the Fourier transform of its time dependence only involves those frequencies that could be observed in the quantum jumps of their radiation.","Uncertainty principle\n\nHeisenberg's paper did not admit any unobservable quantities like the exact position of the electron in an orbit at any time; he only allowed the theorist to talk about the Fourier components of the motion. Since the Fourier components were not defined at the classical frequencies, they could not be used to construct an exact trajectory, so that the formalism could not answer certain overly precise questions about where the electron was or how fast it was going.","Uncertainty principle\n\nIn March 1926, working in Bohr's institute, Heisenberg realized that the non-commutativity implies the uncertainty principle. This implication provided a clear physical interpretation for the non-commutativity, and it laid the foundation for what became known as the Copenhagen interpretation of quantum mechanics. Heisenberg showed that the commutation relation implies an uncertainty, or in Bohr's language a complementarity. Any two variables that do not commute cannot be measured simultaneously—the more precisely one is known, the less precisely the other can be known. Heisenberg wrote:It can be expressed in its simplest form as follows: One can never know with perfect accuracy both of those two important factors which determine the movement of one of the smallest particles—its position and its velocity. It is impossible to determine accurately both the position and the direction and speed of a particle at the same instant.","Uncertainty principle\n\nIn his celebrated 1927 paper, \"Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik\" (\"On the Perceptual Content of Quantum Theoretical Kinematics and Mechanics\"), Heisenberg established this expression as the minimum amount of unavoidable momentum disturbance caused by any position measurement, but he did not give a precise definition for the uncertainties Δx and Δp. Instead, he gave some plausible estimates in each case separately. In his Chicago lecture he refined his principle:","Uncertainty principle\n\nKennard in 1927 first proved the modern inequality:","Uncertainty principle\n\nwhere , and , are the standard deviations of position and momentum. Heisenberg only proved relation () for the special case of Gaussian states.","Uncertainty principle\n\nTerminology and translation","Uncertainty principle\n\nThroughout the main body of his original 1927 paper, written in German, Heisenberg used the word, \"Ungenauigkeit\" (\"indeterminacy\"),\nto describe the basic theoretical principle. Only in the endnote did he switch to the word, \"Unsicherheit\" (\"uncertainty\"). When the English-language version of Heisenberg's textbook, The Physical Principles of the Quantum Theory, was published in 1930, however, the translation \"uncertainty\" was used, and it became the more commonly used term in the English language thereafter.","Uncertainty principle\n\nHeisenberg's microscope","Uncertainty principle\n\nThe principle is quite counter-intuitive, so the early students of quantum theory had to be reassured that naive measurements to violate it were bound always to be unworkable. One way in which Heisenberg originally illustrated the intrinsic impossibility of violating the uncertainty principle is by using an imaginary microscope as a measuring device.","Uncertainty principle\n\nHe imagines an experimenter trying to measure the position and momentum of an electron by shooting a photon at it.\nProblem 1 – If the photon has a short wavelength, and therefore, a large momentum, the position can be measured accurately. But the photon scatters in a random direction, transferring a large and uncertain amount of momentum to the electron. If the photon has a long wavelength and low momentum, the collision does not disturb the electron's momentum very much, but the scattering will reveal its position only vaguely.","Uncertainty principle\n\nProblem 2 – If a large aperture is used for the microscope, the electron's location can be well resolved (see Rayleigh criterion); but by the principle of conservation of momentum, the transverse momentum of the incoming photon affects the electrons beamline momentum and hence, the new momentum of the electron resolves poorly. If a small aperture is used, the accuracy of both resolutions is the other way around.","Uncertainty principle\n\nThe combination of these trade-offs imply that no matter what photon wavelength and aperture size are used, the product of the uncertainty in measured position and measured momentum is greater than or equal to a lower limit, which is (up to a small numerical factor) equal to Planck's constant. Heisenberg did not care to formulate the uncertainty principle as an exact limit (which is elaborated below), and preferred to use it instead, as a heuristic quantitative statement, correct up to small numerical factors, which makes the radically new noncommutativity of quantum mechanics inevitable.","Uncertainty principle\n\nCritical reactions","Uncertainty principle\n\nThe Copenhagen interpretation of quantum mechanics and Heisenberg's Uncertainty Principle were, in fact, seen as twin targets by detractors who believed in an underlying determinism and realism. According to the Copenhagen interpretation of quantum mechanics, there is no fundamental reality that the quantum state describes, just a prescription for calculating experimental results. There is no way to say what the state of a system fundamentally is, only what the result of observations might be.","Uncertainty principle\n\nAlbert Einstein believed that randomness is a reflection of our ignorance of some fundamental property of reality, while Niels Bohr believed that the probability distributions are fundamental and irreducible, and depend on which measurements we choose to perform. Einstein and Bohr debated the uncertainty principle for many years. Some experiments within the first decade of the twenty-first century have cast doubt on observer effect aspects of the uncertainty principle.","Uncertainty principle\n\nEinstein's slit","Uncertainty principle\n\nThe first of Einstein's thought experiments challenging the uncertainty principle went as follows:","Uncertainty principle\n\nConsider a particle passing through a slit of width . The slit introduces an uncertainty in momentum of approximately because the particle passes through the wall. But let us determine the momentum of the particle by measuring the recoil of the wall. In doing so, we find the momentum of the particle to arbitrary accuracy by conservation of momentum.","Uncertainty principle\n\nBohr's response was that the wall is quantum mechanical as well, and that to measure the recoil to accuracy , the momentum of the wall must be known to this accuracy before the particle passes through. This introduces an uncertainty in the position of the wall and therefore the position of the slit equal to , and if the wall's momentum is known precisely enough to measure the recoil, the slit's position is uncertain enough to disallow a position measurement.","Uncertainty principle\n\nA similar analysis with particles diffracting through multiple slits is given by Richard Feynman.","Uncertainty principle\n\nEinstein's box","Uncertainty principle\n\nBohr was present when Einstein proposed the thought experiment which has become known as Einstein's box. Einstein argued that \"Heisenberg's uncertainty equation implied that the uncertainty in time was related to the uncertainty in energy, the product of the two being related to Planck's constant.\" Consider, he said, an ideal box, lined with mirrors so that it can contain light indefinitely. The box could be weighed before a clockwork mechanism opened an ideal shutter at a chosen instant to allow one single photon to escape. \"We now know, explained Einstein, precisely the time at which the photon left the box.\" \"Now, weigh the box again. The change of mass tells the energy of the emitted light. In this manner, said Einstein, one could measure the energy emitted and the time it was released with any desired precision, in contradiction to the uncertainty principle.\"","Uncertainty principle\n\nBohr spent a sleepless night considering this argument, and eventually realized that it was flawed. He pointed out that if the box were to be weighed, say by a spring and a pointer on a scale, \"since the box must move vertically with a change in its weight, there will be uncertainty in its vertical velocity and therefore an uncertainty in its height above the table. ... Furthermore, the uncertainty about the elevation above the earth's surface will result in an uncertainty in the rate of the clock,\" because of Einstein's own theory of gravity's effect on time.\n\"Through this chain of uncertainties, Bohr showed that Einstein's light box experiment could not simultaneously measure exactly both the energy of the photon and the time of its escape.\"","Uncertainty principle\n\nEPR paradox for entangled particles","Uncertainty principle\n\nBohr was compelled to modify his understanding of the uncertainty principle after another thought experiment by Einstein. In 1935, Einstein, Podolsky and Rosen (see EPR paradox) published an analysis of widely separated entangled particles. Measuring one particle, Einstein realized, would alter the probability distribution of the other, yet here the other particle could not possibly be disturbed. This example led Bohr to revise his understanding of the principle, concluding that the uncertainty was not caused by a direct interaction.","Uncertainty principle\n\nBut Einstein came to much more far-reaching conclusions from the same thought experiment. He believed the \"natural basic assumption\" that a complete description of reality, would have to predict the results of experiments from \"locally changing deterministic quantities\", and therefore, would have to include more information than the maximum possible allowed by the uncertainty principle.","Uncertainty principle\n\nIn 1964, John Bell showed that this assumption can be falsified, since it would imply a certain inequality between the probabilities of different experiments. Experimental results confirm the predictions of quantum mechanics, ruling out Einstein's basic assumption that led him to the suggestion of his hidden variables. Ironically this fact is one of the best pieces of evidence supporting Karl Popper's philosophy of invalidation of a theory by falsification-experiments. That is to say, here Einstein's \"basic assumption\" became falsified by experiments based on Bell's inequalities. For the objections of Karl Popper to the Heisenberg inequality itself, see below.","Uncertainty principle\n\nWhile it is possible to assume that quantum mechanical predictions are due to nonlocal, hidden variables, and in fact David Bohm invented such a formulation, this resolution is not satisfactory to the vast majority of physicists. The question of whether a random outcome is predetermined by a nonlocal theory can be philosophical, and it can be potentially intractable. If the hidden variables are not constrained, they could just be a list of random digits that are used to produce the measurement outcomes. To make it sensible, the assumption of nonlocal hidden variables is sometimes augmented by a second assumption—that the size of the observable universe puts a limit on the computations that these variables can do. A nonlocal theory of this sort predicts that a quantum computer would encounter fundamental obstacles when attempting to factor numbers of approximately 10,000 digits or more; a potentially achievable task in quantum mechanics.","Uncertainty principle\n\nPopper's criticism","Uncertainty principle\n\nKarl Popper approached the problem of indeterminacy as a logician and metaphysical realist. He disagreed with the application of the uncertainty relations to individual particles rather than to ensembles of identically prepared particles, referring to them as \"statistical scatter relations\". In this statistical interpretation, a particular measurement may be made to arbitrary precision without invalidating the quantum theory. This directly contrasts with the Copenhagen interpretation of quantum mechanics, which is non-deterministic but lacks local hidden variables.","Uncertainty principle\n\nIn 1934, Popper published Zur Kritik der Ungenauigkeitsrelationen (Critique of the Uncertainty Relations) in Naturwissenschaften, and in the same year Logik der Forschung (translated and updated by the author as The Logic of Scientific Discovery in 1959), outlining his arguments for the statistical interpretation. In 1982, he further developed his theory in Quantum theory and the schism in Physics, writing:\n[Heisenberg's] formulae are, beyond all doubt, derivable statistical formulae of the quantum theory. But they have been habitually misinterpreted by those quantum theorists who said that these formulae can be interpreted as determining some upper limit to the precision of our measurements.[original emphasis]","Uncertainty principle\n\nPopper proposed an experiment to falsify the uncertainty relations, although he later withdrew his initial version after discussions with Weizsäcker, Heisenberg, and Einstein; this experiment may have influenced the formulation of the EPR experiment.","Uncertainty principle\n\nMany-worlds uncertainty","Uncertainty principle\n\nThe many-worlds interpretation originally outlined by Hugh Everett III in 1957 is partly meant to reconcile the differences between Einstein's and Bohr's views by replacing Bohr's wave function collapse with an ensemble of deterministic and independent universes whose distribution is governed by wave functions and the Schrödinger equation. Thus, uncertainty in the many-worlds interpretation follows from each observer within any universe having no knowledge of what goes on in the other universes.","Uncertainty principle\n\nFree will","Uncertainty principle\n\nSome scientists including Arthur Compton and Martin Heisenberg have suggested that the uncertainty principle, or at least the general probabilistic nature of quantum mechanics, could be evidence for the two-stage model of free will. One critique, however, is that apart from the basic role of quantum mechanics as a foundation for chemistry, nontrivial biological mechanisms requiring quantum mechanics are unlikely, due to the rapid decoherence time of quantum systems at room temperature. The standard view, however, is that this decoherence is overcome by both screening and decoherence-free subspaces found in biological cells."],"string":"[\n \"Werner Heisenberg\\n\\nWerner Karl Heisenberg (; 5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the key pioneers of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent series of papers with Max Born and Pascual Jordan, during the same year, this matrix formulation of quantum mechanics was substantially elaborated. In 1927 he published his uncertainty principle, upon which he built his philosophy and for which he is best known. Heisenberg was awarded the Nobel Prize in Physics for 1932 \\\"for the creation of quantum mechanics\\\". He also made important contributions to the theories of the hydrodynamics of turbulent flows, the atomic nucleus, ferromagnetism, cosmic rays, and subatomic particles, and he was instrumental in planning the first West German nuclear reactor at Karlsruhe, together with a research reactor in Munich, in 1957. Considerable controversy surrounds his work on atomic research during World War II.\",\n \"Werner Heisenberg\\n\\nFollowing World War II, he was appointed director of the Kaiser Wilhelm Institute for Physics, which soon thereafter was renamed the Max Planck Institute for Physics. He was director of the institute until it was moved to Munich in 1958, when it was expanded and renamed the Max Planck Institute for Physics and Astrophysics.\",\n \"Werner Heisenberg\\n\\nHeisenberg was also president of the German Research Council, chairman of the Commission for Atomic Physics, chairman of the Nuclear Physics Working Group, and president of the Alexander von Humboldt Foundation.\",\n \"Werner Heisenberg\\n\\nLife and career\",\n \"Werner Heisenberg\\n\\nEarly years\",\n \"Werner Heisenberg\\n\\nWerner Karl Heisenberg was born in Würzburg, Germany, to Kaspar Ernst August Heisenberg, a secondary school teacher of classical languages who became Germany's only ordentlicher Professor (ordinarius professor) of medieval and modern Greek studies in the university system, and his wife, Annie Wecklein.\",\n \"Werner Heisenberg\\n\\nHe studied physics and mathematics from 1920 to 1923 at the Ludwig-Maximilians-Universität München and the Georg-August-Universität Göttingen. At Munich, he studied under Arnold Sommerfeld and Wilhelm Wien. At Göttingen, he studied physics with Max Born and James Franck, and he studied mathematics with David Hilbert. He received his doctorate in 1923, at Munich under Sommerfeld. He completed his Habilitation in 1924, at Göttingen under Born.\",\n \"Werner Heisenberg\\n\\nBecause Sommerfeld had a sincere interest in his students and knew of Heisenberg's interest in Niels Bohr's theories on atomic physics, Sommerfeld took Heisenberg to Göttingen to the Bohr-Festspiele (Bohr Festival) in June 1922. At the event, Bohr was a guest lecturer and gave a series of comprehensive lectures on quantum atomic physics. There, Heisenberg met Bohr for the first time, and it had a significant and continuing effect on him.\",\n \"Werner Heisenberg\\n\\nHeisenberg's doctoral thesis, the topic of which was suggested by Sommerfeld, was on turbulence; the thesis discussed both the stability of laminar flow and the nature of turbulent flow. The problem of stability was investigated by the use of the Orr–Sommerfeld equation, a fourth order linear differential equation for small disturbances from laminar flow. He briefly returned to this topic after World War II.\",\n \"Werner Heisenberg\\n\\nHeisenberg's paper on the anomalous Zeeman effect was accepted as his Habilitationsschrift (Habilitation thesis) under Max Born at Göttingen.\",\n \"Werner Heisenberg\\n\\nIn his youth he was a member and Scoutleader of the Neupfadfinder, a German Scout association and part of the German Youth Movement. In August 1923 Robert Honsell and Heisenberg organized a trip (Großfahrt) to Finland with a Scout group of this association from Munich. \\nHeisenberg arrived at Munich in 1919 as a member of Freikorps to fight the Bavarian Soviet Republic established a year earlier. Five decades later he recalled those days as youthful fun, like \\\"playing cops and robbers and so on; it was nothing serious at all.\\\"\",\n \"Werner Heisenberg\\n\\nCareer\",\n \"Werner Heisenberg\\n\\nGöttingen, Copenhagen, and Leipzig\",\n \"Werner Heisenberg\\n\\nFrom 1924 to 1927, Heisenberg was a Privatdozent at Göttingen. From 17 September 1924 to 1 May 1925, under an International Education Board Rockefeller Foundation fellowship, Heisenberg went to do research with Niels Bohr, director of the Institute of Theoretical Physics at the University of Copenhagen. His seminal paper, Über quantentheoretischer Umdeutung was published in September 1925. He returned to Göttingen and with Max Born and Pascual Jordan, over a period of about six months, developed the matrix mechanics formulation of quantum mechanics. On 1 May 1926, Heisenberg began his appointment as a university lecturer and assistant to Bohr in Copenhagen. It was in Copenhagen, in 1927, that Heisenberg developed his uncertainty principle, while working on the mathematical foundations of quantum mechanics. On 23 February, Heisenberg wrote a letter to fellow physicist Wolfgang Pauli, in which he first described his new principle. In his paper on the uncertainty principle, Heisenberg used the word \\\"Ungenauigkeit\\\" (imprecision).\",\n \"Werner Heisenberg\\n\\nIn 1927, Heisenberg was appointed ordentlicher Professor (ordinarius professor) of theoretical physics and head of the department of physics at the Universität Leipzig; he gave his inaugural lecture on 1 February 1928. In his first paper published from Leipzig, Heisenberg used the Pauli exclusion principle to solve the mystery of ferromagnetism.\",\n \"Werner Heisenberg\\n\\nIn Heisenberg's tenure at Leipzig, the quality of doctoral students, post-graduate and research associates who studied and worked with Heisenberg there is attested to by the acclaim later earned by these people; at various times, they included: Erich Bagge, Felix Bloch, Ugo Fano, Siegfried Flügge, William Vermillion Houston, Friedrich Hund, Robert S. Mulliken, Rudolf Peierls, George Placzek, Isidor Isaac Rabi, Fritz Sauter, John C. Slater, Edward Teller, John Hasbrouck van Vleck, Victor Frederick Weisskopf, Carl Friedrich von Weizsäcker, Gregor Wentzel and Clarence Zener.\",\n \"Werner Heisenberg\\n\\nIn early 1929, Heisenberg and Pauli submitted the first of two papers laying the foundation for relativistic quantum field theory. Also in 1929, Heisenberg went on a lecture tour in China, Japan, India, and the United States.\",\n \"Werner Heisenberg\\n\\nShortly after the discovery of the neutron by James Chadwick in 1932, Heisenberg submitted the first of three papers on his neutron-proton model of the nucleus. He was awarded the 1932 Nobel Prize in Physics.\",\n \"Werner Heisenberg\\n\\nIn 1928, the British mathematical physicist P. A. M. Dirac had derived the relativistic wave equation of quantum mechanics, which implied the existence of positive electrons, later to be named positrons. In 1932, from a cloud chamber photograph of cosmic rays, the American physicist Carl David Anderson identified a track as having been made by a positron. In mid-1933, Heisenberg presented his theory of the positron. His thinking on Dirac's theory and further development of the theory were set forth in two papers. The first, Bemerkungen zur Diracschen Theorie des Positrons (Remarks on Dirac's theory of the positron) was published in 1934, and the second, Folgerungen aus der Diracschen Theorie des Positrons (Consequences of Dirac's Theory of the Positron), was published in 1936. In these papers Heisenberg was the first to reinterpret the Dirac equation as a \\\"classical\\\" field equation for any point particle of spin ħ/2, itself subject to quantization conditions involving anti-commutators. Thus reinterpreting it as a (quantum) field equation accurately describing electrons, Heisenberg put matter on the same footing as electromagnetism: as being described by relativistic quantum field equations which allowed the possibility of particle creation and destruction.\",\n \"Werner Heisenberg\\n\\n(Hermann Weyl had already described this in a 1929 letter to Einstein.)\",\n \"Werner Heisenberg\\n\\nIn the early 1930s in Germany, the Deutsche Physik movement was anti-Semitic and anti-theoretical physics, especially including quantum mechanics and the theory of relativity. As applied in the university environment, political factors took priority over the historically applied concept of scholarly ability, even though its two most prominent supporters were the Nobel Laureates in Physics Philipp Lenard and Johannes Stark.\",\n \"Werner Heisenberg\\n\\nAfter Adolf Hitler came to power in 1933, Heisenberg was attacked in the press as a \\\"White Jew\\\" by elements of the Deutsche Physik (German Physics) movement for his insistence on teaching about the roles of Jewish scientists. As a result, he came under investigation by the SS. This was over an attempt to appoint Heisenberg as successor to Arnold Sommerfeld at the University of Munich. The issue was resolved in 1938 by Heinrich Himmler, head of the SS. While Heisenberg was not chosen as Sommerfeld's successor, he was rehabilitated to the physics community during the Third Reich. Nevertheless, supporters of Deutsche Physik launched vicious attacks against leading theoretical physicists, including Arnold Sommerfeld and Heisenberg. On 29 June 1936, a National Socialist Party newspaper published a column attacking Heisenberg. On 15 July 1937, he was attacked in a journal of the SS. This was the beginning of what is called the Heisenberg Affair.\",\n \"Werner Heisenberg\\n\\nIn mid-1936, Heisenberg presented his theory of cosmic-ray showers in two papers. Four more papers appeared in the next two years.\",\n \"Werner Heisenberg\\n\\nIn June 1939, Heisenberg bought a summer home for his family in Urfeld am Walchensee, in southern Germany. He also traveled to the United States in June and July, visiting Samuel Abraham Goudsmit, at the University of Michigan in Ann Arbor. However, Heisenberg refused an invitation to emigrate to the United States. He did not see Goudsmit again until six years later, when Goudsmit was the chief scientific advisor to the American Operation Alsos at the close of World War II. Ironically, Heisenberg was arrested under Operation Alsos and detained in England under Operation Epsilon.\",\n \"Werner Heisenberg\\n\\nMatrix mechanics and the Nobel Prize\",\n \"Werner Heisenberg\\n\\nHeisenberg’s paper establishing quantum mechanics has puzzled physicists and historians. His methods assume that the reader is familiar with Kramers-Heisenberg transition probability calculations. The main new idea, noncommuting matrices, is justified only by a rejection of unobservable quantities. It introduces the non-commutative multiplication of matrices by physical reasoning, based on the correspondence principle, despite the fact that Heisenberg was not then familiar with the mathematical theory of matrices. The path leading to these results has been reconstructed in MacKinnon, 1977, and the detailed calculations are worked out in Aitchison et al.\",\n \"Werner Heisenberg\\n\\nIn Copenhagen, Heisenberg and Hans Kramers collaborated on a paper on dispersion, or the scattering from atoms of radiation whose wavelength is larger than the atoms. They showed that the successful formula Kramers had developed earlier could not be based on Bohr orbits, because the transition frequencies are based on level spacings which are not constant. The frequencies which occur in the Fourier transform of sharp classical orbits, by contrast, are equally spaced. But these results could be explained by a semi-classical Virtual State model: the incoming radiation excites the valence, or outer, electron to a virtual state from which it decays. In a subsequent paper Heisenberg showed that this virtual oscillator model could also explain the polarization of fluorescent radiation.\",\n \"Werner Heisenberg\\n\\nThese two successes, and the continuing failure of the Bohr-Sommerfeld model to explain the outstanding problem of the anomalous Zeeman effect, led Heisenberg to use the virtual oscillator model to try to calculate spectral frequencies. The method proved too difficult to immediately apply to realistic problems, so Heisenberg turned to a simpler example, the anharmonic oscillator.\",\n \"Werner Heisenberg\\n\\nThe dipole oscillator consists of a simple harmonic oscillator, which is thought of as a charged particle on a spring, perturbed by an external force, like an external charge. The motion of the oscillating charge can be expressed as a Fourier series in the frequency of the oscillator. Heisenberg solved for the quantum behavior by two different methods. First, he treated the system with the virtual oscillator method, calculating the transitions between the levels that would be produced by the external source.\",\n \"Werner Heisenberg\\n\\nHe then solved the same problem by treating the anharmonic potential term as a perturbation to the harmonic oscillator and using the perturbation methods that he and Born had developed. Both methods led to the same results for the first and the very complicated second order correction terms. This suggested that behind the very complicated calculations lay a consistent scheme.\",\n \"Werner Heisenberg\\n\\nSo Heisenberg set out to formulate these results without any explicit dependence on the virtual oscillator model. To do this, he replaced the Fourier expansions for the spatial coordinates by matrices, matrices which corresponded to the transition coefficients in the virtual oscillator method. He justified this replacement by an appeal to Bohr’s correspondence principle and the Pauli doctrine that quantum mechanics must be limited to observables.\",\n \"Werner Heisenberg\\n\\nOn 9 July, Heisenberg gave Born this paper to review and submit for publication. When Born read the paper, he recognized the formulation as one which could be transcribed and extended to the systematic language of matrices, which he had learned from his study under Jakob Rosanes at Breslau University. Born, with the help of his assistant and former student Pascual Jordan, began immediately to make the transcription and extension, and they submitted their results for publication; the paper was received for publication just 60 days after Heisenberg's paper. A follow-on paper was submitted for publication before the end of the year by all three authors.\",\n \"Werner Heisenberg\\n\\nUp until this time, matrices were seldom used by physicists; they were considered to belong to the realm of pure mathematics. Gustav Mie had used them in a paper on electrodynamics in 1912 and Born had used them in his work on the lattice theory of crystals in 1921. While matrices were used in these cases, the algebra of matrices with their multiplication did not enter the picture as they did in the matrix formulation of quantum mechanics.\",\n \"Werner Heisenberg\\n\\nIn 1928, Albert Einstein nominated Heisenberg, Born, and Jordan for the Nobel Prize in Physics, but it was not to be. The announcement of the Nobel Prize in Physics for 1932 was delayed until November 1933. It was at that time that it was announced Heisenberg had won the Prize for 1932 \\\"for the creation of quantum mechanics, the application of which has, inter alia, led to the discovery of the allotropic forms of hydrogen\\\".\",\n \"Werner Heisenberg\\n\\nThe Deutsche Physik movement\",\n \"Werner Heisenberg\\n\\nOn 1 April 1935, the eminent theoretical physicist Arnold Sommerfeld, Heisenberg's doctoral advisor at the University of Munich, achieved emeritus status. However, Sommerfeld stayed in his chair during the selection process for his successor, which took until 1 December 1939. The process was lengthy due to academic and political differences between the Munich Faculty's selection and that of the Reichserziehungsministerium (REM, Reich Education Ministry) and the supporters of Deutsche Physik, which was anti-Semitic and had a bias against theoretical physics, especially quantum mechanics and the theory of relativity.\",\n \"Werner Heisenberg\\n\\nIn 1935, the Munich Faculty drew up a list of candidates to replace Sommerfeld as ordinarius professor of theoretical physics and head of the Institute for Theoretical Physics at the University of Munich. There were three names on the list: Werner Heisenberg, who received the Nobel Prize in Physics for 1932, Peter Debye, who received the Nobel Prize in Chemistry in 1936, and Richard Becker – all former students of Sommerfeld. The Munich Faculty was firmly behind these candidates, with Heisenberg as their first choice. However, supporters of Deutsche Physik and elements in the REM had their own list of candidates, and the battle dragged on for over four years. During this time, Heisenberg came under vicious attack by the Deutsche Physik supporters. One attack was published in Das Schwarze Korps, the newspaper of the Schutzstaffel (SS), headed by Heinrich Himmler. In this, Heisenberg was called a \\\"White Jew\\\" (i.e. an Aryan who acts like a Jew) who should be made to \\\"disappear\\\". These attacks were taken seriously, as Jews were violently attacked and incarcerated. Heisenberg fought back with an editorial and a letter to Himmler, in an attempt to resolve this matter and regain his honour.\",\n \"Werner Heisenberg\\n\\nAt one point, Heisenberg's mother visited Himmler's mother. The two women knew each other, as Heisenberg's maternal grandfather and Himmler's father were rectors and members of a Bavarian hiking club. Eventually, Himmler settled the Heisenberg affair by sending two letters, one to SS Gruppenführer Reinhard Heydrich and one to Heisenberg, both on 21 July 1938. In the letter to Heydrich, Himmler said Germany could not afford to lose or silence Heisenberg, as he would be useful for teaching a generation of scientists. To Heisenberg, Himmler said the letter came on recommendation of his family and he cautioned Heisenberg to make a distinction between professional physics research results and the personal and political attitudes of the involved scientists. The letter to Heisenberg was signed under the closing \\\"Mit freundlichem Gruß und, Heil Hitler!\\\" (With friendly greetings, Heil Hitler!\\\") Overall, the Heisenberg affair was a victory for academic standards and professionalism. However, the appointment of Wilhelm Müller to replace Sommerfeld was a political victory over academic standards. Müller was not a theoretical physicist, had not published in a physics journal, and was not a member of the Deutsche Physikalische Gesellschaft; his appointment was considered a travesty and detrimental to educating theoretical physicists.\",\n \"Werner Heisenberg\\n\\nDocument #55 [https://books.google.com/books?id\\nsl69XGiohsoC&pgPA152 ’White Jews’ in Science [15 July 1937]]pp. 175–6 Document #63 [https://books.google.com/books?id\\nsl69XGiohsoC&pgPA175 Heinrich Himmler: Letter to Reinhard Heydrich [21 July 1938]]pp. 176–7 Document #64 [https://books.google.com/books?id\\nsl69XGiohsoC&pg=PA176 Heinrich Himmler: Letter to Werner Heisenberg [21 July 1938]]pp. 261–6 Document #85 Ludwig Prandtl: Attachment to the letter to Reich Marschal (sic) Hermann Göring [28 April 1941] pp. 290–2 Document #93 Carl Ramsauer: The Munich Conciliation and Pacification Attempt [20 January 1942]\",\n \"Werner Heisenberg\\n\\nDuring the SS investigation of Heisenberg, the three investigators had training in physics. Heisenberg had participated in the doctoral examination of one of them at the Universität Leipzig. The most influential of the three, however, was Johannes Juilfs. During their investigation, they had become supporters of Heisenberg as well as his position against the ideological policies of the Deutsche Physik movement in theoretical physics and academia.\",\n \"Werner Heisenberg\\n\\nWorld War II\",\n \"Werner Heisenberg\\n\\nIn 1939, shortly after the discovery of nuclear fission, the German nuclear energy project, also known as the Uranverein (Uranium Club), had begun. Heisenberg was one of the principal scientists leading research and development in the project.\",\n \"Werner Heisenberg\\n\\nFrom 15 to 22 September 1941, Heisenberg traveled to German-occupied Copenhagen to lecture and discuss nuclear research and theoretical physics with Niels Bohr. The meeting, and specifically what it might reveal about Heisenberg's intentions concerning developing nuclear weapons for the Nazi regime, is the subject of the award-winning Michael Frayn play titled Copenhagen. A television film version of the play was made by the BBC in 2002, with Stephen Rea as Bohr, and Daniel Craig as Heisenberg. The same meeting had previously been dramatised by the BBC's Horizon science documentary series in 1992, with Anthony Bate as Bohr, and Philip Anthony as Heisenberg. Documents relating to the Bohr-Heisenberg meeting were released in 2002 by the Niels Bohr Archive and by the Heisenberg family. A dramatized account of Heisenberg's work during the war is featured in the 2015 TV series The Heavy Water War.\",\n \"Werner Heisenberg\\n\\nOn 26 February 1942, Heisenberg presented a lecture to Reich officials on energy acquisition from nuclear fission, after the army withdrew most of its funding. The Uranium Club was transferred to the Reich Research Council (RFR) in July 1942. On 4 June 1942, Heisenberg was summoned to report to Albert Speer, Germany's Minister of Armaments, on the prospects for converting the Uranium Club's research toward developing nuclear weapons. During the meeting, Heisenberg told Speer that a bomb could not be built before 1945, and would require significant monetary and manpower resources. Five days later, on 9 June 1942, Adolf Hitler issued a decree for the reorganization of the RFR as a separate legal entity under the Reich Ministry for Armament and Ammunition; the decree appointed Reich Marshall Hermann Göring as the president.\",\n \"Werner Heisenberg\\n\\nIn September 1942, Heisenberg submitted his first paper of a three-part series on the scattering matrix, or S-matrix, in elementary particle physics. The first two papers were published in 1943 and the third in 1944. The S-matrix described only observables, i.e., the states of incident particles in a collision process, the states of those emerging from the collision, and stable bound states; there would be no reference to the intervening states. This was the same precedent as he followed in 1925 in what turned out to be the foundation of the matrix formulation of quantum mechanics through only the use of observables.\",\n \"Werner Heisenberg\\n\\nIn February 1943, Heisenberg was appointed to the Chair for Theoretical Physics at the Friedrich-Wilhelms-Universität (today, the Humboldt-Universität zu Berlin). In April, his election to the Preußische Akademie der Wissenschaften (Prussian Academy of Sciences) was approved. That same month, he moved his family to their retreat in Urfeld as Allied bombing increased in Berlin. In the summer, he dispatched the first of his staff at the Kaiser-Wilhelm Institut für Physik to Hechingen and its neighboring town of Haigerloch, on the edge of the Black Forest, for the same reasons. From 18–26 October, he traveled to German-occupied Netherlands. In December 1943, Heisenberg visited German-occupied Poland.\",\n \"Werner Heisenberg\\n\\nFrom 24 January to 4 February 1944, Heisenberg traveled to occupied Copenhagen, after the German army confiscated Bohr's Institute of Theoretical Physics. He made a short return trip in April. In December, Heisenberg lectured in neutral Switzerland. The United States Office of Strategic Services sent former major league baseball catcher and OSS agent Moe Berg to attend the lecture carrying a pistol, with orders to shoot Heisenberg if his lecture indicated that Germany was close to completing an atomic bomb. Heisenberg did not give such an indication, so Berg decided not to shoot him, a decision Berg later described as his own \\\"uncertainty principle\\\".\",\n \"Werner Heisenberg\\n\\nIn January 1945, Heisenberg, with most of the rest of his staff, moved from the Kaiser-Wilhelm Institut für Physik to the facilities in the Black Forest.\",\n \"Werner Heisenberg\\n\\nUranium Club\",\n \"Werner Heisenberg\\n\\nIn December 1938, the German chemists Otto Hahn and Fritz Strassmann sent a manuscript to Naturwissenschaften reporting they had detected the element barium after bombarding uranium with neutrons and Otto Hahn concluded a bursting of the uranium nucleus; simultaneously, Hahn communicated these results to his friend Lise Meitner, who had in July of that year fled to the Netherlands and then went to Sweden.\",\n \"Werner Heisenberg\\n\\nMeitner, and her nephew Otto Robert Frisch, correctly interpreted Hahn's and Strassmann's results as being nuclear fission. Frisch confirmed this experimentally on 13 January 1939. Frisch along with Rudolf Peierls, by then both in Britain, subsequently wrote the Frisch–Peierls memorandum and joined the British Tube Alloys project.\",\n \"Werner Heisenberg\\n\\nPaul Harteck was director of the physical chemistry department at the University of Hamburg and an advisor to the Heereswaffenamt (HWA, Army Ordnance Office). On 24 April 1939, along with his teaching assistant Wilhelm Groth, Harteck made contact with the Reichskriegsministerium (RKM, Reich Ministry of War) to alert them to the potential of military applications of nuclear chain reactions. Two days earlier, on 22 April 1939, after hearing a colloquium paper by Wilhelm Hanle on the use of uranium fission in a Uranmaschine (uranium machine, i.e., nuclear reactor), Georg Joos, along with Hanle, notified Wilhelm Dames, at the Reichserziehungsministerium (REM, Reich Ministry of Education), of potential military applications of nuclear energy. The communication was given to Abraham Esau, head of the physics section of the Reichsforschungsrat (RFR, Reich Research Council) at the REM. On 29 April, a group, organized by Esau, met at the REM to discuss the potential of a sustained nuclear chain reaction.\",\n \"Werner Heisenberg\\n\\nThe group included the physicists Walther Bothe, Robert Döpel, Hans Geiger, Wolfgang Gentner (probably sent by Walther Bothe), Wilhelm Hanle, Gerhard Hoffmann and Georg Joos; Peter Debye was invited, but he did not attend. After this, informal work began at the Georg-August University of Göttingen by Joos, Hanle and their colleague Reinhold Mannfopff; the group of physicists was known informally as the first Uranverein (Uranium Club) and formally as Arbeitsgemeinschaft für Kernphysik. The group's work was discontinued in August 1939, when the three were called to military training.\",\n \"Werner Heisenberg\\n\\nThe second Uranverein began after the Heereswaffenamt (HWA, Army Ordnance Office) squeezed the Reichsforschungsrat (RFR, Reich Research Council) out of the Reichserziehungsministerium (REM, Reich Ministry of Education) and started the formal German nuclear energy project under military auspices. The second Uranverein was formed on 1 September 1939, the day World War II began, and it had its first meeting on 16 September 1939. The meeting was organized by Kurt Diebner, advisor to the HWA, and held in Berlin. The invitees included Walther Bothe, Siegfried Flügge, Hans Geiger, Otto Hahn, Paul Harteck, Gerhard Hoffmann, Josef Mattauch and Georg Stetter. A second meeting was held soon thereafter and included Klaus Clusius, Robert Döpel, Werner Heisenberg and Carl Friedrich von Weizsäcker. Also at this time, the Kaiser-Wilhelm Institut für Physik (KWIP, Kaiser Wilhelm Institute for Physics, after World War II the Max Planck Institute for Physics), in Berlin-Dahlem, was placed under HWA authority, with Diebner as the administrative director, and the military control of the nuclear research commenced.\",\n \"Werner Heisenberg\\n\\nWhen it was apparent that the nuclear energy project would not make a decisive contribution to ending the war effort in the near term, control of the KWIP was returned in January 1942 to its umbrella organization, the Kaiser-Wilhelm Gesellschaft (KWG, Kaiser Wilhelm Society, after World War II the Max-Planck Gesellschaft), and HWA control of the project was relinquished to the RFR in July 1942. The nuclear energy project thereafter maintained its kriegswichtig (important for the war) designation and funding continued from the military. However, the German nuclear power project was then broken down into the following main areas: uranium and heavy water production, uranium isotope separation and the Uranmaschine (uranium machine, i.e., nuclear reactor). Also, the project was then essentially split up between a number of institutes, where the directors dominated the research and set their own research agendas.\",\n \"Werner Heisenberg\\n\\nThe dominant personnel and facilities were the following: \\n* Institut für Physik (Walther Bothe) of the Kaiser-Wilhelm Institut für medizinische Forschung (KWImF, Kaiser Wilhelm Institute for Medical Research),\\n* Institute for Physical Chemistry (Klaus Clusius) at the Ludwig Maximilian University of Munich,\\n* HWA Versuchsstelle (testing station) in Gottow (Kurt Diebner),\\n* Kaiser-Wilhelm-Institut für Chemie (Otto Hahn),\\n* Physical Chemistry Department (Paul Harteck) of the University of Hamburg,\\n* Kaiser-Wilhelm-Institut für Physik (Werner Heisenberg),\\n* Second Experimental Physics Institute (Hans Kopfermann) at the Georg-August University of Göttingen,\\n* Auergesellschaft (Nikolaus Riehl), and\\n* II. Physikalisches Institut (Georg Stetter) at the University of Vienna.\",\n \"Werner Heisenberg\\n\\nHeisenberg was appointed director-in-residence of the KWIP on 1 July 1942, as Peter Debye was still officially the director and on leave in the United States; Debye had gone on leave as he was a citizen of The Netherlands and had refused to become a German citizen when the HWA took administrative control of the KWIP. Heisenberg still also had his department of physics at the University of Leipzig where work was done for the Uranverein by Robert Döpel and his wife Klara Döpel. During the period Kurt Diebner administered the KWIP under the HWA program, considerable personal and professional animosity developed between Diebner and the Heisenberg inner circle – Heisenberg, Karl Wirtz, and Carl Friedrich von Weizsäcker.\",\n \"Werner Heisenberg\\n\\nThe point in 1942, when the army relinquished its control of the German nuclear energy project, was the zenith of the project relative to the number of personnel devoting time to the effort. There were only about 70 scientists working on the project, with about 40 devoting more than half their time to nuclear fission research. After this, the number of scientists working on applied nuclear fission diminished dramatically. Many of the scientists not working with the main institutes stopped working on nuclear fission and devoted their efforts to more pressing war related work.\",\n \"Werner Heisenberg\\n\\nOver time, the HWA and then the RFR controlled the German nuclear energy project. The most influential people in the project were Kurt Diebner, Abraham Esau, Walther Gerlach and Erich Schumann. Schumann was one of the most powerful and influential physicists in Germany. Schumann was director of the Physics Department II at the Frederick William University (later, University of Berlin), which was commissioned and funded by the Oberkommando des Heeres (OKH, Army High Command) to conduct physics research projects. He was also head of the research department of the HWA, assistant secretary of the Science Department of the OKH and Bevollmächtiger (plenipotentiary) for high explosives. Diebner, throughout the life of the nuclear energy project, had more control over nuclear fission research than did Walther Bothe, Klaus Clusius, Otto Hahn, Paul Harteck or Werner Heisenberg.\",\n \"Werner Heisenberg\\n\\n1945: Alsos Mission and Operation Epsilon\",\n \"Werner Heisenberg\\n\\nAlsos Mission was an Allied effort commanded by the Russian-American Colonel Boris T. Pash. He reported directly to General Leslie Groves, commander of the Manhattan Engineer District, which was developing atomic weapons for the United States. The chief scientific advisor to Alsos Mission was the physicist Samuel Goudsmit. Goudsmit was selected for this task because of his knowledge of physics, he spoke German, and he personally knew a number of the German scientists working on the German nuclear energy project. He also knew little of the Manhattan Project, so, if he were captured, he would have little intelligence value to the Germans.\",\n \"Werner Heisenberg\\n\\nThe objectives of the Alsos Mission were to determine if the Germans had an atomic bomb program and to exploit German atomic related facilities, intellectual materials, materiel resources, and scientific personnel for the benefit of the US. Personnel on this operation generally swept into areas which had just come under control of the Allied military forces, but sometimes they operated in areas still under control by German forces.\",\n \"Werner Heisenberg\\n\\nBerlin had been a location of many German scientific research facilities. To limit casualties and loss of equipment, many of these facilities were dispersed to other locations in the latter years of the war. The Kaiser-Wilhelm-Institut für Physik (KWIP, Kaiser Wilhelm Institute for Physics) had mostly been moved in 1943 and 1944 to Hechingen and its neighboring town of Haigerloch, on the edge of the Black Forest, which eventually became the French occupation zone. This move, some scheming, and a fast-moving American task force allowed them to take into custody a large number of German scientists associated with nuclear research. The only section of the institute which remained in Berlin was the low-temperature physics section, headed by Ludwig Bewilogua (1906–83), who was in charge of the exponential uranium pile.\",\n \"Werner Heisenberg\\n\\nNine of the prominent German scientists who published reports in Kernphysikalische Forschungsberichte as members of the Uranverein were picked up by Operation Alsos and incarcerated in England under Operation Epsilon: Erich Bagge, Kurt Diebner, Walther Gerlach, Otto Hahn, Paul Harteck, Werner Heisenberg, Horst Korsching, Carl Friedrich von Weizsäcker and Karl Wirtz. Also incarcerated was Max von Laue, although he had nothing to do with the nuclear energy project. Goudsmit, the chief scientific advisor to Operation Alsos, thought von Laue might be beneficial to the postwar rebuilding of Germany and would benefit from the high level contacts he would have in England.\",\n \"Werner Heisenberg\\n\\nHeisenberg had been captured and arrested by Colonel Pash at Heisenberg's retreat in Urfeld, on 3 May 1945, in an alpine operation in territory still under control by German forces. He was taken to Heidelberg, where, on 5 May, he met Goudsmit for the first time since the Ann Arbor visit in 1939. Germany surrendered just two days later. Heisenberg did not see his family again for eight months. Heisenberg was moved across France and Belgium and flown to England on 3 July 1945.\",\n \"Werner Heisenberg\\n\\nThe 10 German scientists were held at Farm Hall in England. The facility had been a safe house of the British foreign intelligence MI6. During their detention, their conversations were recorded. Conversations thought to be of intelligence value were transcribed and translated into English. The transcripts were released in 1992. Bernstein has published an annotated version of the transcripts in his book Hitler's Uranium Club: The Secret Recordings at Farm Hall, along with an introduction to put them in perspective. A complete, unedited publication of the British version of the reports appeared as Operation Epsilon: The Farm Hall Transcripts, which was published in 1993 by the Institute of Physics in Bristol and by the University of California Press in the US.\",\n \"Werner Heisenberg\\n\\nPost 1945\",\n \"Werner Heisenberg\\n\\nOn 3 January 1946, the 10 Operation Epsilon detainees were transported to Alswede in Germany, which was in the British occupation zone. Heisenberg settled in Göttingen, also in the British zone. In July, he was named director of the Kaiser-Wilhelm-Institut für Physik (KWIP, Kaiser Wilhelm Institute for Physics), then located in Göttingen. Shortly thereafter, it was renamed the Max-Planck-Institut für Physik, in honor of Max Planck and to assuage political objections to the continuation of the institute. Heisenberg was its director until 1958. In 1958, the institute was moved to Munich, expanded, and renamed Max-Planck-Institut für Physik und Astrophysik (MPIFA). Heisenberg was its director from 1960 to 1970; in the interim, Heisenberg and the astrophysicist Ludwig Biermann were co-directors. Heisenberg resigned his directorship of the MPIFA on 31 December 1970. Upon the move to Munich, Heisenberg also became an ordentlicher Professor (ordinarius professor) at the University of Munich.\",\n \"Werner Heisenberg\\n\\nJust as the Americans did with Operation Alsos, the Soviets inserted special search teams into Germany and Austria in the wake of their troops. Their objective, under the Russian Alsos, was also the exploitation of German atomic related facilities, intellectual materials, materiel resources and scientific personnel for the benefit of the Soviet Union. One of the German scientists recruited under this Soviet operation was the nuclear physicist Heinz Pose, who was made head of Laboratory V in Obninsk. When he returned to Germany on a recruiting trip for his laboratory, Pose wrote a letter to Werner Heisenberg inviting him to work in the USSR. The letter lauded the working conditions in the USSR and the available resources, as well as the favorable attitude of the Soviets towards German scientists. A courier hand delivered the recruitment letter, dated 18 July 1946, to Heisenberg; Heisenberg politely declined in a return letter to Pose.\",\n \"Werner Heisenberg\\n\\nIn 1947, Heisenberg presented lectures in Cambridge, Edinburgh and Bristol. Heisenberg also contributed to the understanding of the phenomenon of superconductivity with a paper in 1947 and two papers in 1948, one of them with Max von Laue.\",\n \"Werner Heisenberg\\n\\nIn the period shortly after World War II, Heisenberg briefly returned to the subject of his doctoral thesis, turbulence. Three papers were published in 1948 and one in 1950.\",\n \"Werner Heisenberg\\n\\nIn the post-war period, Heisenberg continued his interests in cosmic-ray showers with considerations on multiple production of mesons. He published three papers in 1949, two in 1952, and one in 1955.\",\n \"Werner Heisenberg\\n\\nOn 9 March 1949, the Deutsche Forschungsrat (German Research Council) was established by the Max-Planck Gesellschaft (MPG, Max Planck Society, successor organization to the Kaiser-Wilhelm Gesellschaft). Heisenberg was appointed president of the Deutsche Forschungsrat. In 1951, the organization was fused with the Notgemeinschaft der Deutschen Wissenschaft (NG, Emergency Association of German Science) and that same year renamed the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation). With the merger, Heisenberg was appointed to the presidium.\",\n \"Werner Heisenberg\\n\\nIn 1952, Heisenberg served as the chairman of the Commission for Atomic Physics of the DFG. Also that year, he headed the German delegation to the European Council for Nuclear Research.\",\n \"Werner Heisenberg\\n\\nIn 1953, Heisenberg was appointed president of the Alexander von Humboldt-Stiftung by Konrad Adenauer. Heisenberg served until 1975. Also, from 1953, Heisenberg's theoretical work concentrated on the unified field theory of elementary particles.\",\n \"Werner Heisenberg\\n\\nIn late 1955 to early 1956, Heisenberg gave the Gifford Lectures at St Andrews University, in Scotland, on the intellectual history of physics. The lectures were later published as Physics and Philosophy: The Revolution in Modern Science.\",\n \"Werner Heisenberg\\n\\nDuring 1956 and 1957, Heisenberg was the chairman of the Arbeitskreis Kernphysik (Nuclear Physics Working Group) of the Fachkommission II \\\"Forschung und Nachwuchs\\\" (Commission II \\\"Research and Growth\\\") of the Deutschen Atomkommission (DAtK, German Atomic Energy Commission). Other members of the Nuclear Physics Working Group in both 1956 and 1957 were: Walther Bothe, Hans Kopfermann (vice-chairman), Fritz Bopp, Wolfgang Gentner, Otto Haxel, Willibald Jentschke, Heinz Maier-Leibnitz, Josef Mattauch, Wolfgang Riezler, Wilhelm Walcher and Carl Friedrich von Weizsäcker. Wolfgang Paul was also a member of the group during 1957.\",\n \"Werner Heisenberg\\n\\nIn 1957, Heisenberg was a signatory of the manifesto of the Göttinger Achtzehn (Göttingen Eighteen).\",\n \"Werner Heisenberg\\n\\nFrom 1957, Heisenberg was interested in plasma physics and the process of nuclear fusion. He also collaborated with the International Institute of Atomic Physics in Geneva. He was a member of the Institute's Scientific Policy Committee, and for several years was the Committee's chairman.\",\n \"Werner Heisenberg\\n\\nIn 1973, Heisenberg gave a lecture at Harvard University on the historical development of the concepts of quantum theory.\",\n \"Werner Heisenberg\\n\\nOn 24 March 1973, Heisenberg gave a speech before the Catholic Academy of Bavaria, accepting the Romano Guardini Prize. An English translation of its title is \\\"Scientific and Religious Truth.\\\" And its stated goal was \\\"In what follows, then, we shall first of all deal with the unassailability and value of scientific truth, and then with the much wider field of religion, of which – so far as the Christian religion is concerned – Guardini himself has so persuasively written; finally – and this will be the hardest part to formulate – we shall speak of the relationship of the two truths.\\\"Chapter 16 \\\"Scientific and Religious Truth\\\" in Across the Frontiers, 1974, Harper & Row, p.213-229 A more detailed insight into Heisenberg's view on religion has been discussed by Wilfried Schröder in \\\"Natural science and religion\\\" (Bremen 1999, Science edition) and Wilfried Schröder \\\"Naturerkenntnis und Religion\\\" (Bremen, science edition 2008).\",\n \"Werner Heisenberg\\n\\nPersonal life\",\n \"Werner Heisenberg\\n\\nIn January 1937 Heisenberg met Elisabeth Schumacher (1914–1998) at a private music recital. Elisabeth was the daughter of a well-known Berlin economics professor, and her brother was the economist E. F. Schumacher, author of Small is Beautiful. Heisenberg married her on 29 April. Fraternal twins Maria and Wolfgang were born in January 1938, whereupon Wolfgang Pauli congratulated Heisenberg on his \\\"pair creation\\\" – a word play on a process from elementary particle physics, pair production. They had five more children over the next 12 years: Barbara, Christine, Jochen, Martin and Verena. Jochen became a physics professor at the University of New Hampshire.\",\n \"Werner Heisenberg\\n\\nHeisenberg enjoyed classical music and was an accomplished pianist.\",\n \"Werner Heisenberg\\n\\nHeisenberg was raised and lived as a Lutheran Christian, publishing and giving several talks reconciling science with his faith.\",\n \"Werner Heisenberg\\n\\nIn his speech Scientific and Religious Truth (1974) while accepting the Romano Guardini Prize, Heisenberg affirmed:“In the history of science, ever since the famous trial of Galileo, it has repeatedly been claimed that scientific truth cannot be reconciled with the religious interpretation of the world. Although I am now convinced that scientific truth is unassailable in its own field, I have never found it possible to dismiss the content of religious thinking as simply part of an outmoded phase in the consciousness of mankind, a part we shall have to give up from now on. Thus in the course of my life I have repeatedly been compelled to ponder on the relationship of these two regions of thought, for I have never been able to doubt the reality of that to which they point.” (Heisenberg 1974, 213) “Where no guiding ideals are left to point the way, the scale of values disappears and with it the meaning of our deeds and sufferings, and at the end can lie only negation and despair. Religion is therefore the foundation of ethics, and ethics the presupposition of life.” (Heisenberg 1974, 219).\",\n \"Werner Heisenberg\\n\\nIn his autobiographical article in the journal Truth, Henry Margenau (Professor Emeritus of Physics and Natural Philosophy at Yale University) pointed out: “I have said nothing about the years between 1936 and 1950. There were, however, a few experiences I cannot forget. One was my first meeting with Heisenberg, who came to America soon after the end of the Second World War. Our conversation was intimate and he impressed me by his deep religious conviction. He was a true Christian in every sense of that word.”\",\n \"Werner Heisenberg\\n\\nHeisenberg also enjoyed mountaineering. In his autobiography, he included photographs from this activity.\",\n \"Werner Heisenberg\\n\\nHeisenberg died of cancer of the kidneys and gall bladder at his home, on 1 February 1976. The next evening, his colleagues and friends walked in remembrance from the Institute of Physics to his home and each put a candle near the front door. He is buried at Munich Waldfriedhof.\",\n \"Werner Heisenberg\\n\\nHonors and awards\",\n \"Werner Heisenberg\\n\\nHeisenberg was awarded a number of honors:\\n* Honorary doctorates from the University of Bruxelles, the Technological University of Karlsruhe, and the University of Budapest.\\n* Order of Merit of Bavaria\\n* Romano Guardini Prize\\n* Grand Cross for Federal Service with Star\\n* Knight of the Order of Merit (Civil Class)\\n* Elected a Foreign Member of the Royal Society (ForMemRS) in 1955\\n* Member of the Academies of Sciences of Göttingen, Bavaria, Saxony, Prussia, Sweden, Romania, Norway, Spain, The Netherlands (1939), Rome (Pontifical), the Deutsche Akademie der Naturforscher Leopoldina (Halle), the Accademia dei Lincei (Rome), and the American Academy of Sciences.\\n* 1932–Nobel Prize in Physics \\\"for the creation of quantum mechanics, the application of which has, inter alia, led to the discovery of the allotropic forms of hydrogen\\\".\\n* 1933–Max-Planck-Medaille of the Deutsche Physikalische Gesellschaft\",\n \"Werner Heisenberg\\n\\nResearch Reports in Nuclear Physics\",\n \"Werner Heisenberg\\n\\nThe following reports were published in Kernphysikalische Forschungsberichte (Research Reports in Nuclear Physics), an internal publication of the German Uranverein. The reports were classified Top Secret, they had very limited distribution, and the authors were not allowed to keep copies. The reports were confiscated under the Allied Operation Alsos and sent to the United States Atomic Energy Commission for evaluation. In 1971, the reports were declassified and returned to Germany. The reports are available at the Karlsruhe Nuclear Research Center and the American Institute of Physics. * Robert Döpel, K. Döpel, and Werner Heisenberg Bestimmung der Diffusionslänge thermischer Neutronen in Präparat 38 G-22 (5 December 1940)\\n* Robert Döpel, K. Döpel, and Werner Heisenberg Bestimmung der Diffusionslänge thermischer Neutronen in schwerem Wasser G-23 (7 August 1940)\\n* Werner Heisenberg Die Möglichkeit der technischer Energiegewinnung aus der Uranspaltung G-39 (6 December 1939)\\n* Werner Heisenberg Bericht über die Möglichkeit technischer Energiegewinnung aus der Uranspaltung (II) G-40 (29 February 1940)\\n* Robert Döpel, K.\",\n \"Werner Heisenberg\\n\\nDöpel, and Werner Heisenberg Versuche mit Schichtenanordnungen von D2O und 38 G-75 (28 October 1941)\\n* Werner Heisenberg Über die Möglichkeit der Energieerzeugung mit Hilfe des Isotops 238 G-92 (1941)\\n* Werner Heisenberg Bericht über Versuche mit Schichtenanordnungen von Präparat 38 und Paraffin am Kaiser Wilhelm Institut für Physik in Berlin-Dahlem G-93 (May 1941)\\n* Fritz Bopp, Erich Fischer, Werner Heisenberg, Carl-Friedrich von Weizsäcker, and Karl Wirtz Untersuchungen mit neuen Schichtenanordnungen aus U-metall und Paraffin G-127 (March 1942)\\n* Robert Döpel Bericht über Unfälle beim Umgang mit Uranmetall G-135 (9 July 1942)\\n* Werner Heisenberg Bemerkungen zu dem geplanten halbtechnischen Versuch mit 1,5 to D2O und 3 to 38-Metall G-161 (31 July 1942)\\n* Werner Heisenberg, Fritz Bopp, Erich Fischer, Carl-Friedrich von Weizsäcker, and Karl Wirtz Messungen an Schichtenanordnungen aus 38-Metall und Paraffin G-162 (30 October 1942)\\n* Robert Döpel, K. Döpel, and Werner Heisenberg Der experimentelle Nachweis der effektiven Neutronenvermehrung in einem Kugel-Schichten-System aus D2O und Uran-Metall G-136 (July 1942)\\n* Werner Heisenberg Die Energiegewinnung aus der Atomkernspaltung G-217 (6 May 1943)\\n* Fritz Bopp, Walther Bothe, Erich Fischer, Erwin Fünfer, Werner Heisenberg, O.\",\n \"Werner Heisenberg\\n\\nRitter, and Karl Wirtz Bericht über einen Versuch mit 1.5 to D2O und U und 40 cm Kohlerückstreumantel (B7) G-300 (3 January 1945)\\n* Robert Döpel, K. Döpel, and Werner Heisenberg Die Neutronenvermehrung in einem D2O-38-Metallschichtensystem G-373 (March 1942)\",\n \"Werner Heisenberg\\n\\nPublications\",\n \"Werner Heisenberg\\n\\n; Collected bibliographies\\n*\\n* \\n*\\n*\\n*\\n; Selected articles:\",\n \"Werner Heisenberg\\n\\n*\\n*\\n*\\n*\\n*\\n*\\n*\\n*\\n* The paper was received on 29 July 1925. [English translation in: ] This is the first paper in the famous trilogy which launched the matrix mechanics formulation of quantum mechanics. * The paper was received on 27 September 1925. [English translation in: ] This is the second paper in the famous trilogy which launched the matrix mechanics formulation of quantum mechanics. * The paper was received on 16 November 1925. [English translation in: ] This is the third paper in the famous trilogy which launched the matrix mechanics formulation of quantum mechanics. *\\n*\\n*\\n*\\n*\\n*\\n*\\n* The author was cited as being at Leipzig. The paper was received on 21 June 1934. *\\n* The authors were cited as being at Leipzig. The paper was received on 22 December 1935. A translation of this paper has been done by W. Korolevski and H. Kleinert: [http://arxiv.org/abs/physics/0605038v1 arXiv:physics/0605038v1]. *\\n*W. Heisenberg Der Durchgang sehr energiereicher Korpuskeln durch den Atomkern, Ber. Sächs, Akad. Wiss. Volume 89, 369; Die Naturwissenschaften Volume 25, 749–750 (1937)\\n*\\n*\\n*W. Heisenberg Der Durchgang sehr energiereicher Korpuskeln durch den Atomkern, Nuovo Cimento Volume 15, 31–34; Verh. Dtsch. physik. Ges.\",\n \"Werner Heisenberg\\n\\nVolume 19, 2 (1938)\\n*\\n*\\n*\\n*W. Heisenberg Zur Theorie der Supraleitung, Forsch. Fortschr. Volumes 21/23, 243–244 (1947); Z. Naturforsch. Volume 2a, 185–201 (1947)\\n*\\n*\\n*\\n*\\n*\\n*\\n*\\n*\\n*W. Heisenberg On the stability of laminar flow, Proc. International Congress Mathematicians Volume II, 292–296 (1950)\\n*\\n*\\n*\\n* The substance of this article was presented by Heisenberg in a lecture at Harvard University.\",\n \"Werner Heisenberg\\n\\nBooks\",\n \"Werner Heisenberg\\n\\n*\\n*\\n*\\n* Werner Heisenberg Physics and Beyond: Encounters and Conversations (Harper & Row, 1971)\\n*\\n*\\n* Werner Heisenberg Physik und Philosophie: Weltperspektiven. (Ullstein Taschenbuchvlg., 1988)\\n*\\n* Werner Heisenberg and F. S. C. Northrop Physics and Philosophy: The Revolution in Modern Science (Great Minds Series) (Prometheus, 1999)\\n*\\n*\\n* Werner Heisenberg Physik und Philosophie (Hirzel, 2007)\\n* ([https://archive.org/details/PhysicsPhilosophy full text of 1958 version])\",\n \"Uncertainty principle\\n\\nIn quantum mechanics, the uncertainty principle, also known as Heisenberg's uncertainty principle, is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known.\",\n \"Uncertainty principle\\n\\nIntroduced first in 1927, by the German physicist Werner Heisenberg, it states that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa. The formal inequality relating the standard deviation of position σx and the standard deviation of momentum σp was derived by Earle Hesse Kennard later that year and by Hermann Weyl in 1928:\",\n \"Uncertainty principle\\n\\n( is the reduced Planck constant, / ).\",\n \"Uncertainty principle\\n\\nHistorically, the uncertainty principle has been confused with a somewhat similar effect in physics, called the observer effect, which notes that measurements of certain systems cannot be made without affecting the systems. Heisenberg offered such an observer effect at the quantum level (see below) as a physical \\\"explanation\\\" of quantum uncertainty. It has since become clear, however, that the uncertainty principle is inherent in the properties of all wave-like systems, and that it arises in quantum mechanics simply due to the matter wave nature of all quantum objects. Thus, the uncertainty principle actually states a fundamental property of quantum systems, and is not a statement about the observational success of current technology. It must be emphasized that measurement does not mean only a process in which a physicist-observer takes part, but rather any interaction between classical and quantum objects regardless of any observer. (N.B.\",\n \"Uncertainty principle\\n\\non precision: If δx and δp are the precisions of position and momentum obtained in an individual measurement and \\\\sigma_{x}, \\\\sigma_{p} their standard deviations in an ensemble of individual measurements on similarly prepared systems, then \\\"There are, in principle, no restrictions on the precisions of individual measurements \\\\delta x and \\\\delta p, but the standard deviations will always satisfy \\\\sigma_{x}\\\\sigma_{p} \\\\ge \\\\hbar/2\\\". )\",\n \"Uncertainty principle\\n\\nSince the uncertainty principle is such a basic result in quantum mechanics, typical experiments in quantum mechanics routinely observe aspects of it. Certain experiments, however, may deliberately test a particular form of the uncertainty principle as part of their main research program. These include, for example, tests of number–phase uncertainty relations in superconducting or quantum optics systems. Applications dependent on the uncertainty principle for their operation include extremely low noise technology such as that required in gravitational-wave interferometers.\",\n \"Uncertainty principle\\n\\nIntroduction\",\n \"Uncertainty principle\\n\\nThe uncertainty principle is not readily apparent on the macroscopic scales of everyday experience. So it is helpful to demonstrate how it applies to more easily understood physical situations. Two alternative frameworks for quantum physics offer different explanations for the uncertainty principle. The wave mechanics picture of the uncertainty principle is more visually intuitive, but the more abstract matrix mechanics picture formulates it in a way that generalizes more easily.\",\n \"Uncertainty principle\\n\\nMathematically, in wave mechanics, the uncertainty relation between position and momentum arises because the expressions of the wavefunction in the two corresponding orthonormal bases in Hilbert space are Fourier transforms of one another (i.e., position and momentum are conjugate variables). A nonzero function and its Fourier transform cannot both be sharply localized. A similar tradeoff between the variances of Fourier conjugates arises in all systems underlain by Fourier analysis, for example in sound waves: A pure tone is a sharp spike at a single frequency, while its Fourier transform gives the shape of the sound wave in the time domain, which is a completely delocalized sine wave. In quantum mechanics, the two key points are that the position of the particle takes the form of a matter wave, and momentum is its Fourier conjugate, assured by the de Broglie relation , where is the wavenumber.\",\n \"Uncertainty principle\\n\\nIn matrix mechanics, the mathematical formulation of quantum mechanics, any pair of non-commuting self-adjoint operators representing observables are subject to similar uncertainty limits. An eigenstate of an observable represents the state of the wavefunction for a certain measurement value (the eigenvalue). For example, if a measurement of an observable is performed, then the system is in a particular eigenstate of that observable. However, the particular eigenstate of the observable need not be an eigenstate of another observable : If so, then it does not have a unique associated measurement for it, as the system is not in an eigenstate of that observable.\",\n \"Uncertainty principle\\n\\nWave mechanics interpretation\",\n \"Uncertainty principle\\n\\n(Ref )\",\n \"Uncertainty principle\\n\\nAccording to the de Broglie hypothesis, every object in the universe is a wave, a situation which gives rise to this phenomenon. The position of the particle is described by a wave function \\\\Psi(x,t). The time-independent wave function of a single-moded plane wave of wavenumber k0 or momentum p0 is\",\n \"Uncertainty principle\\n\\n\\\\psi(x) \\\\propto e^{ik_0 x} = e^{ip_0 x/\\\\hbar} ~.\",\n \"Uncertainty principle\\n\\nThe Born rule states that this should be interpreted as a probability density amplitude function in the sense that the probability of finding the particle between a and b is\",\n \"Uncertainty principle\\n\\n\\\\operatorname P [a \\\\leq X \\\\leq b] = \\\\int_a^b |\\\\psi(x)|^2 \\\\, \\\\mathrm{d}x ~.\",\n \"Uncertainty principle\\n\\nIn the case of the single-moded plane wave, |\\\\psi(x)|^2 is a uniform distribution. In other words, the particle position is extremely uncertain in the sense that it could be essentially anywhere along the wave packet. Consider a wave function that is a sum of many waves, however, we may write this as\",\n \"Uncertainty principle\\n\\n\\\\psi(x) \\\\propto \\\\sum_{n} A_n e^{i p_n x/\\\\hbar}~, \\nwhere An represents the relative contribution of the mode pn to the overall total. The figures to the right show how with the addition of many plane waves, the wave packet can become more localized. We may take this a step further to the continuum limit, where the wave function is an integral over all possible modes\",\n \"Uncertainty principle\\n\\n\\\\psi(x) = \\\\frac{1}{\\\\sqrt{2 \\\\pi \\\\hbar}} \\\\int_{-\\\\infty}^{\\\\infty} \\\\phi(p) \\\\cdot e^{i p x/\\\\hbar}\\\\, dp ~,\",\n \"Uncertainty principle\\n\\nwith \\\\phi(p) representing the amplitude of these modes and is called the wave function in momentum space. In mathematical terms, we say that \\\\phi(p) is the Fourier transform of \\\\psi(x) and that x and p are conjugate variables. Adding together all of these plane waves comes at a cost, namely the momentum has become less precise, having become a mixture of waves of many different momenta.\",\n \"Uncertainty principle\\n\\nOne way to quantify the precision of the position and momentum is the standard deviation σ. Since |\\\\psi(x)|^2 is a probability density function for position, we calculate its standard deviation.\",\n \"Uncertainty principle\\n\\nThe precision of the position is improved, i.e. reduced σx, by using many plane waves, thereby weakening the precision of the momentum, i.e. increased σp. Another way of stating this is that σx and σp have an inverse relationship or are at least bounded from below. This is the uncertainty principle, the exact limit of which is the Kennard bound. Click the show button below to see a semi-formal derivation of the Kennard inequality using wave mechanics.\",\n \"Uncertainty principle\\n\\nMatrix mechanics interpretation\",\n \"Uncertainty principle\\n\\n(Ref )\",\n \"Uncertainty principle\\n\\nIn matrix mechanics, observables such as position and momentum are represented by self-adjoint operators. When considering pairs of observables, an important quantity is the commutator. For a pair of operators and , one defines their commutator as\\n[\\\\hat{A},\\\\hat{B}]=\\\\hat{A}\\\\hat{B}-\\\\hat{B}\\\\hat{A}.\\nIn the case of position and momentum, the commutator is the canonical commutation relation\\n[\\\\hat{x},\\\\hat{p}]=i \\\\hbar.\",\n \"Uncertainty principle\\n\\nThe physical meaning of the non-commutativity can be understood by considering the effect of the commutator on position and momentum eigenstates. Let |\\\\psi\\\\rangle be a right eigenstate of position with a constant eigenvalue . By definition, this means that \\\\hat{x}|\\\\psi\\\\rangle = x_0 |\\\\psi\\\\rangle. Applying the commutator to |\\\\psi\\\\rangle yields\\n[\\\\hat{x},\\\\hat{p}] | \\\\psi \\\\rangle (\\\\hat{x}\\\\hat{p}-\\\\hat{p}\\\\hat{x}) | \\\\psi \\\\rangle \\n (\\\\hat{x} - x_0 \\\\hat{I}) \\\\cdot \\\\hat{p} \\\\, | \\\\psi \\\\rangle = i \\\\hbar | \\\\psi \\\\rangle,\\nwhere is the identity operator.\",\n \"Uncertainty principle\\n\\nSuppose, for the sake of proof by contradiction, that |\\\\psi\\\\rangle is also a right eigenstate of momentum, with constant eigenvalue . If this were true, then one could write\\n(\\\\hat{x} - x_0 \\\\hat{I}) \\\\cdot \\\\hat{p} \\\\, | \\\\psi \\\\rangle (\\\\hat{x} - x_0 \\\\hat{I}) \\\\cdot p_0 \\\\, | \\\\psi \\\\rangle \\n (x_0 \\\\hat{I} - x_0 \\\\hat{I}) \\\\cdot p_0 \\\\, | \\\\psi \\\\rangle=0.\\nOn the other hand, the above canonical commutation relation requires that\\n[\\\\hat{x},\\\\hat{p}] | \\\\psi \\\\rangle=i \\\\hbar | \\\\psi \\\\rangle \\\\ne 0.\\nThis implies that no quantum state can simultaneously be both a position and a momentum eigenstate.\",\n \"Uncertainty principle\\n\\nWhen a state is measured, it is projected onto an eigenstate in the basis of the relevant observable. For example, if a particle's position is measured, then the state amounts to a position eigenstate. This means that the state is not a momentum eigenstate, however, but rather it can be represented as a sum of multiple momentum basis eigenstates. In other words, the momentum must be less precise. This precision may be quantified by the standard deviations, \\n\\\\sigma_{x}=\\\\sqrt{\\\\langle \\\\hat{x}^{2} \\\\rangle-\\\\langle \\\\hat{x}\\\\rangle ^{2}}\\n\\\\sigma_{p}=\\\\sqrt{\\\\langle \\\\hat{p}^{2} \\\\rangle-\\\\langle \\\\hat{p}\\\\rangle ^{2}}.\",\n \"Uncertainty principle\\n\\nAs in the wave mechanics interpretation above, one sees a tradeoff between the respective precisions of the two, quantified by the uncertainty principle.\",\n \"Uncertainty principle\\n\\nRobertson–Schrödinger uncertainty relations\",\n \"Uncertainty principle\\n\\nThe most common general form of the uncertainty principle is the Robertson uncertainty relation.\",\n \"Uncertainty principle\\n\\nFor an arbitrary Hermitian operator \\\\hat{\\\\mathcal{O}} we can associate a standard deviation\",\n \"Uncertainty principle\\n\\n::\\\\sigma_{\\\\mathcal{O}}=\\\\sqrt{\\\\langle \\\\hat{\\\\mathcal{O}}^2 \\\\rangle-\\\\langle \\\\hat{\\\\mathcal{O}}\\\\rangle^2},\",\n \"Uncertainty principle\\n\\nwhere the brackets \\\\langle\\\\mathcal{O}\\\\rangle indicate an expectation value. For a pair of operators and , we may define their commutator as\",\n \"Uncertainty principle\\n\\n::[\\\\hat{A},\\\\hat{B}]=\\\\hat{A}\\\\hat{B}-\\\\hat{B}\\\\hat{A},\",\n \"Uncertainty principle\\n\\nIn this notation, the Robertson uncertainty relation is given by\",\n \"Uncertainty principle\\n\\n:: \\\\sigma_{A}\\\\sigma_{B} \\\\geq \\\\left| \\\\frac{1}{2i}\\\\langle[\\\\hat{A},\\\\hat{B}]\\\\rangle \\\\right| = \\\\frac{1}{2}\\\\left|\\\\langle[\\\\hat{A},\\\\hat{B}]\\\\rangle \\\\right|,\",\n \"Uncertainty principle\\n\\nThe Robertson uncertainty relation immediately follows from a slightly stronger inequality, the Schrödinger uncertainty relation,\",\n \"Uncertainty principle\\n\\nwhere we have introduced the anticommutator,\\n::\\\\{\\\\hat{A},\\\\hat{B}\\\\}=\\\\hat{A}\\\\hat{B}+\\\\hat{B}\\\\hat{A}.\",\n \"Uncertainty principle\\n\\nSince the Robertson and Schrödinger relations are for general operators, the relations can be applied to any two observables to obtain specific uncertainty relations. A few of the most common relations found in the literature are given below.\\n* For position and linear momentum, the canonical commutation relation [\\\\hat{x},\\\\hat{p}]=i\\\\hbar implies the Kennard inequality from above:\",\n \"Uncertainty principle\\n\\n: \\\\sigma_{x}\\\\sigma_{p} \\\\geq \\\\frac{\\\\hbar}{2}\\n* For two orthogonal components of the total angular momentum operator of an object:\",\n \"Uncertainty principle\\n\\n: \\\\sigma_{J_i} \\\\sigma_{J_j} \\\\geq \\\\tfrac{\\\\hbar}{2} \\\\left|\\\\left\\\\langle J_k\\\\right\\\\rangle\\\\right|, ~\\n: where i, j, k are distinct and Ji denotes angular momentum along the xi axis. This relation implies that unless all three components vanish together, only a single component of a system's angular momentum can be defined with arbitrary precision, normally the component parallel to an external (magnetic or electric) field. Moreover, for [{J_x}, {J_y}] i \\\\hbar \\\\epsilon_{xyz} {J_z} , a choice \\\\hat{A}\\n J_x, ~~\\\\hat{B}J_y, in angular momentum multiplets, ψ \\n |j, m 〉, bounds the Casimir invariant (angular momentum squared, \\\\langle J_x^2+ J_y^2 + J_z^2 \\\\rangle ) from below and thus yields useful constraints such as j (j + 1) ≥ m (m + 1), and hence j ≥ m, among others.\\n* In non-relativistic mechanics, time is privileged as an independent variable. Nevertheless, in 1945, L. I. Mandelshtam and I. E. Tamm derived a non-relativistic time–energy uncertainty relation, as follows. For a quantum system in a non-stationary state and an observable B represented by a self-adjoint operator \\\\hat B, the following formula holds:\",\n \"Uncertainty principle\\n\\n: \\\\sigma_E ~ \\\\frac{\\\\sigma_B}{\\\\left| \\\\frac{\\\\mathrm{d}\\\\langle \\\\hat B \\\\rangle}{\\\\mathrm{d}t}\\\\right |} \\\\ge \\\\frac{\\\\hbar}{2}.\",\n \"Uncertainty principle\\n\\nwhere σE is the standard deviation of the energy operator (Hamiltonian) in the state , σB stands for the standard deviation of B. Although the second factor in the left-hand side has dimension of time, it is different from the time parameter that enters the Schrödinger equation. It is a lifetime of the state with respect to the observable B: In other words, this is the time interval (Δt) after which the expectation value \\\\langle\\\\hat B\\\\rangle changes appreciably. An informal, heuristic meaning of the principle is the following: A state that only exists for a short time cannot have a definite energy. To have a definite energy, the frequency of the state must be defined accurately, and this requires the state to hang around for many cycles, the reciprocal of the required accuracy. For example, in spectroscopy, excited states have a finite lifetime. By the time–energy uncertainty principle, they do not have a definite energy, and, each time they decay, the energy they release is slightly different. The average energy of the outgoing photon has a peak at the theoretical energy of the state, but the distribution has a finite width called the natural linewidth.\",\n \"Uncertainty principle\\n\\nFast-decaying states have a broad linewidth, while slow decaying states have a narrow linewidth. The same linewidth effect also makes it difficult to specify the rest mass of unstable, fast-decaying particles in particle physics. The faster the particle decays (the shorter its lifetime), the less certain is its mass (the larger the particle's width). * For the number of electrons in a superconductor and the phase of its Ginzburg–Landau order parameter\",\n \"Uncertainty principle\\n\\n: \\\\Delta N \\\\Delta \\\\phi \\\\geq 1. ~\",\n \"Uncertainty principle\\n\\nExamples\",\n \"Uncertainty principle\\n\\n(Refs )\",\n \"Uncertainty principle\\n\\nQuantum harmonic oscillator stationary states\",\n \"Uncertainty principle\\n\\nConsider a one-dimensional quantum harmonic oscillator (QHO). It is possible to express the position and momentum operators in terms of the creation and annihilation operators:\\n\\\\hat x = \\\\sqrt{\\\\frac{\\\\hbar}{2m\\\\omega}}(a+a^{\\\\dagger})\\n\\\\hat p = i\\\\sqrt{\\\\frac{m \\\\omega\\\\hbar}{2}}(a^{\\\\dagger}-a).\",\n \"Uncertainty principle\\n\\nUsing the standard rules for creation and annihilation operators on the eigenstates of the QHO,\\na^{\\\\dagger}|n\\\\rangle=\\\\sqrt{n+1}|n+1\\\\rangle\\na|n\\\\rangle=\\\\sqrt{n}|n-1\\\\rangle ~ , \\nthe variances may be computed directly,\\n\\\\sigma_x^2 = \\\\frac{\\\\hbar}{m\\\\omega} \\\\left( n+\\\\frac{1}{2}\\\\right)\\n\\\\sigma_p^2 = \\\\hbar m\\\\omega \\\\left( n+\\\\frac{1}{2}\\\\right)\\\\, .\\nThe product of these standard deviations is then\\n\\\\sigma_x \\\\sigma_p = \\\\hbar \\\\left(n+\\\\frac{1}{2}\\\\right) \\\\ge \\\\frac{\\\\hbar}{2}.~\",\n \"Uncertainty principle\\n\\nIn particular, the above Kennard bound is saturated for the ground state , for which the probability density is just the normal distribution.\",\n \"Uncertainty principle\\n\\nQuantum harmonic oscillator with Gaussian initial condition\",\n \"Uncertainty principle\\n\\nIn a quantum harmonic oscillator of characteristic angular frequency ω, place a state that is offset from the bottom of the potential by some displacement x0 as\\n\\\\psi(x)=\\\\left(\\\\frac{m \\\\Omega}{\\\\pi \\\\hbar}\\\\right)^{1/4} \\\\exp{\\\\left( -\\\\frac{m \\\\Omega (x-x_0)^2}{2\\\\hbar}\\\\right)},\\nwhere Ω describes the width of the initial state but need not be the same as ω. Through integration over the propagator, we can solve for the -dependent solution. After many cancelations, the probability densities reduce to\\n|\\\\Psi(x,t)|^2 \\\\sim \\\\mathcal{N}\\\\left( x_0 \\\\cos{(\\\\omega t)} , \\\\frac{\\\\hbar}{2 m \\\\Omega} \\\\left( \\\\cos^2{(\\\\omega t)} + \\\\frac{\\\\Omega^2}{\\\\omega^2} \\\\sin^2{(\\\\omega t)} \\\\right)\\\\right)\\n|\\\\Phi(p,t)|^2 \\\\sim \\\\mathcal{N}\\\\left( -m x_0 \\\\omega \\\\sin{(\\\\omega t)} , \\\\frac{\\\\hbar m \\\\Omega}{2} \\\\left( \\\\cos^2{(\\\\omega t)} + \\\\frac{\\\\omega^2}{\\\\Omega^2} \\\\sin^2{(\\\\omega t)} \\\\right)\\\\right),\\nwhere we have used the notation \\\\mathcal{N}(\\\\mu, \\\\sigma^2) to denote a normal distribution of mean μ and variance σ2. Copying the variances above and applying trigonometric identities, we can write the product of the standard deviations as\\n\\\\begin{align}\\\\sigma_x \\\\sigma_p&=\\\\frac{\\\\hbar}{2}\\\\sqrt{\\\\left( \\\\cos^2{(\\\\omega t)} + \\\\frac{\\\\Omega^2}{\\\\omega^2} \\\\sin^2{(\\\\omega t)} \\\\right)\\\\left( \\\\cos^2{(\\\\omega t)} + \\\\frac{\\\\omega^2}{\\\\Omega^2} \\\\sin^2{(\\\\omega t)} \\\\right)} \\\\\\\\\\n&= \\\\frac{\\\\hbar}{4}\\\\sqrt{3+\\\\frac{1}{2}\\\\left(\\\\frac{\\\\Omega^2}{\\\\omega^2}+\\\\frac{\\\\omega^2}{\\\\Omega^2}\\\\right)-\\\\left(\\\\frac{1}{2}\\\\left(\\\\frac{\\\\Omega^2}{\\\\omega^2}+\\\\frac{\\\\omega^2}{\\\\Omega^2}\\\\right)-1\\\\right) \\\\cos{(4 \\\\omega t)}}\\\\end{align}\\nFrom the relations\\n\\\\frac{\\\\Omega^2}{\\\\omega^2}+\\\\frac{\\\\omega^2}{\\\\Omega^2} \\\\ge 2, \\\\, \\\\, \\\\, |\\\\cos{(4 \\\\omega t)}| \\\\le 1,\\nwe can conclude\\n\\\\sigma_x \\\\sigma_p \\\\ge \\\\frac{\\\\hbar}{4}\\\\sqrt{3+\\\\frac{1}{2}\\\\left(\\\\frac{\\\\Omega^2}{\\\\omega^2}+\\\\frac{\\\\omega^2}{\\\\Omega^2}\\\\right)-\\\\left(\\\\frac{1}{2}\\\\left(\\\\frac{\\\\Omega^2}{\\\\omega^2}+\\\\frac{\\\\omega^2}{\\\\Omega^2}\\\\right)-1\\\\right)} = \\\\frac{\\\\hbar}{2}.\",\n \"Uncertainty principle\\n\\nCoherent states\",\n \"Uncertainty principle\\n\\nA coherent state is a right eigenstate of the annihilation operator,\\n\\\\hat{a}|\\\\alpha\\\\rangle=\\\\alpha|\\\\alpha\\\\rangle,\\nwhich may be represented in terms of Fock states as\\n|\\\\alpha\\\\rangle e^{- \\\\bigl(\\\\|f\\\\|_{L^2(S^c)} + \\\\| \\\\hat{f} \\\\|_{L^2(\\\\Sigma^c)} \\\\bigr) ~.\",\n \"Uncertainty principle\\n\\nOne expects that the factor may be replaced by , \\nwhich is only known if either or is convex.\",\n \"Uncertainty principle\\n\\nHardy's uncertainty principle\",\n \"Uncertainty principle\\n\\nThe mathematician G. H. Hardy formulated the following uncertainty principle: it is not possible for and to both be \\\"very rapidly decreasing.\\\" Specifically, if in is such that\\n|f(x)|\\\\leq C(1+|x|)^Ne^{-a\\\\pi x^2}\\nand\\n|\\\\hat{f}(\\\\xi)|\\\\leq C(1+|\\\\xi|)^Ne^{-b\\\\pi \\\\xi^2} (C>0,N an integer),\",\n \"Uncertainty principle\\n\\nthen, if , while if , then there is a polynomial of degree such that\",\n \"Uncertainty principle\\n\\n:f(x)=P(x)e^{-a\\\\pi x^2}. \\\\,\",\n \"Uncertainty principle\\n\\nThis was later improved as follows: if is such that\",\n \"Uncertainty principle\\n\\n\\\\int_{\\\\mathbf{R}^d}\\\\int_{\\\\mathbf{R}^d}|f(x)||\\\\hat{f}(\\\\xi)|\\\\frac{e^{\\\\pi|\\\\langle x,\\\\xi\\\\rangle|}}{(1+|x|+|\\\\xi|)^N} \\\\, dx \\\\, d\\\\xi \\nthen\\n:f(x)=P(x)e^{-\\\\pi\\\\langle Ax,x\\\\rangle} ~,\\nwhere is a polynomial of degree and is a real positive definite matrix.\",\n \"Uncertainty principle\\n\\nThis result was stated in Beurling's complete works without proof and proved in Hörmander (the case d1,N\\n0) and Bonami, Demange, and Jaming for the general case. Note that Hörmander–Beurling's version implies the case in Hardy's Theorem while the version by Bonami–Demange–Jaming covers the full strength of Hardy's Theorem. A different proof of Beurling's theorem based on Liouville's theorem appeared in\\nref.\",\n \"Uncertainty principle\\n\\nA full description of the case as well as the following extension to Schwartz class distributions appears in ref.\",\n \"Uncertainty principle\\n\\nTheorem. If a tempered distribution f\\\\in\\\\mathcal{S}'(\\\\R^d) is such that\",\n \"Uncertainty principle\\n\\ne^{\\\\pi|x|^2}f\\\\in\\\\mathcal{S} '(\\\\R^d)\\nand\\ne^{\\\\pi|\\\\xi|^2}\\\\hat f\\\\in\\\\mathcal{S}'(\\\\R^d) ~,\\nthen\\n:f(x)=P(x)e^{-\\\\pi\\\\langle Ax,x\\\\rangle} ~,\\nfor some convenient polynomial and real positive definite matrix of type .\",\n \"Uncertainty principle\\n\\nHistory\",\n \"Uncertainty principle\\n\\nWerner Heisenberg formulated the Uncertainty Principle at Niels Bohr's institute in Copenhagen, while working on the mathematical foundations of quantum mechanics.\",\n \"Uncertainty principle\\n\\nIn 1925, following pioneering work with Hendrik Kramers, Heisenberg developed matrix mechanics, which replaced the ad hoc old quantum theory with modern quantum mechanics. The central premise was that the classical concept of motion does not fit at the quantum level, as electrons in an atom do not travel on sharply defined orbits. Rather, their motion is smeared out in a strange way: the Fourier transform of its time dependence only involves those frequencies that could be observed in the quantum jumps of their radiation.\",\n \"Uncertainty principle\\n\\nHeisenberg's paper did not admit any unobservable quantities like the exact position of the electron in an orbit at any time; he only allowed the theorist to talk about the Fourier components of the motion. Since the Fourier components were not defined at the classical frequencies, they could not be used to construct an exact trajectory, so that the formalism could not answer certain overly precise questions about where the electron was or how fast it was going.\",\n \"Uncertainty principle\\n\\nIn March 1926, working in Bohr's institute, Heisenberg realized that the non-commutativity implies the uncertainty principle. This implication provided a clear physical interpretation for the non-commutativity, and it laid the foundation for what became known as the Copenhagen interpretation of quantum mechanics. Heisenberg showed that the commutation relation implies an uncertainty, or in Bohr's language a complementarity. Any two variables that do not commute cannot be measured simultaneously—the more precisely one is known, the less precisely the other can be known. Heisenberg wrote:It can be expressed in its simplest form as follows: One can never know with perfect accuracy both of those two important factors which determine the movement of one of the smallest particles—its position and its velocity. It is impossible to determine accurately both the position and the direction and speed of a particle at the same instant.\",\n \"Uncertainty principle\\n\\nIn his celebrated 1927 paper, \\\"Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik\\\" (\\\"On the Perceptual Content of Quantum Theoretical Kinematics and Mechanics\\\"), Heisenberg established this expression as the minimum amount of unavoidable momentum disturbance caused by any position measurement, but he did not give a precise definition for the uncertainties Δx and Δp. Instead, he gave some plausible estimates in each case separately. In his Chicago lecture he refined his principle:\",\n \"Uncertainty principle\\n\\nKennard in 1927 first proved the modern inequality:\",\n \"Uncertainty principle\\n\\nwhere , and , are the standard deviations of position and momentum. Heisenberg only proved relation () for the special case of Gaussian states.\",\n \"Uncertainty principle\\n\\nTerminology and translation\",\n \"Uncertainty principle\\n\\nThroughout the main body of his original 1927 paper, written in German, Heisenberg used the word, \\\"Ungenauigkeit\\\" (\\\"indeterminacy\\\"),\\nto describe the basic theoretical principle. Only in the endnote did he switch to the word, \\\"Unsicherheit\\\" (\\\"uncertainty\\\"). When the English-language version of Heisenberg's textbook, The Physical Principles of the Quantum Theory, was published in 1930, however, the translation \\\"uncertainty\\\" was used, and it became the more commonly used term in the English language thereafter.\",\n \"Uncertainty principle\\n\\nHeisenberg's microscope\",\n \"Uncertainty principle\\n\\nThe principle is quite counter-intuitive, so the early students of quantum theory had to be reassured that naive measurements to violate it were bound always to be unworkable. One way in which Heisenberg originally illustrated the intrinsic impossibility of violating the uncertainty principle is by using an imaginary microscope as a measuring device.\",\n \"Uncertainty principle\\n\\nHe imagines an experimenter trying to measure the position and momentum of an electron by shooting a photon at it.\\nProblem 1 – If the photon has a short wavelength, and therefore, a large momentum, the position can be measured accurately. But the photon scatters in a random direction, transferring a large and uncertain amount of momentum to the electron. If the photon has a long wavelength and low momentum, the collision does not disturb the electron's momentum very much, but the scattering will reveal its position only vaguely.\",\n \"Uncertainty principle\\n\\nProblem 2 – If a large aperture is used for the microscope, the electron's location can be well resolved (see Rayleigh criterion); but by the principle of conservation of momentum, the transverse momentum of the incoming photon affects the electrons beamline momentum and hence, the new momentum of the electron resolves poorly. If a small aperture is used, the accuracy of both resolutions is the other way around.\",\n \"Uncertainty principle\\n\\nThe combination of these trade-offs imply that no matter what photon wavelength and aperture size are used, the product of the uncertainty in measured position and measured momentum is greater than or equal to a lower limit, which is (up to a small numerical factor) equal to Planck's constant. Heisenberg did not care to formulate the uncertainty principle as an exact limit (which is elaborated below), and preferred to use it instead, as a heuristic quantitative statement, correct up to small numerical factors, which makes the radically new noncommutativity of quantum mechanics inevitable.\",\n \"Uncertainty principle\\n\\nCritical reactions\",\n \"Uncertainty principle\\n\\nThe Copenhagen interpretation of quantum mechanics and Heisenberg's Uncertainty Principle were, in fact, seen as twin targets by detractors who believed in an underlying determinism and realism. According to the Copenhagen interpretation of quantum mechanics, there is no fundamental reality that the quantum state describes, just a prescription for calculating experimental results. There is no way to say what the state of a system fundamentally is, only what the result of observations might be.\",\n \"Uncertainty principle\\n\\nAlbert Einstein believed that randomness is a reflection of our ignorance of some fundamental property of reality, while Niels Bohr believed that the probability distributions are fundamental and irreducible, and depend on which measurements we choose to perform. Einstein and Bohr debated the uncertainty principle for many years. Some experiments within the first decade of the twenty-first century have cast doubt on observer effect aspects of the uncertainty principle.\",\n \"Uncertainty principle\\n\\nEinstein's slit\",\n \"Uncertainty principle\\n\\nThe first of Einstein's thought experiments challenging the uncertainty principle went as follows:\",\n \"Uncertainty principle\\n\\nConsider a particle passing through a slit of width . The slit introduces an uncertainty in momentum of approximately because the particle passes through the wall. But let us determine the momentum of the particle by measuring the recoil of the wall. In doing so, we find the momentum of the particle to arbitrary accuracy by conservation of momentum.\",\n \"Uncertainty principle\\n\\nBohr's response was that the wall is quantum mechanical as well, and that to measure the recoil to accuracy , the momentum of the wall must be known to this accuracy before the particle passes through. This introduces an uncertainty in the position of the wall and therefore the position of the slit equal to , and if the wall's momentum is known precisely enough to measure the recoil, the slit's position is uncertain enough to disallow a position measurement.\",\n \"Uncertainty principle\\n\\nA similar analysis with particles diffracting through multiple slits is given by Richard Feynman.\",\n \"Uncertainty principle\\n\\nEinstein's box\",\n \"Uncertainty principle\\n\\nBohr was present when Einstein proposed the thought experiment which has become known as Einstein's box. Einstein argued that \\\"Heisenberg's uncertainty equation implied that the uncertainty in time was related to the uncertainty in energy, the product of the two being related to Planck's constant.\\\" Consider, he said, an ideal box, lined with mirrors so that it can contain light indefinitely. The box could be weighed before a clockwork mechanism opened an ideal shutter at a chosen instant to allow one single photon to escape. \\\"We now know, explained Einstein, precisely the time at which the photon left the box.\\\" \\\"Now, weigh the box again. The change of mass tells the energy of the emitted light. In this manner, said Einstein, one could measure the energy emitted and the time it was released with any desired precision, in contradiction to the uncertainty principle.\\\"\",\n \"Uncertainty principle\\n\\nBohr spent a sleepless night considering this argument, and eventually realized that it was flawed. He pointed out that if the box were to be weighed, say by a spring and a pointer on a scale, \\\"since the box must move vertically with a change in its weight, there will be uncertainty in its vertical velocity and therefore an uncertainty in its height above the table. ... Furthermore, the uncertainty about the elevation above the earth's surface will result in an uncertainty in the rate of the clock,\\\" because of Einstein's own theory of gravity's effect on time.\\n\\\"Through this chain of uncertainties, Bohr showed that Einstein's light box experiment could not simultaneously measure exactly both the energy of the photon and the time of its escape.\\\"\",\n \"Uncertainty principle\\n\\nEPR paradox for entangled particles\",\n \"Uncertainty principle\\n\\nBohr was compelled to modify his understanding of the uncertainty principle after another thought experiment by Einstein. In 1935, Einstein, Podolsky and Rosen (see EPR paradox) published an analysis of widely separated entangled particles. Measuring one particle, Einstein realized, would alter the probability distribution of the other, yet here the other particle could not possibly be disturbed. This example led Bohr to revise his understanding of the principle, concluding that the uncertainty was not caused by a direct interaction.\",\n \"Uncertainty principle\\n\\nBut Einstein came to much more far-reaching conclusions from the same thought experiment. He believed the \\\"natural basic assumption\\\" that a complete description of reality, would have to predict the results of experiments from \\\"locally changing deterministic quantities\\\", and therefore, would have to include more information than the maximum possible allowed by the uncertainty principle.\",\n \"Uncertainty principle\\n\\nIn 1964, John Bell showed that this assumption can be falsified, since it would imply a certain inequality between the probabilities of different experiments. Experimental results confirm the predictions of quantum mechanics, ruling out Einstein's basic assumption that led him to the suggestion of his hidden variables. Ironically this fact is one of the best pieces of evidence supporting Karl Popper's philosophy of invalidation of a theory by falsification-experiments. That is to say, here Einstein's \\\"basic assumption\\\" became falsified by experiments based on Bell's inequalities. For the objections of Karl Popper to the Heisenberg inequality itself, see below.\",\n \"Uncertainty principle\\n\\nWhile it is possible to assume that quantum mechanical predictions are due to nonlocal, hidden variables, and in fact David Bohm invented such a formulation, this resolution is not satisfactory to the vast majority of physicists. The question of whether a random outcome is predetermined by a nonlocal theory can be philosophical, and it can be potentially intractable. If the hidden variables are not constrained, they could just be a list of random digits that are used to produce the measurement outcomes. To make it sensible, the assumption of nonlocal hidden variables is sometimes augmented by a second assumption—that the size of the observable universe puts a limit on the computations that these variables can do. A nonlocal theory of this sort predicts that a quantum computer would encounter fundamental obstacles when attempting to factor numbers of approximately 10,000 digits or more; a potentially achievable task in quantum mechanics.\",\n \"Uncertainty principle\\n\\nPopper's criticism\",\n \"Uncertainty principle\\n\\nKarl Popper approached the problem of indeterminacy as a logician and metaphysical realist. He disagreed with the application of the uncertainty relations to individual particles rather than to ensembles of identically prepared particles, referring to them as \\\"statistical scatter relations\\\". In this statistical interpretation, a particular measurement may be made to arbitrary precision without invalidating the quantum theory. This directly contrasts with the Copenhagen interpretation of quantum mechanics, which is non-deterministic but lacks local hidden variables.\",\n \"Uncertainty principle\\n\\nIn 1934, Popper published Zur Kritik der Ungenauigkeitsrelationen (Critique of the Uncertainty Relations) in Naturwissenschaften, and in the same year Logik der Forschung (translated and updated by the author as The Logic of Scientific Discovery in 1959), outlining his arguments for the statistical interpretation. In 1982, he further developed his theory in Quantum theory and the schism in Physics, writing:\\n[Heisenberg's] formulae are, beyond all doubt, derivable statistical formulae of the quantum theory. But they have been habitually misinterpreted by those quantum theorists who said that these formulae can be interpreted as determining some upper limit to the precision of our measurements.[original emphasis]\",\n \"Uncertainty principle\\n\\nPopper proposed an experiment to falsify the uncertainty relations, although he later withdrew his initial version after discussions with Weizsäcker, Heisenberg, and Einstein; this experiment may have influenced the formulation of the EPR experiment.\",\n \"Uncertainty principle\\n\\nMany-worlds uncertainty\",\n \"Uncertainty principle\\n\\nThe many-worlds interpretation originally outlined by Hugh Everett III in 1957 is partly meant to reconcile the differences between Einstein's and Bohr's views by replacing Bohr's wave function collapse with an ensemble of deterministic and independent universes whose distribution is governed by wave functions and the Schrödinger equation. Thus, uncertainty in the many-worlds interpretation follows from each observer within any universe having no knowledge of what goes on in the other universes.\",\n \"Uncertainty principle\\n\\nFree will\",\n \"Uncertainty principle\\n\\nSome scientists including Arthur Compton and Martin Heisenberg have suggested that the uncertainty principle, or at least the general probabilistic nature of quantum mechanics, could be evidence for the two-stage model of free will. One critique, however, is that apart from the basic role of quantum mechanics as a foundation for chemistry, nontrivial biological mechanisms requiring quantum mechanics are unlikely, due to the rapid decoherence time of quantum systems at room temperature. The standard view, however, is that this decoherence is overcome by both screening and decoherence-free subspaces found in biological cells.\"\n]","isConversational":false}}},{"rowIdx":1784,"cells":{"id":{"kind":"string","value":"tc_2756"},"question":{"kind":"string","value":"What did Heike Kamerlingh-Onnes discover?"},"answer":{"kind":"string","value":"Superconductivity"},"answer_aliases":{"kind":"list like","value":["super conduction manipulation","supraconductivity","superconducting transition","superconduction","super conductivity","superconducting","superconductor engineering","super conductors","superconductivivty","superconductive","superconductor engineer","superconducting engineer","superconductors","super conducotr","superconductor","superconducting ring","superconducting engineering","superconductivity","super conductor"],"string":"[\n \"super conduction manipulation\",\n \"supraconductivity\",\n \"superconducting transition\",\n \"superconduction\",\n \"super conductivity\",\n \"superconducting\",\n \"superconductor engineering\",\n \"super conductors\",\n \"superconductivivty\",\n \"superconductive\",\n \"superconductor engineer\",\n \"superconducting engineer\",\n \"superconductors\",\n \"super conducotr\",\n \"superconductor\",\n \"superconducting ring\",\n \"superconducting engineering\",\n \"superconductivity\",\n \"super conductor\"\n]","isConversational":false},"documents":{"kind":"list like","value":["Heike Kamerlingh Onnes\n\nHeike Kamerlingh Onnes (; 21 September 1853 – 21 February 1926) was a Dutch physicist and Nobel laureate. He exploited the Hampson-Linde cycle to investigate how materials behave when cooled to nearly absolute zero and later to liquefy helium for the first time. His production of extreme cryogenic temperatures led to his discovery of superconductivity in 1911: for certain materials, electrical resistance abruptly vanishes at very low temperatures.","Heike Kamerlingh Onnes\n\nBiography","Heike Kamerlingh Onnes\n\nEarly years","Heike Kamerlingh Onnes\n\nKamerlingh Onnes was born in Groningen, Netherlands. His father, Harm Kamerlingh Onnes, was a brickworks owner. His mother was Anna Gerdina Coers of Arnhem.","Heike Kamerlingh Onnes\n\nIn 1870, Kamerlingh Onnes attended the University of Groningen. He studied under Robert Bunsen and Gustav Kirchhoff at the University of Heidelberg from 1871 to 1873. Again at Groningen, he obtained his masters in 1878 and a doctorate in 1879. His thesis was \"Nieuwe bewijzen voor de aswenteling der aarde\" (tr. New proofs of the rotation of the earth). From 1878 to 1882 he was assistant to Johannes Bosscha, the director of the Delft Polytechnic, for whom he substituted as lecturer in 1881 and 1882.","Heike Kamerlingh Onnes\n\nFamily","Heike Kamerlingh Onnes\n\nHe was married to Maria Adriana Wilhelmina Elisabeth Bijleveld (m. 1887) and had one child, named Albert. His brother Menso Kamerlingh Onnes (1860–1925) was a fairly well known painter (and father of another painter, Harm Kamerlingh Onnes), while his sister Jenny married another famous painter, Floris Verster (1861–1927).","Heike Kamerlingh Onnes\n\nUniversity of Leiden","Heike Kamerlingh Onnes\n\nFrom 1882 to 1923 Kamerlingh Onnes served as professor of experimental physics at the University of Leiden. In 1904 he founded a very large cryogenics laboratory and invited other researchers to the location, which made him highly regarded in the scientific community. The laboratory is known now as Kamerlingh Onnes Laboratory. Only one year after his appointment as professor he became member of the Royal Netherlands Academy of Arts and Sciences.","Heike Kamerlingh Onnes\n\nLiquefaction of helium","Heike Kamerlingh Onnes\n\nOn 10 July 1908, he was the first to liquefy helium, using several precooling stages and the Hampson-Linde cycle based on the Joule-Thomson effect. This way he lowered the temperature to the boiling point of helium (−269 °C, 4.2 K). By reducing the pressure of the liquid helium he achieved a temperature near 1.5 K. These were the coldest temperatures achieved on earth at the time. The equipment employed is at the Boerhaave Museum in Leiden.","Heike Kamerlingh Onnes\n\nSuperconductivity","Heike Kamerlingh Onnes\n\nIn 1911 Kamerlingh Onnes measured the electrical conductivity of pure metals (mercury, and later tin and lead) at very low temperatures. Some scientists, such as William Thomson (Lord Kelvin), believed that electrons flowing through a conductor would come to a complete halt or, in other words, metal resistivity would become infinitely large at absolute zero. Others, including Kamerlingh Onnes, felt that a conductor's electrical resistance would steadily decrease and drop to nil. Augustus Matthiessen pointed out when the temperature decreases, the metal conductivity usually improves or in other words, the electrical resistivity usually decreases with a decrease of temperature.","Heike Kamerlingh Onnes\n\nOn 8 April 1911, Kamerlingh Onnes found that at 4.2 K the resistance in a solid mercury wire immersed in liquid helium suddenly vanished. He immediately realized the significance of the discovery (as became clear when his notebook was deciphered a century later). He reported that \"Mercury has passed into a new state, which on account of its extraordinary electrical properties may be called the superconductive state\". He published more articles about the phenomenon, initially referring to it as \"supraconductivity\" and, only later adopting the term \"superconductivity\".","Heike Kamerlingh Onnes\n\nKamerlingh Onnes received widespread recognition for his work, including the 1913 Nobel Prize in Physics for (in the words of the committee) \"his investigations on the properties of matter at low temperatures which led, inter alia, to the production of liquid helium\".","Heike Kamerlingh Onnes\n\nLegacy","Heike Kamerlingh Onnes\n\nSome of the instruments he devised for his experiments can be seen at the Boerhaave Museum in Leiden. The apparatus he used to first liquefy helium is on display in the lobby of the physics department at Leiden University, where the low-temperature lab is also named in his honor. His student and successor as director of the lab Willem Hendrik Keesom was the first person who was able to solidify helium, in 1926. The former Kamerlingh Onnes laboratory building is currently the Law Faculty at Leiden University and is known as \"Kamerlingh Onnes Gebouw\" (Kamerlingh Onnes Building), often shortened to \"KOG\". The current science faculty has a \"Kamerlingh Onnes Laboratorium\" named after him, as well as a plaque and several machines used by Kamerling Onnes in the main hall of the physics department.","Heike Kamerlingh Onnes\n\nThe Onnes effect referring to the creeping of superfluid helium is named in his honor.","Heike Kamerlingh Onnes\n\nThe crater Kamerlingh Onnes on the Moon is named after him.","Heike Kamerlingh Onnes\n\nOnnes is also credited with coining the word \"enthalpy\".","Heike Kamerlingh Onnes\n\nOnnes' discovery of superconductivity was named an IEEE Milestone in 2011.","Heike Kamerlingh Onnes\n\nHonors and awards","Heike Kamerlingh Onnes\n\n*Matteucci Medal (1910)\n*Rumford Medal (1912)\n*Nobel Prize in Physics (1913)\n*Franklin Medal (1915)","Heike Kamerlingh Onnes\n\nSelected publications","Heike Kamerlingh Onnes\n\n* Kamerlingh Onnes, H., \"Nieuwe bewijzen voor de aswenteling der aarde.\" Ph.D. dissertation. Groningen, Netherlands, 1879. * Kamerlingh Onnes, H., \"Algemeene theorie der vloeistoffen.\" Amsterdam Akad. Verhandl; 21, 1881. * Kamerlingh Onnes, H., \"On the Cryogenic Laboratory at Leyden and on the Production of Very Low Temperature.\" Comm. Phys. Lab. Univ. Leiden; 14, 1894. * Kamerlingh Onnes, H., \"Théorie générale de l'état fluide.\" Haarlem Arch. Neerl.; 30, 1896. * Kamerlingh Onnes, H., \"Further experiments with liquid helium. C. On the change of electric resistance of pure metals at very low temperatures, etc. IV. The resistance of pure mercury at helium temperatures.\" Comm. Phys. Lab. Univ. Leiden; No. 120b, 1911. * Kamerlingh Onnes, H., \"Further experiments with liquid helium. D. On the change of electric resistance of pure metals at very low temperatures, etc. V. The disappearance of the resistance of mercury.\" Comm. Phys. Lab. Univ. Leiden; No. 122b, 1911. * Kamerlingh Onnes, H., \"Further experiments with liquid helium. G. On the electrical resistance of pure metals, etc. VI. On the sudden change in the rate at which the resistance of mercury disappears.\" Comm. Phys. Lab. Univ. Leiden; No. 124c, 1911. * Kamerlingh Onnes, H., \"On the Lowest Temperature Yet Obtained.\" Comm. Phys. Lab. Univ. Leiden; No. 159, 1922."],"string":"[\n \"Heike Kamerlingh Onnes\\n\\nHeike Kamerlingh Onnes (; 21 September 1853 – 21 February 1926) was a Dutch physicist and Nobel laureate. He exploited the Hampson-Linde cycle to investigate how materials behave when cooled to nearly absolute zero and later to liquefy helium for the first time. His production of extreme cryogenic temperatures led to his discovery of superconductivity in 1911: for certain materials, electrical resistance abruptly vanishes at very low temperatures.\",\n \"Heike Kamerlingh Onnes\\n\\nBiography\",\n \"Heike Kamerlingh Onnes\\n\\nEarly years\",\n \"Heike Kamerlingh Onnes\\n\\nKamerlingh Onnes was born in Groningen, Netherlands. His father, Harm Kamerlingh Onnes, was a brickworks owner. His mother was Anna Gerdina Coers of Arnhem.\",\n \"Heike Kamerlingh Onnes\\n\\nIn 1870, Kamerlingh Onnes attended the University of Groningen. He studied under Robert Bunsen and Gustav Kirchhoff at the University of Heidelberg from 1871 to 1873. Again at Groningen, he obtained his masters in 1878 and a doctorate in 1879. His thesis was \\\"Nieuwe bewijzen voor de aswenteling der aarde\\\" (tr. New proofs of the rotation of the earth). From 1878 to 1882 he was assistant to Johannes Bosscha, the director of the Delft Polytechnic, for whom he substituted as lecturer in 1881 and 1882.\",\n \"Heike Kamerlingh Onnes\\n\\nFamily\",\n \"Heike Kamerlingh Onnes\\n\\nHe was married to Maria Adriana Wilhelmina Elisabeth Bijleveld (m. 1887) and had one child, named Albert. His brother Menso Kamerlingh Onnes (1860–1925) was a fairly well known painter (and father of another painter, Harm Kamerlingh Onnes), while his sister Jenny married another famous painter, Floris Verster (1861–1927).\",\n \"Heike Kamerlingh Onnes\\n\\nUniversity of Leiden\",\n \"Heike Kamerlingh Onnes\\n\\nFrom 1882 to 1923 Kamerlingh Onnes served as professor of experimental physics at the University of Leiden. In 1904 he founded a very large cryogenics laboratory and invited other researchers to the location, which made him highly regarded in the scientific community. The laboratory is known now as Kamerlingh Onnes Laboratory. Only one year after his appointment as professor he became member of the Royal Netherlands Academy of Arts and Sciences.\",\n \"Heike Kamerlingh Onnes\\n\\nLiquefaction of helium\",\n \"Heike Kamerlingh Onnes\\n\\nOn 10 July 1908, he was the first to liquefy helium, using several precooling stages and the Hampson-Linde cycle based on the Joule-Thomson effect. This way he lowered the temperature to the boiling point of helium (−269 °C, 4.2 K). By reducing the pressure of the liquid helium he achieved a temperature near 1.5 K. These were the coldest temperatures achieved on earth at the time. The equipment employed is at the Boerhaave Museum in Leiden.\",\n \"Heike Kamerlingh Onnes\\n\\nSuperconductivity\",\n \"Heike Kamerlingh Onnes\\n\\nIn 1911 Kamerlingh Onnes measured the electrical conductivity of pure metals (mercury, and later tin and lead) at very low temperatures. Some scientists, such as William Thomson (Lord Kelvin), believed that electrons flowing through a conductor would come to a complete halt or, in other words, metal resistivity would become infinitely large at absolute zero. Others, including Kamerlingh Onnes, felt that a conductor's electrical resistance would steadily decrease and drop to nil. Augustus Matthiessen pointed out when the temperature decreases, the metal conductivity usually improves or in other words, the electrical resistivity usually decreases with a decrease of temperature.\",\n \"Heike Kamerlingh Onnes\\n\\nOn 8 April 1911, Kamerlingh Onnes found that at 4.2 K the resistance in a solid mercury wire immersed in liquid helium suddenly vanished. He immediately realized the significance of the discovery (as became clear when his notebook was deciphered a century later). He reported that \\\"Mercury has passed into a new state, which on account of its extraordinary electrical properties may be called the superconductive state\\\". He published more articles about the phenomenon, initially referring to it as \\\"supraconductivity\\\" and, only later adopting the term \\\"superconductivity\\\".\",\n \"Heike Kamerlingh Onnes\\n\\nKamerlingh Onnes received widespread recognition for his work, including the 1913 Nobel Prize in Physics for (in the words of the committee) \\\"his investigations on the properties of matter at low temperatures which led, inter alia, to the production of liquid helium\\\".\",\n \"Heike Kamerlingh Onnes\\n\\nLegacy\",\n \"Heike Kamerlingh Onnes\\n\\nSome of the instruments he devised for his experiments can be seen at the Boerhaave Museum in Leiden. The apparatus he used to first liquefy helium is on display in the lobby of the physics department at Leiden University, where the low-temperature lab is also named in his honor. His student and successor as director of the lab Willem Hendrik Keesom was the first person who was able to solidify helium, in 1926. The former Kamerlingh Onnes laboratory building is currently the Law Faculty at Leiden University and is known as \\\"Kamerlingh Onnes Gebouw\\\" (Kamerlingh Onnes Building), often shortened to \\\"KOG\\\". The current science faculty has a \\\"Kamerlingh Onnes Laboratorium\\\" named after him, as well as a plaque and several machines used by Kamerling Onnes in the main hall of the physics department.\",\n \"Heike Kamerlingh Onnes\\n\\nThe Onnes effect referring to the creeping of superfluid helium is named in his honor.\",\n \"Heike Kamerlingh Onnes\\n\\nThe crater Kamerlingh Onnes on the Moon is named after him.\",\n \"Heike Kamerlingh Onnes\\n\\nOnnes is also credited with coining the word \\\"enthalpy\\\".\",\n \"Heike Kamerlingh Onnes\\n\\nOnnes' discovery of superconductivity was named an IEEE Milestone in 2011.\",\n \"Heike Kamerlingh Onnes\\n\\nHonors and awards\",\n \"Heike Kamerlingh Onnes\\n\\n*Matteucci Medal (1910)\\n*Rumford Medal (1912)\\n*Nobel Prize in Physics (1913)\\n*Franklin Medal (1915)\",\n \"Heike Kamerlingh Onnes\\n\\nSelected publications\",\n \"Heike Kamerlingh Onnes\\n\\n* Kamerlingh Onnes, H., \\\"Nieuwe bewijzen voor de aswenteling der aarde.\\\" Ph.D. dissertation. Groningen, Netherlands, 1879. * Kamerlingh Onnes, H., \\\"Algemeene theorie der vloeistoffen.\\\" Amsterdam Akad. Verhandl; 21, 1881. * Kamerlingh Onnes, H., \\\"On the Cryogenic Laboratory at Leyden and on the Production of Very Low Temperature.\\\" Comm. Phys. Lab. Univ. Leiden; 14, 1894. * Kamerlingh Onnes, H., \\\"Théorie générale de l'état fluide.\\\" Haarlem Arch. Neerl.; 30, 1896. * Kamerlingh Onnes, H., \\\"Further experiments with liquid helium. C. On the change of electric resistance of pure metals at very low temperatures, etc. IV. The resistance of pure mercury at helium temperatures.\\\" Comm. Phys. Lab. Univ. Leiden; No. 120b, 1911. * Kamerlingh Onnes, H., \\\"Further experiments with liquid helium. D. On the change of electric resistance of pure metals at very low temperatures, etc. V. The disappearance of the resistance of mercury.\\\" Comm. Phys. Lab. Univ. Leiden; No. 122b, 1911. * Kamerlingh Onnes, H., \\\"Further experiments with liquid helium. G. On the electrical resistance of pure metals, etc. VI. On the sudden change in the rate at which the resistance of mercury disappears.\\\" Comm. Phys. Lab. Univ. Leiden; No. 124c, 1911. * Kamerlingh Onnes, H., \\\"On the Lowest Temperature Yet Obtained.\\\" Comm. Phys. Lab. Univ. Leiden; No. 159, 1922.\"\n]","isConversational":false}}},{"rowIdx":1785,"cells":{"id":{"kind":"string","value":"tc_2757"},"question":{"kind":"string","value":"What science is the study of missiles in motion?"},"answer":{"kind":"string","value":"Ballistics"},"answer_aliases":{"kind":"list like","value":["science of bullet","ballistic trajectories","ballistics","firearm and tool mark examiners","ballistically","ballistics test","ballistic vehicle","forensic ballistics","criminal ballistics","ballistic body"],"string":"[\n \"science of bullet\",\n \"ballistic trajectories\",\n \"ballistics\",\n \"firearm and tool mark examiners\",\n \"ballistically\",\n \"ballistics test\",\n \"ballistic vehicle\",\n \"forensic ballistics\",\n \"criminal ballistics\",\n \"ballistic body\"\n]","isConversational":false},"documents":{"kind":"list like","value":["ballistics - Infoplease\n\nballistics\nEncyclopedia > Science and Technology > Physics > Physics\nballistics\nballistics (bəlĭsˈtĭks) [ key ], science of projectiles. Interior ballistics deals with the propulsion and the motion of a projectile within a gun or firing device. Its problems include the ignition and burning of the propellant powder, the pressure produced by the expanding gases, the movement of the projectile through the bore, and the designing of the barrel to resist resulting stresses and strains. Exterior ballistics is concerned with the motion of a projectile while in flight and includes the study not only of the flight path of bullets but also of bombs, rockets, and missiles. All projectiles traveling through the air are affected by wind, air resistance, and the force of gravity. These forces induce a curved path known as a trajectory. The trajectory varies with the weight and shape of the projectile, with its initial velocity, and with the angle at which it is fired. The general shape of a trajectory is that of a parabola. The total distance traveled by a projectile is known as its range. A ballistic missile in the first stage of its flight is powered and guided by rocket engines.","ballistics - Infoplease\n\nAfter the engines burn out, the warhead travels in a fixed arc as does an artillery shell. In criminology the term ballistics is applied to the identification of the weapon from which a bullet was fired. Microscopic imperfections in a gun barrel make characteristic scratches and grooves on bullets fired through it, but use causes the marks a particular gun makes to change over time. See E. D. Lowry, Interior Ballistics (1968); R. C. Labile, Ballistic Materials and Penetration Mechanics (1980); A. J. Pejsa, Modern Practical Ballistics (1989); M. Denny, Their Arrows Will Darken the Sun: The Evolution and Science of Ballistics (2011). The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved. See more Encyclopedia articles on: Physics"],"string":"[\n \"ballistics - Infoplease\\n\\nballistics\\nEncyclopedia > Science and Technology > Physics > Physics\\nballistics\\nballistics (bəlĭsˈtĭks) [ key ], science of projectiles. Interior ballistics deals with the propulsion and the motion of a projectile within a gun or firing device. Its problems include the ignition and burning of the propellant powder, the pressure produced by the expanding gases, the movement of the projectile through the bore, and the designing of the barrel to resist resulting stresses and strains. Exterior ballistics is concerned with the motion of a projectile while in flight and includes the study not only of the flight path of bullets but also of bombs, rockets, and missiles. All projectiles traveling through the air are affected by wind, air resistance, and the force of gravity. These forces induce a curved path known as a trajectory. The trajectory varies with the weight and shape of the projectile, with its initial velocity, and with the angle at which it is fired. The general shape of a trajectory is that of a parabola. The total distance traveled by a projectile is known as its range. A ballistic missile in the first stage of its flight is powered and guided by rocket engines.\",\n \"ballistics - Infoplease\\n\\nAfter the engines burn out, the warhead travels in a fixed arc as does an artillery shell. In criminology the term ballistics is applied to the identification of the weapon from which a bullet was fired. Microscopic imperfections in a gun barrel make characteristic scratches and grooves on bullets fired through it, but use causes the marks a particular gun makes to change over time. See E. D. Lowry, Interior Ballistics (1968); R. C. Labile, Ballistic Materials and Penetration Mechanics (1980); A. J. Pejsa, Modern Practical Ballistics (1989); M. Denny, Their Arrows Will Darken the Sun: The Evolution and Science of Ballistics (2011). The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved. See more Encyclopedia articles on: Physics\"\n]","isConversational":false}}},{"rowIdx":1786,"cells":{"id":{"kind":"string","value":"tc_2759"},"question":{"kind":"string","value":"What kind of elements are found in a pure state in nature?"},"answer":{"kind":"string","value":"Native elements"},"answer_aliases":{"kind":"list like","value":["native elements"],"string":"[\n \"native elements\"\n]","isConversational":false},"documents":{"kind":"list like","value":["Chemical element\n\nA chemical element or element is a species of atoms having the same number of protons in their atomic nuclei (i.e. the same atomic number, Z). There are 118 elements that have been identified, of which the first 94 occur naturally on Earth with the remaining 24 being synthetic elements. There are 80 elements that have at least one stable isotope and 38 that have exclusively radioactive isotopes, which decay over time into other elements. Iron is the most abundant element (by mass) making up Earth, while oxygen is the most common element in the crust of Earth.","Chemical element\n\nChemical elements constitute all of the ordinary matter of the universe. However astronomical observations suggest that ordinary observable matter is only approximately 15% of the matter in the universe: the remainder is dark matter, the composition of which is unknown, but it is not composed of chemical elements. \nThe two lightest elements, hydrogen and helium were mostly formed in the Big Bang and are the most common elements in the universe. The next three elements (lithium, beryllium and boron) were formed mostly by cosmic ray spallation, and are thus more rare than those that follow. Formation of elements with from six to twenty six protons occurred and continues to occur in main sequence stars via stellar nucleosynthesis. The high abundance of oxygen, silicon, and iron on Earth reflects their common production in such stars. Elements with greater than twenty-six protons are formed by supernova nucleosynthesis in supernovae, which, when they explode, blast these elements far into space as supernova remnants, where they may become incorporated into planets when they are formed.","Chemical element\n\nThe term \"element\" is used for a kind of atoms with a given number of protons (regardless of whether they are or they are not ionized or chemically bonded, e.g. hydrogen in water) as well as for a pure chemical substance consisting of a single element (e.g. hydrogen gas). For the second meaning, the terms \"elementary substance\" and \"simple substance\" have been suggested, but they have not gained much acceptance in the English-language chemical literature, whereas in some other languages their equivalent is widely used (e.g. French corps simple, Russian простое вещество). One element can form multiple substances different by their structure; they are called allotropes of the element.","Chemical element\n\nWhen different elements are chemically combined, with the atoms held together by chemical bonds, they form chemical compounds. Only a minority of elements are found uncombined as relatively pure minerals. Among the more common of such \"native elements\" are copper, silver, gold, carbon (as coal, graphite, or diamonds), and sulfur. All but a few of the most inert elements, such as noble gases and noble metals, are usually found on Earth in chemically combined form, as chemical compounds. While about 32 of the chemical elements occur on Earth in native uncombined forms, most of these occur as mixtures. For example, atmospheric air is primarily a mixture of nitrogen, oxygen, and argon, and native solid elements occur in alloys, such as that of iron and nickel.","Chemical element\n\nThe history of the discovery and use of the elements began with primitive human societies that found native elements like carbon, sulfur, copper and gold. Later civilizations extracted elemental copper, tin, lead and iron from their ores by smelting, using charcoal. Alchemists and chemists subsequently identified many more, with almost all of the naturally-occurring elements becoming known by 1900.","Chemical element\n\nThe properties of the chemical elements are summarized on the periodic table, which organizes the elements by increasing atomic number into rows (\"periods\") in which the columns (\"groups\") share recurring (\"periodic\") physical and chemical properties. Save for unstable radioactive elements with short half-lives, all of the elements are available industrially, most of them in high degrees of purity.","Chemical element\n\nDescription","Chemical element\n\nThe lightest chemical elements are hydrogen and helium, both created by Big Bang nucleosynthesis during the first 20 minutes of the universe in a ratio of around 3:1 by mass (or 12:1 by number of atoms), along with tiny traces of the next two elements, lithium and beryllium. Almost all other elements found in nature were made by various natural methods of nucleosynthesis. On Earth, small amounts of new atoms are naturally produced in nucleogenic reactions, or in cosmogenic processes, such as cosmic ray spallation. New atoms are also naturally produced on Earth as radiogenic daughter isotopes of ongoing radioactive decay processes such as alpha decay, beta decay, spontaneous fission, cluster decay, and other rarer modes of decay.","Chemical element\n\nOf the 94 naturally occurring elements, those with atomic numbers 1 through 82 each have at least one stable isotope (except for technetium, element 43 and promethium, element 61, which have no stable isotopes). Isotopes considered stable are those for which no radioactive decay has yet been observed. Elements with atomic numbers 83 through 94 are unstable to the point that radioactive decay of all isotopes can be detected. Some of these elements, notably bismuth (atomic number 83), thorium (atomic number 90), uranium (atomic number 92) and plutonium (atomic number 94), have one or more isotopes with half-lives long enough to survive as remnants of the explosive stellar nucleosynthesis that produced the heavy elements before the formation of our solar system. For example, at over 1.9 years, over a billion times longer than the current estimated age of the universe, bismuth-209 (atomic number 83) has the longest known alpha decay half-life of any naturally occurring element. The very heaviest elements (those beyond plutonium, element 94) undergo radioactive decay with half-lives so short that they are not found in nature and must be synthesized.","Chemical element\n\nAs of 2010, there are 118 known elements (in this context, \"known\" means observed well enough, even from just a few decay products, to have been differentiated from other elements). Of these 118 elements, 94 occur naturally on Earth. Six of these occur in extreme trace quantities: technetium, atomic number 43; promethium, number 61; astatine, number 85; francium, number 87; neptunium, number 93; and plutonium, number 94. These 94 elements have been detected in the universe at large, in the spectra of stars and also supernovae, where short-lived radioactive elements are newly being made. The first 94 elements have been detected directly on Earth as primordial nuclides present from the formation of the solar system, or as naturally-occurring fission or transmutation products of uranium and thorium.","Chemical element\n\nThe remaining 24 heavier elements, not found today either on Earth or in astronomical spectra, have been produced artificially: these are all radioactive, with very short half-lives; if any atoms of these elements were present at the formation of Earth, they are extremely likely, to the point of certainty, to have already decayed, and if present in novae, have been in quantities too small to have been noted. Technetium was the first purportedly non-naturally occurring element synthesized, in 1937, although trace amounts of technetium have since been found in nature (and also the element may have been discovered naturally in 1925). This pattern of artificial production and later natural discovery has been repeated with several other radioactive naturally-occurring rare elements.","Chemical element\n\nLists of the elements are available by name, by symbol, by atomic number, by density, by melting point, and by boiling point as well as ionization energies of the elements. The nuclides of stable and radioactive elements are also available as a list of nuclides, sorted by length of half-life for those that are unstable. One of the most convenient, and certainly the most traditional presentation of the elements, is in the form of the periodic table, which groups together elements with similar chemical properties (and usually also similar electronic structures).","Chemical element\n\nAtomic number","Chemical element\n\nThe atomic number of an element is equal to the number of protons in each atom, and defines the element. For example, all carbon atoms contain 6 protons in their atomic nucleus; so the atomic number of carbon is 6. Carbon atoms may have different numbers of neutrons; atoms of the same element having different numbers of neutrons are known as isotopes of the element.","Chemical element\n\nThe number of protons in the atomic nucleus also determines its electric charge, which in turn determines the number of electrons of the atom in its non-ionized state. The electrons are placed into atomic orbitals that determine the atom's various chemical properties. The number of neutrons in a nucleus usually has very little effect on an element's chemical properties (except in the case of hydrogen and deuterium). Thus, all carbon isotopes have nearly identical chemical properties because they all have six protons and six electrons, even though carbon atoms may, for example, have 6 or 8 neutrons. That is why the atomic number, rather than mass number or atomic weight, is considered the identifying characteristic of a chemical element.","Chemical element\n\nThe symbol for atomic number is Z.","Chemical element\n\nIsotopes","Chemical element\n\nIsotopes are atoms of the same element (that is, with the same number of protons in their atomic nucleus), but having different numbers of neutrons. Most (66 of 94) naturally occurring elements have more than one stable isotope. Thus, for example, there are three main isotopes of carbon. All carbon atoms have 6 protons in the nucleus, but they can have either 6, 7, or 8 neutrons. Since the mass numbers of these are 12, 13 and 14 respectively, the three isotopes of carbon are known as carbon-12, carbon-13, and carbon-14, often abbreviated to 12C, 13C, and 14C. Carbon in everyday life and in chemistry is a mixture of 12C (about 98.9%), 13C (about 1.1%) and about 1 atom per trillion of 14C.","Chemical element\n\nExcept in the case of the isotopes of hydrogen (which differ greatly from each other in relative mass—enough to cause chemical effects), the isotopes of a given element are chemically nearly indistinguishable.","Chemical element\n\nAll of the elements have some isotopes that are radioactive (radioisotopes), although not all of these radioisotopes occur naturally. The radioisotopes typically decay into other elements upon radiating an alpha or beta particle. If an element has isotopes that are not radioactive, these are termed \"stable\" isotopes. All of the known stable isotopes occur naturally (see primordial isotope). The many radioisotopes that are not found in nature have been characterized after being artificially made. Certain elements have no stable isotopes and are composed only of radioactive isotopes: specifically the elements without any stable isotopes are technetium (atomic number 43), promethium (atomic number 61), and all observed elements with atomic numbers greater than 82.","Chemical element\n\nOf the 80 elements with at least one stable isotope, 26 have only one single stable isotope. The mean number of stable isotopes for the 80 stable elements is 3.1 stable isotopes per element. The largest number of stable isotopes that occur for a single element is 10 (for tin, element 50).","Chemical element\n\nIsotopic mass and atomic mass","Chemical element\n\nThe mass number of an element, A, is the number of nucleons (protons and neutrons) in the atomic nucleus. Different isotopes of a given element are distinguished by their mass numbers, which are conventionally written as a superscript on the left hand side of the atomic symbol (e.g., 238U). The mass number is always a simple whole number and has units of \"nucleons.\" An example of a referral to a mass number is \"magnesium-24,\" which is an atom with 24 nucleons (12 protons and 12 neutrons).","Chemical element\n\nWhereas the mass number simply counts the total number of neutrons and protons and is thus a natural (or whole) number, the atomic mass of a single atom is a real number for the mass of a particular isotope of the element, the unit being u. In general, when expressed in u it differs in value slightly from the mass number for a given nuclide (or isotope) since the mass of the protons and neutrons is not exactly 1 u, since the electrons contribute a lesser share to the atomic mass as neutron number exceeds proton number, and (finally) because of the nuclear binding energy. For example, the atomic mass of chlorine-35 to five significant digits is 34.969 u and that of chlorine-37 is 36.966 u. However, the atomic mass in u of each isotope is quite close to its simple mass number (always within 1%). The only isotope whose atomic mass is exactly a natural number is 12C, which by definition has a mass of exactly 12, because u is defined as 1/12 of the mass of a free neutral carbon-12 atom in the ground state.","Chemical element\n\nThe relative atomic mass (historically and commonly also called \"atomic weight\") of an element is the average of the atomic masses of all the chemical element's isotopes as found in a particular environment, weighted by isotopic abundance, relative to the atomic mass unit (u). This number may be a fraction that is not close to a whole number, due to the averaging process. For example, the relative atomic mass of chlorine is 35.453 u, which differs greatly from a whole number due to being made of an average of 76% chlorine-35 and 24% chlorine-37. Whenever a relative atomic mass value differs by more than 1% from a whole number, it is due to this averaging effect resulting from significant amounts of more than one isotope being naturally present in the sample of the element in question.","Chemical element\n\nChemically pure and isotopically pure","Chemical element\n\nChemists and nuclear scientists have different definitions of a pure element. In chemistry, a pure element means a substance whose atoms all (or in practice almost all) have the same atomic number, or number of protons. Nuclear scientists, however, define a pure element as one that consists of only one stable isotope.","Chemical element\n\nFor example, a copper wire is 99.99% chemically pure if 99.99% of its atoms are copper, with 29 protons each. However it is not isotopically pure since ordinary copper consists of two stable isotopes, 69% 63Cu and 31% 65Cu, with different numbers of neutrons. However, a pure gold ingot would be both chemically and isotopically pure, since ordinary gold consists only of one isotope, 197Au.","Chemical element\n\nAllotropes","Chemical element\n\nAtoms of chemically pure elements may bond to each other chemically in more than one way, allowing the pure element to exist in multiple structures (spatial arrangements of atoms), known as allotropes, which differ in their properties. For example, carbon can be found as diamond, which has a tetrahedral structure around each carbon atom; graphite, which has layers of carbon atoms with a hexagonal structure stacked on top of each other; graphene, which is a single layer of graphite that is very strong; fullerenes, which have nearly spherical shapes; and carbon nanotubes, which are tubes with a hexagonal structure (even these may differ from each other in electrical properties). The ability of an element to exist in one of many structural forms is known as 'allotropy'.","Chemical element\n\nThe standard state, also known as reference state, of an element is defined as its thermodynamically most stable state at 1 bar at a given temperature (typically at 298.15 K). In thermochemistry, an element is defined to have an enthalpy of formation of zero in its standard state. For example, the reference state for carbon is graphite, because the structure of graphite is more stable than that of the other allotropes.","Chemical element\n\nProperties","Chemical element\n\nSeveral kinds of descriptive categorizations can be applied broadly to the elements, including consideration of their general physical and chemical properties, their states of matter under familiar conditions, their melting and boiling points, their densities, their crystal structures as solids, and their origins.","Chemical element\n\nGeneral properties","Chemical element\n\nSeveral terms are commonly used to characterize the general physical and chemical properties of the chemical elements. A first distinction is between metals, which readily conduct electricity, nonmetals, which do not, and a small group, (the metalloids), having intermediate properties and often behaving as semiconductors.","Chemical element\n\nA more refined classification is often shown in colored presentations of the periodic table. This system restricts the terms \"metal\" and \"nonmetal\" to only certain of the more broadly defined metals and nonmetals, adding additional terms for certain sets of the more broadly viewed metals and nonmetals. The version of this classification used in the periodic tables presented here includes: actinides, alkali metals, alkaline earth metals, halogens, lanthanides, transition metals, post-transition metals, metalloids, polyatomic nonmetals, diatomic nonmetals, and noble gases. In this system, the alkali metals, alkaline earth metals, and transition metals, as well as the lanthanides and the actinides, are special groups of the metals viewed in a broader sense. Similarly, the polyatomic nonmetals, diatomic nonmetals and the noble gases are nonmetals viewed in the broader sense. In some presentations, the halogens are not distinguished, with astatine identified as a metalloid and the others identified as nonmetals.","Chemical element\n\nStates of matter","Chemical element\n\nAnother commonly used basic distinction among the elements is their state of matter (phase), whether solid, liquid, or gas, at a selected standard temperature and pressure (STP). Most of the elements are solids at conventional temperatures and atmospheric pressure, while several are gases. Only bromine and mercury are liquids at 0 degrees Celsius (32 degrees Fahrenheit) and normal atmospheric pressure; caesium and gallium are solids at that temperature, but melt at 28.4 °C (83.2 °F) and 29.8 °C (85.6 °F), respectively.","Chemical element\n\nMelting and boiling points","Chemical element\n\nMelting and boiling points, typically expressed in degrees Celsius at a pressure of one atmosphere, are commonly used in characterizing the various elements. While known for most elements, either or both of these measurements is still undetermined for some of the radioactive elements available in only tiny quantities. Since helium remains a liquid even at absolute zero at atmospheric pressure, it has only a boiling point, and not a melting point, in conventional presentations.","Chemical element\n\nDensities","Chemical element\n\nThe density at a selected standard temperature and pressure (STP) is frequently used in characterizing the elements. Density is often expressed in grams per cubic centimeter (g/cm3). Since several elements are gases at commonly encountered temperatures, their densities are usually stated for their gaseous forms; when liquefied or solidified, the gaseous elements have densities similar to those of the other elements.","Chemical element\n\nWhen an element has allotropes with different densities, one representative allotrope is typically selected in summary presentations, while densities for each allotrope can be stated where more detail is provided. For example, the three familiar allotropes of carbon (amorphous carbon, graphite, and diamond) have densities of 1.8–2.1, 2.267, and 3.515 g/cm3, respectively.","Chemical element\n\nCrystal structures","Chemical element\n\nThe elements studied to date as solid samples have eight kinds of crystal structures: cubic, body-centered cubic, face-centered cubic, hexagonal, monoclinic, orthorhombic, rhombohedral, and tetragonal. For some of the synthetically produced transuranic elements, available samples have been too small to determine crystal structures.","Chemical element\n\nOccurrence and origin on Earth","Chemical element\n\nChemical elements may also be categorized by their origin on Earth, with the first 94 considered naturally occurring, while those with atomic numbers beyond 94 have only been produced artificially as the synthetic products of man-made nuclear reactions.","Chemical element\n\nOf the 94 naturally occurring elements, 84 are considered primordial and either stable or weakly radioactive. The remaining 10 naturally occurring elements possess half lives too short for them to have been present at the beginning of the Solar System, and are therefore considered transient elements. (Plutonium is sometimes also considered a transient element because primordial plutonium has by now decayed to almost undetectable traces.) Of these 10 transient elements, 5 (polonium, radon, radium, actinium, and protactinium) are relatively common decay products of thorium, uranium, and plutonium. The remaining 5 transient elements (technetium, promethium, astatine, francium, and neptunium) occur only rarely, as products of rare decay modes or nuclear reaction processes involving uranium or other heavy elements.","Chemical element\n\nElements with atomic numbers 1 through 40 are all stable, while those with atomic numbers 41 through 82 (except technetium and promethium) are metastable. The half-lives of these metastable \"theoretical radionuclides\" are so long (at least 100 million times longer than the estimated age of the universe) that their radioactive decay has yet to be detected by experiment. Elements with atomic numbers 83 through 94 are unstable to the point that their radioactive decay can be detected. Four of these elements, bismuth (element 83), thorium (element 90), uranium (element 92), and plutonium (element 94), have one or more isotopes with half-lives long enough to survive as remnants of the explosive stellar nucleosynthesis that produced the heavy elements before the formation of our solar system. For example, at over 1.9 years, over a billion times longer than the current estimated age of the universe, bismuth-209 has the longest known alpha decay half-life of any naturally occurring element. The very heaviest elements (those beyond plutonium, element 94) undergo radioactive decay with short half-lives and do not occur in nature.","Chemical element\n\nThe periodic table","Chemical element\n\nThe properties of the chemical elements are often summarized using the periodic table, which powerfully and elegantly organizes the elements by increasing atomic number into rows (\"periods\") in which the columns (\"groups\") share recurring (\"periodic\") physical and chemical properties. The current standard table contains 118 confirmed elements as of 10 April 2010.","Chemical element\n\nAlthough earlier precursors to this presentation exist, its invention is generally credited to the Russian chemist Dmitri Mendeleev in 1869, who intended the table to illustrate recurring trends in the properties of the elements. The layout of the table has been refined and extended over time as new elements have been discovered and new theoretical models have been developed to explain chemical behavior.","Chemical element\n\nUse of the periodic table is now ubiquitous within the academic discipline of chemistry, providing an extremely useful framework to classify, systematize and compare all the many different forms of chemical behavior. The table has also found wide application in physics, geology, biology, materials science, engineering, agriculture, medicine, nutrition, environmental health, and astronomy. Its principles are especially important in chemical engineering.","Chemical element\n\nNomenclature and symbols","Chemical element\n\nThe various chemical elements are formally identified by their unique atomic numbers, by their accepted names, and by their symbols.","Chemical element\n\nAtomic numbers","Chemical element\n\nThe known elements have atomic numbers from 1 through 118, conventionally presented as Arabic numerals. Since the elements can be uniquely sequenced by atomic number, conventionally from lowest to highest (as in a periodic table), sets of elements are sometimes specified by such notation as \"through\", \"beyond\", or \"from ... through\", as in \"through iron\", \"beyond uranium\", or \"from lanthanum through lutetium\". The terms \"light\" and \"heavy\" are sometimes also used informally to indicate relative atomic numbers (not densities), as in \"lighter than carbon\" or \"heavier than lead\", although technically the weight or mass of atoms of an element (their atomic weights or atomic masses) do not always increase monotonically with their atomic numbers.","Chemical element\n\nElement names","Chemical element\n\nThe naming of various substances now known as elements precedes the atomic theory of matter, as names were given locally by various cultures to various minerals, metals, compounds, alloys, mixtures, and other materials, although at the time it was not known which chemicals were elements and which compounds. As they were identified as elements, the existing names for anciently-known elements (e.g., gold, mercury, iron) were kept in most countries. National differences emerged over the names of elements either for convenience, linguistic niceties, or nationalism. For a few illustrative examples: German speakers use \"Wasserstoff\" (water substance) for \"hydrogen\", \"Sauerstoff\" (acid substance) for \"oxygen\" and \"Stickstoff\" (smothering substance) for \"nitrogen\", while English and some romance languages use \"sodium\" for \"natrium\" and \"potassium\" for \"kalium\", and the French, Italians, Greeks, Portuguese and Poles prefer \"azote/azot/azoto\" (from roots meaning \"no life\") for \"nitrogen\".","Chemical element\n\nFor purposes of international communication and trade, the official names of the chemical elements both ancient and more recently recognized are decided by the International Union of Pure and Applied Chemistry (IUPAC), which has decided on a sort of international English language, drawing on traditional English names even when an element's chemical symbol is based on a Latin or other traditional word, for example adopting \"gold\" rather than \"aurum\" as the name for the 79th element (Au). IUPAC prefers the British spellings \"aluminium\" and \"caesium\" over the U.S. spellings \"aluminum\" and \"cesium\", and the U.S. \"sulfur\" over the British \"sulphur\". However, elements that are practical to sell in bulk in many countries often still have locally used national names, and countries whose national language does not use the Latin alphabet are likely to use the IUPAC element names.","Chemical element\n\nAccording to IUPAC, chemical elements are not proper nouns in English; consequently, the full name of an element is not routinely capitalized in English, even if derived from a proper noun, as in californium and einsteinium. Isotope names of chemical elements are also uncapitalized if written out, e.g., carbon-12 or uranium-235. Chemical element symbols (such as Cf for californium and Es for einsteinium), are always capitalized (see below).","Chemical element\n\nIn the second half of the twentieth century, physics laboratories became able to produce nuclei of chemical elements with half-lives too short for an appreciable amount of them to exist at any time. These are also named by IUPAC, which generally adopts the name chosen by the discoverer. This practice can lead to the controversial question of which research group actually discovered an element, a question that delayed the naming of elements with atomic number of 104 and higher for a considerable amount of time. (See element naming controversy).","Chemical element\n\nPrecursors of such controversies involved the nationalistic namings of elements in the late 19th century. For example, lutetium was named in reference to Paris, France. The Germans were reluctant to relinquish naming rights to the French, often calling it cassiopeium. Similarly, the British discoverer of niobium originally named it columbium, in reference to the New World. It was used extensively as such by American publications prior to the international standardization.","Chemical element\n\nChemical symbols","Chemical element\n\nSpecific chemical elements","Chemical element\n\nBefore chemistry became a science, alchemists had designed arcane symbols for both metals and common compounds. These were however used as abbreviations in diagrams or procedures; there was no concept of atoms combining to form molecules. With his advances in the atomic theory of matter, John Dalton devised his own simpler symbols, based on circles, to depict molecules.","Chemical element\n\nThe current system of chemical notation was invented by Berzelius. In this typographical system, chemical symbols are not mere abbreviations—though each consists of letters of the Latin alphabet. They are intended as universal symbols for people of all languages and alphabets.","Chemical element\n\nThe first of these symbols were intended to be fully universal. Since Latin was the common language of science at that time, they were abbreviations based on the Latin names of metals. Cu comes from Cuprum, Fe comes from Ferrum, Ag from Argentum. The symbols were not followed by a period (full stop) as with abbreviations. Later chemical elements were also assigned unique chemical symbols, based on the name of the element, but not necessarily in English. For example, sodium has the chemical symbol 'Na' after the Latin natrium. The same applies to \"W\" (wolfram) for tungsten, \"Fe\" (ferrum) for iron, \"Hg\" (hydrargyrum) for mercury, \"Sn\" (stannum) for tin, \"K\" (kalium) for potassium, \"Au\" (aurum) for gold, \"Ag\" (argentum) for silver, \"Pb\" (plumbum) for lead, \"Cu\" (cuprum) for copper, and \"Sb\" (stibium) for antimony.","Chemical element\n\nChemical symbols are understood internationally when element names might require translation. There have sometimes been differences in the past. For example, Germans in the past have used \"J\" (for the alternate name Jod) for iodine, but now use \"I\" and \"Iod\".","Chemical element\n\nThe first letter of a chemical symbol is always capitalized, as in the preceding examples, and the subsequent letters, if any, are always lower case (small letters). Thus, the symbols for californium or einsteinium are Cf and Es.","Chemical element\n\nGeneral chemical symbols","Chemical element\n\nThere are also symbols in chemical equations for groups of chemical elements, for example in comparative formulas. These are often a single capital letter, and the letters are reserved and not used for names of specific elements. For example, an \"X\" indicates a variable group (usually a halogen) in a class of compounds, while \"R\" is a radical, meaning a compound structure such as a hydrocarbon chain. The letter \"Q\" is reserved for \"heat\" in a chemical reaction. \"Y\" is also often used as a general chemical symbol, although it is also the symbol of yttrium. \"Z\" is also frequently used as a general variable group. \"E\" is used in organic chemistry to denote an electron-withdrawing group. \"L\" is used to represent a general ligand in inorganic and organometallic chemistry. \"M\" is also often used in place of a general metal.","Chemical element\n\nAt least two additional, two-letter generic chemical symbols are also in informal usage, \"Ln\" for any lanthanide element and \"An\" for any actinide element. \"Rg\" was formerly used for any rare gas element, but the group of rare gases has now been renamed noble gases and the symbol \"Rg\" has now been assigned to the element roentgenium.","Chemical element\n\nIsotope symbols","Chemical element\n\nIsotopes are distinguished by the atomic mass number (total protons and neutrons) for a particular isotope of an element, with this number combined with the pertinent element's symbol. IUPAC prefers that isotope symbols be written in superscript notation when practical, for example 12C and 235U. However, other notations, such as carbon-12 and uranium-235, or C-12 and U-235, are also used.","Chemical element\n\nAs a special case, the three naturally occurring isotopes of the element hydrogen are often specified as H for 1H (protium), D for 2H (deuterium), and T for 3H (tritium). This convention is easier to use in chemical equations, replacing the need to write out the mass number for each atom. For example, the formula for heavy water may be written D2O instead of 2H2O.","Chemical element\n\nOrigin of the elements","Chemical element\n\nOnly about 4% of the total mass of the universe is made of atoms or ions, and thus represented by chemical elements. This fraction is about 15% of the total matter, with the remainder of the matter (85%) being dark matter. The nature of dark matter is unknown, but it is not composed of atoms of chemical elements because it contains no protons, neutrons, or electrons. (The remaining non-matter part of the mass of the universe is composed of the even more mysterious dark energy).","Chemical element\n\nThe universe's 94 naturally occurring chemical elements are thought to have been produced by at least four cosmic processes. Most of the hydrogen and helium in the universe was produced primordially in the first few minutes of the Big Bang. Three recurrently occurring later processes are thought to have produced the remaining elements. Stellar nucleosynthesis, an ongoing process, produces all elements from carbon through iron in atomic number, but little lithium, beryllium, or boron. Elements heavier in atomic number than iron, as heavy as uranium and plutonium, are produced by explosive nucleosynthesis in supernovas and other cataclysmic cosmic events. Cosmic ray spallation (fragmentation) of carbon, nitrogen, and oxygen is important to the production of lithium, beryllium and boron.","Chemical element\n\nDuring the early phases of the Big Bang, nucleosynthesis of hydrogen nuclei resulted in the production of hydrogen-1 (protium, 1H) and helium-4 (4He), as well as a smaller amount of deuterium (2H) and very minuscule amounts (on the order of 10−10) of lithium and beryllium. Even smaller amounts of boron may have been produced in the Big Bang, since it has been observed in some very old stars, while carbon has not. It is generally agreed that no heavier elements than boron were produced in the Big Bang. As a result, the primordial abundance of atoms (or ions) consisted of roughly 75% 1H, 25% 4He, and 0.01% deuterium, with only tiny traces of lithium, beryllium, and perhaps boron. Subsequent enrichment of galactic halos occurred due to stellar nucleosynthesis and supernova nucleosynthesis. However, the element abundance in intergalactic space can still closely resemble primordial conditions, unless it has been enriched by some means.","Chemical element\n\nOn Earth (and elsewhere), trace amounts of various elements continue to be produced from other elements as products of natural transmutation processes. These include some produced by cosmic rays or other nuclear reactions (see cosmogenic and nucleogenic nuclides), and others produced as decay products of long-lived primordial nuclides. For example, trace (but detectable) amounts of carbon-14 (14C) are continually produced in the atmosphere by cosmic rays impacting nitrogen atoms, and argon-40 (40Ar) is continually produced by the decay of primordially occurring but unstable potassium-40 (40K). Also, three primordially occurring but radioactive actinides, thorium, uranium, and plutonium, decay through a series of recurrently produced but unstable radioactive elements such as radium and radon, which are transiently present in any sample of these metals or their ores or compounds. Three other radioactive elements, technetium, promethium, and neptunium, occur only incidentally in natural materials, produced as individual atoms by natural fission of the nuclei of various heavy elements or in other rare nuclear processes.","Chemical element\n\nHuman technology has produced various additional elements beyond these first 94, with those through atomic number 118 now known.","Chemical element\n\nAbundance","Chemical element\n\nThe following graph (note log scale) shows the abundance of elements in our solar system. The table shows the twelve most common elements in our galaxy (estimated spectroscopically), as measured in parts per million, by mass. Nearby galaxies that have evolved along similar lines have a corresponding enrichment of elements heavier than hydrogen and helium. The more distant galaxies are being viewed as they appeared in the past, so their abundances of elements appear closer to the primordial mixture. As physical laws and processes appear common throughout the visible universe, however, scientist expect that these galaxies evolved elements in similar abundance.","Chemical element\n\nThe abundance of elements in the Solar System is in keeping with their origin from nucleosynthesis in the Big Bang and a number of progenitor supernova stars. Very abundant hydrogen and helium are products of the Big Bang, but the next three elements are rare since they had little time to form in the Big Bang and are not made in stars (they are, however, produced in small quantities by the breakup of heavier elements in interstellar dust, as a result of impact by cosmic rays). Beginning with carbon, elements are produced in stars by buildup from alpha particles (helium nuclei), resulting in an alternatingly larger abundance of elements with even atomic numbers (these are also more stable). In general, such elements up to iron are made in large stars in the process of becoming supernovas. Iron-56 is particularly common, since it is the most stable element that can easily be made from alpha particles (being a product of decay of radioactive nickel-56, ultimately made from 14 helium nuclei). Elements heavier than iron are made in energy-absorbing processes in large stars, and their abundance in the universe (and on Earth) generally decreases with their atomic number.","Chemical element\n\nThe abundance of the chemical elements on Earth varies from air to crust to ocean, and in various types of life. The abundance of elements in Earth's crust differs from that in the Solar system (as seen in the Sun and heavy planets like Jupiter) mainly in selective loss of the very lightest elements (hydrogen and helium) and also volatile neon, carbon (as hydrocarbons), nitrogen and sulfur, as a result of solar heating in the early formation of the solar system. Oxygen, the most abundant Earth element by mass, is retained on Earth by combination with silicon. Aluminum at 8% by mass is more common in the Earth's crust than in the universe and solar system, but the composition of the far more bulky mantle, which has magnesium and iron in place of aluminum (which occurs there only at 2% of mass) more closely mirrors the elemental composition of the solar system, save for the noted loss of volatile elements to space, and loss of iron which has migrated to the Earth's core.","Chemical element\n\nThe composition of the human body, by contrast, more closely follows the composition of seawater—save that the human body has additional stores of carbon and nitrogen necessary to form the proteins and nucleic acids, together with phosphorus in the nucleic acids and energy transfer molecule adenosine triphosphate (ATP) that occurs in the cells of all living organisms. Certain kinds of organisms require particular additional elements, for example the magnesium in chlorophyll in green plants, the calcium in mollusc shells, or the iron in the hemoglobin in vertebrate animals' red blood cells.","Chemical element\n\nHistory","Chemical element\n\nEvolving definitions","Chemical element\n\nThe concept of an \"element\" as an undivisible substance has developed through three major historical phases: Classical definitions (such as those of the ancient Greeks), chemical definitions, and atomic definitions.","Chemical element\n\nClassical definitions","Chemical element\n\nAncient philosophy posited a set of classical elements to explain observed patterns in nature. These elements originally referred to earth, water, air and fire rather than the chemical elements of modern science.","Chemical element\n\nThe term 'elements' (stoicheia) was first used by the Greek philosopher Plato in about 360 BCE in his dialogue Timaeus, which includes a discussion of the composition of inorganic and organic bodies and is a speculative treatise on chemistry. Plato believed the elements introduced a century earlier by Empedocles were composed of small polyhedral forms: tetrahedron (fire), octahedron (air), icosahedron (water), and cube (earth).","Chemical element\n\nAristotle, c. 350 BCE, also used the term stoicheia and added a fifth element called aether, which formed the heavens. Aristotle defined an element as:","Chemical element\n\nChemical definitions","Chemical element\n\nIn 1661, Robert Boyle proposed his theory of corpuscularism which favoured the analysis of matter as constituted by irreducible units of matter (atoms) and, choosing to side with neither Aristotle's view of the four elements nor Paracelsus' view of three fundamental elements, left open the question of the number of elements. The first modern list of chemical elements was given in Antoine Lavoisier's 1789 Elements of Chemistry, which contained thirty-three elements, including light and caloric. By 1818, Jöns Jakob Berzelius had determined atomic weights for forty-five of the forty-nine then-accepted elements. Dmitri Mendeleev had sixty-six elements in his periodic table of 1869.","Chemical element\n\nFrom Boyle until the early 20th century, an element was defined as a pure substance that could not be decomposed into any simpler substance. Put another way, a chemical element cannot be transformed into other chemical elements by chemical processes. Elements during this time were generally distinguished by their atomic weights, a property measurable with fair accuracy by available analytical techniques.","Chemical element\n\nAtomic definitions","Chemical element\n\nThe 1913 discovery by English physicist Henry Moseley that the nuclear charge is the physical basis for an atom's atomic number, further refined when the nature of protons and neutrons became appreciated, eventually led to the current definition of an element based on atomic number (number of protons per atomic nucleus). The use of atomic numbers, rather than atomic weights, to distinguish elements has greater predictive value (since these numbers are integers), and also resolves some ambiguities in the chemistry-based view due to varying properties of isotopes and allotropes within the same element. Currently, IUPAC defines an element to exist if it has isotopes with a lifetime longer than the 10−14 seconds it takes the nucleus to form an electronic cloud.","Chemical element\n\nBy 1914, seventy-two elements were known, all naturally occurring. The remaining naturally occurring elements were discovered or isolated in subsequent decades, and various additional elements have also been produced synthetically, with much of that work pioneered by Glenn T. Seaborg. In 1955, element 101 was discovered and named mendelevium in honor of D.I. Mendeleev, the first to arrange the elements in a periodic manner. Most recently, the synthesis of element 118 was reported in October 2006, and the synthesis of element 117 was reported in April 2010.","Chemical element\n\nDiscovery and recognition of various elements","Chemical element\n\nTen materials familiar to various prehistoric cultures are now known to be chemical elements: Carbon, copper, gold, iron, lead, mercury, silver, sulfur, tin, and zinc. Three additional materials now accepted as elements, arsenic, antimony, and bismuth, were recognized as distinct substances prior to 1500 AD. Phosphorus, cobalt, and platinum were isolated before 1750.","Chemical element\n\nMost of the remaining naturally occurring chemical elements were identified and characterized by 1900, including:\n* Such now-familiar industrial materials as aluminium, silicon, nickel, chromium, magnesium, and tungsten\n* Reactive metals such as lithium, sodium, potassium, and calcium\n* The halogens fluorine, chlorine, bromine, and iodine\n* Gases such as hydrogen, oxygen, nitrogen, helium, argon, and neon\n* Most of the rare-earth elements, including cerium, lanthanum, gadolinium, and neodymium.\n* The more common radioactive elements, including uranium, thorium, radium, and radon","Chemical element\n\nElements isolated or produced since 1900 include:\n* The three remaining undiscovered regularly occurring stable natural elements: hafnium, lutetium, and rhenium\n* Plutonium, which was first produced synthetically in 1940 by Glenn T. Seaborg, but is now also known from a few long-persisting natural occurrences\n* The three incidentally occurring natural elements (neptunium, promethium, and technetium), which were all first produced synthetically but later discovered in trace amounts in certain geological samples\n* Three scarce decay products of uranium or thorium, (astatine, francium, and protactinium), and\n* Various synthetic transuranic elements, beginning with americium and curium","Chemical element\n\nRecently discovered elements","Chemical element\n\nThe first transuranium element (element with atomic number greater than 92) discovered was neptunium in 1940. Since 1999 claims for the discovery of new elements have been considered by the IUPAC/IUPAP Joint Working Party. As of January 2016, all 118 elements have been confirmed as discovered by IUPAC. The discovery of element 112 was acknowledged in 2009, and the name copernicium and the atomic symbol Cn were suggested for it. The name and symbol were officially endorsed by IUPAC on 19 February 2010. The heaviest element that is believed to have been synthesized to date is element 118, ununoctium, on 9 October 2006, by the Flerov Laboratory of Nuclear Reactions in Dubna, Russia. Element 117 was the latest element claimed to be discovered, in 2009. IUPAC officially recognized flerovium and livermorium, elements 114 and 116, in June 2011 and approved their names in May 2012. In December 2015, IUPAC recognized elements 113, 115, 117 and 118, and announced the elements' proposed final names on 8 June 2016. The names, nihonium (113, Nh), moscovium (115, Mc), tennessine (117, Ts), and oganesson (118, Og), are expected to be approved by the end of 2016.","Chemical element\n\nList of the 118 known chemical elements","Chemical element\n\nThe following sortable table includes the 118 known chemical elements, with the names linking to the Wikipedia articles on each.\n* Atomic number, name, and symbol all serve independently as unique identifiers.\n* Names are those accepted by IUPAC; provisional names for recently produced elements not yet formally named are in parentheses.\n* Group, period, and block refer to an element's position in the periodic table. Group numbers here show the currently accepted numbering; for older alternate numberings, see Group (periodic table).\n* State of matter (solid, liquid, or gas) applies at standard temperature and pressure conditions (STP).\n* Occurrence distinguishes naturally occurring elements, categorized as either primordial or transient (from decay), and additional synthetic elements that have been produced technologically, but are not known to occur naturally.\n* Description summarizes an element's properties using the broad categories commonly presented in periodic tables: Actinide, alkali metal, alkaline earth metal, lanthanide, post-transition metal, metalloid, noble gas, polyatomic or diatomic nonmetal, and transition metal."],"string":"[\n \"Chemical element\\n\\nA chemical element or element is a species of atoms having the same number of protons in their atomic nuclei (i.e. the same atomic number, Z). There are 118 elements that have been identified, of which the first 94 occur naturally on Earth with the remaining 24 being synthetic elements. There are 80 elements that have at least one stable isotope and 38 that have exclusively radioactive isotopes, which decay over time into other elements. Iron is the most abundant element (by mass) making up Earth, while oxygen is the most common element in the crust of Earth.\",\n \"Chemical element\\n\\nChemical elements constitute all of the ordinary matter of the universe. However astronomical observations suggest that ordinary observable matter is only approximately 15% of the matter in the universe: the remainder is dark matter, the composition of which is unknown, but it is not composed of chemical elements. \\nThe two lightest elements, hydrogen and helium were mostly formed in the Big Bang and are the most common elements in the universe. The next three elements (lithium, beryllium and boron) were formed mostly by cosmic ray spallation, and are thus more rare than those that follow. Formation of elements with from six to twenty six protons occurred and continues to occur in main sequence stars via stellar nucleosynthesis. The high abundance of oxygen, silicon, and iron on Earth reflects their common production in such stars. Elements with greater than twenty-six protons are formed by supernova nucleosynthesis in supernovae, which, when they explode, blast these elements far into space as supernova remnants, where they may become incorporated into planets when they are formed.\",\n \"Chemical element\\n\\nThe term \\\"element\\\" is used for a kind of atoms with a given number of protons (regardless of whether they are or they are not ionized or chemically bonded, e.g. hydrogen in water) as well as for a pure chemical substance consisting of a single element (e.g. hydrogen gas). For the second meaning, the terms \\\"elementary substance\\\" and \\\"simple substance\\\" have been suggested, but they have not gained much acceptance in the English-language chemical literature, whereas in some other languages their equivalent is widely used (e.g. French corps simple, Russian простое вещество). One element can form multiple substances different by their structure; they are called allotropes of the element.\",\n \"Chemical element\\n\\nWhen different elements are chemically combined, with the atoms held together by chemical bonds, they form chemical compounds. Only a minority of elements are found uncombined as relatively pure minerals. Among the more common of such \\\"native elements\\\" are copper, silver, gold, carbon (as coal, graphite, or diamonds), and sulfur. All but a few of the most inert elements, such as noble gases and noble metals, are usually found on Earth in chemically combined form, as chemical compounds. While about 32 of the chemical elements occur on Earth in native uncombined forms, most of these occur as mixtures. For example, atmospheric air is primarily a mixture of nitrogen, oxygen, and argon, and native solid elements occur in alloys, such as that of iron and nickel.\",\n \"Chemical element\\n\\nThe history of the discovery and use of the elements began with primitive human societies that found native elements like carbon, sulfur, copper and gold. Later civilizations extracted elemental copper, tin, lead and iron from their ores by smelting, using charcoal. Alchemists and chemists subsequently identified many more, with almost all of the naturally-occurring elements becoming known by 1900.\",\n \"Chemical element\\n\\nThe properties of the chemical elements are summarized on the periodic table, which organizes the elements by increasing atomic number into rows (\\\"periods\\\") in which the columns (\\\"groups\\\") share recurring (\\\"periodic\\\") physical and chemical properties. Save for unstable radioactive elements with short half-lives, all of the elements are available industrially, most of them in high degrees of purity.\",\n \"Chemical element\\n\\nDescription\",\n \"Chemical element\\n\\nThe lightest chemical elements are hydrogen and helium, both created by Big Bang nucleosynthesis during the first 20 minutes of the universe in a ratio of around 3:1 by mass (or 12:1 by number of atoms), along with tiny traces of the next two elements, lithium and beryllium. Almost all other elements found in nature were made by various natural methods of nucleosynthesis. On Earth, small amounts of new atoms are naturally produced in nucleogenic reactions, or in cosmogenic processes, such as cosmic ray spallation. New atoms are also naturally produced on Earth as radiogenic daughter isotopes of ongoing radioactive decay processes such as alpha decay, beta decay, spontaneous fission, cluster decay, and other rarer modes of decay.\",\n \"Chemical element\\n\\nOf the 94 naturally occurring elements, those with atomic numbers 1 through 82 each have at least one stable isotope (except for technetium, element 43 and promethium, element 61, which have no stable isotopes). Isotopes considered stable are those for which no radioactive decay has yet been observed. Elements with atomic numbers 83 through 94 are unstable to the point that radioactive decay of all isotopes can be detected. Some of these elements, notably bismuth (atomic number 83), thorium (atomic number 90), uranium (atomic number 92) and plutonium (atomic number 94), have one or more isotopes with half-lives long enough to survive as remnants of the explosive stellar nucleosynthesis that produced the heavy elements before the formation of our solar system. For example, at over 1.9 years, over a billion times longer than the current estimated age of the universe, bismuth-209 (atomic number 83) has the longest known alpha decay half-life of any naturally occurring element. The very heaviest elements (those beyond plutonium, element 94) undergo radioactive decay with half-lives so short that they are not found in nature and must be synthesized.\",\n \"Chemical element\\n\\nAs of 2010, there are 118 known elements (in this context, \\\"known\\\" means observed well enough, even from just a few decay products, to have been differentiated from other elements). Of these 118 elements, 94 occur naturally on Earth. Six of these occur in extreme trace quantities: technetium, atomic number 43; promethium, number 61; astatine, number 85; francium, number 87; neptunium, number 93; and plutonium, number 94. These 94 elements have been detected in the universe at large, in the spectra of stars and also supernovae, where short-lived radioactive elements are newly being made. The first 94 elements have been detected directly on Earth as primordial nuclides present from the formation of the solar system, or as naturally-occurring fission or transmutation products of uranium and thorium.\",\n \"Chemical element\\n\\nThe remaining 24 heavier elements, not found today either on Earth or in astronomical spectra, have been produced artificially: these are all radioactive, with very short half-lives; if any atoms of these elements were present at the formation of Earth, they are extremely likely, to the point of certainty, to have already decayed, and if present in novae, have been in quantities too small to have been noted. Technetium was the first purportedly non-naturally occurring element synthesized, in 1937, although trace amounts of technetium have since been found in nature (and also the element may have been discovered naturally in 1925). This pattern of artificial production and later natural discovery has been repeated with several other radioactive naturally-occurring rare elements.\",\n \"Chemical element\\n\\nLists of the elements are available by name, by symbol, by atomic number, by density, by melting point, and by boiling point as well as ionization energies of the elements. The nuclides of stable and radioactive elements are also available as a list of nuclides, sorted by length of half-life for those that are unstable. One of the most convenient, and certainly the most traditional presentation of the elements, is in the form of the periodic table, which groups together elements with similar chemical properties (and usually also similar electronic structures).\",\n \"Chemical element\\n\\nAtomic number\",\n \"Chemical element\\n\\nThe atomic number of an element is equal to the number of protons in each atom, and defines the element. For example, all carbon atoms contain 6 protons in their atomic nucleus; so the atomic number of carbon is 6. Carbon atoms may have different numbers of neutrons; atoms of the same element having different numbers of neutrons are known as isotopes of the element.\",\n \"Chemical element\\n\\nThe number of protons in the atomic nucleus also determines its electric charge, which in turn determines the number of electrons of the atom in its non-ionized state. The electrons are placed into atomic orbitals that determine the atom's various chemical properties. The number of neutrons in a nucleus usually has very little effect on an element's chemical properties (except in the case of hydrogen and deuterium). Thus, all carbon isotopes have nearly identical chemical properties because they all have six protons and six electrons, even though carbon atoms may, for example, have 6 or 8 neutrons. That is why the atomic number, rather than mass number or atomic weight, is considered the identifying characteristic of a chemical element.\",\n \"Chemical element\\n\\nThe symbol for atomic number is Z.\",\n \"Chemical element\\n\\nIsotopes\",\n \"Chemical element\\n\\nIsotopes are atoms of the same element (that is, with the same number of protons in their atomic nucleus), but having different numbers of neutrons. Most (66 of 94) naturally occurring elements have more than one stable isotope. Thus, for example, there are three main isotopes of carbon. All carbon atoms have 6 protons in the nucleus, but they can have either 6, 7, or 8 neutrons. Since the mass numbers of these are 12, 13 and 14 respectively, the three isotopes of carbon are known as carbon-12, carbon-13, and carbon-14, often abbreviated to 12C, 13C, and 14C. Carbon in everyday life and in chemistry is a mixture of 12C (about 98.9%), 13C (about 1.1%) and about 1 atom per trillion of 14C.\",\n \"Chemical element\\n\\nExcept in the case of the isotopes of hydrogen (which differ greatly from each other in relative mass—enough to cause chemical effects), the isotopes of a given element are chemically nearly indistinguishable.\",\n \"Chemical element\\n\\nAll of the elements have some isotopes that are radioactive (radioisotopes), although not all of these radioisotopes occur naturally. The radioisotopes typically decay into other elements upon radiating an alpha or beta particle. If an element has isotopes that are not radioactive, these are termed \\\"stable\\\" isotopes. All of the known stable isotopes occur naturally (see primordial isotope). The many radioisotopes that are not found in nature have been characterized after being artificially made. Certain elements have no stable isotopes and are composed only of radioactive isotopes: specifically the elements without any stable isotopes are technetium (atomic number 43), promethium (atomic number 61), and all observed elements with atomic numbers greater than 82.\",\n \"Chemical element\\n\\nOf the 80 elements with at least one stable isotope, 26 have only one single stable isotope. The mean number of stable isotopes for the 80 stable elements is 3.1 stable isotopes per element. The largest number of stable isotopes that occur for a single element is 10 (for tin, element 50).\",\n \"Chemical element\\n\\nIsotopic mass and atomic mass\",\n \"Chemical element\\n\\nThe mass number of an element, A, is the number of nucleons (protons and neutrons) in the atomic nucleus. Different isotopes of a given element are distinguished by their mass numbers, which are conventionally written as a superscript on the left hand side of the atomic symbol (e.g., 238U). The mass number is always a simple whole number and has units of \\\"nucleons.\\\" An example of a referral to a mass number is \\\"magnesium-24,\\\" which is an atom with 24 nucleons (12 protons and 12 neutrons).\",\n \"Chemical element\\n\\nWhereas the mass number simply counts the total number of neutrons and protons and is thus a natural (or whole) number, the atomic mass of a single atom is a real number for the mass of a particular isotope of the element, the unit being u. In general, when expressed in u it differs in value slightly from the mass number for a given nuclide (or isotope) since the mass of the protons and neutrons is not exactly 1 u, since the electrons contribute a lesser share to the atomic mass as neutron number exceeds proton number, and (finally) because of the nuclear binding energy. For example, the atomic mass of chlorine-35 to five significant digits is 34.969 u and that of chlorine-37 is 36.966 u. However, the atomic mass in u of each isotope is quite close to its simple mass number (always within 1%). The only isotope whose atomic mass is exactly a natural number is 12C, which by definition has a mass of exactly 12, because u is defined as 1/12 of the mass of a free neutral carbon-12 atom in the ground state.\",\n \"Chemical element\\n\\nThe relative atomic mass (historically and commonly also called \\\"atomic weight\\\") of an element is the average of the atomic masses of all the chemical element's isotopes as found in a particular environment, weighted by isotopic abundance, relative to the atomic mass unit (u). This number may be a fraction that is not close to a whole number, due to the averaging process. For example, the relative atomic mass of chlorine is 35.453 u, which differs greatly from a whole number due to being made of an average of 76% chlorine-35 and 24% chlorine-37. Whenever a relative atomic mass value differs by more than 1% from a whole number, it is due to this averaging effect resulting from significant amounts of more than one isotope being naturally present in the sample of the element in question.\",\n \"Chemical element\\n\\nChemically pure and isotopically pure\",\n \"Chemical element\\n\\nChemists and nuclear scientists have different definitions of a pure element. In chemistry, a pure element means a substance whose atoms all (or in practice almost all) have the same atomic number, or number of protons. Nuclear scientists, however, define a pure element as one that consists of only one stable isotope.\",\n \"Chemical element\\n\\nFor example, a copper wire is 99.99% chemically pure if 99.99% of its atoms are copper, with 29 protons each. However it is not isotopically pure since ordinary copper consists of two stable isotopes, 69% 63Cu and 31% 65Cu, with different numbers of neutrons. However, a pure gold ingot would be both chemically and isotopically pure, since ordinary gold consists only of one isotope, 197Au.\",\n \"Chemical element\\n\\nAllotropes\",\n \"Chemical element\\n\\nAtoms of chemically pure elements may bond to each other chemically in more than one way, allowing the pure element to exist in multiple structures (spatial arrangements of atoms), known as allotropes, which differ in their properties. For example, carbon can be found as diamond, which has a tetrahedral structure around each carbon atom; graphite, which has layers of carbon atoms with a hexagonal structure stacked on top of each other; graphene, which is a single layer of graphite that is very strong; fullerenes, which have nearly spherical shapes; and carbon nanotubes, which are tubes with a hexagonal structure (even these may differ from each other in electrical properties). The ability of an element to exist in one of many structural forms is known as 'allotropy'.\",\n \"Chemical element\\n\\nThe standard state, also known as reference state, of an element is defined as its thermodynamically most stable state at 1 bar at a given temperature (typically at 298.15 K). In thermochemistry, an element is defined to have an enthalpy of formation of zero in its standard state. For example, the reference state for carbon is graphite, because the structure of graphite is more stable than that of the other allotropes.\",\n \"Chemical element\\n\\nProperties\",\n \"Chemical element\\n\\nSeveral kinds of descriptive categorizations can be applied broadly to the elements, including consideration of their general physical and chemical properties, their states of matter under familiar conditions, their melting and boiling points, their densities, their crystal structures as solids, and their origins.\",\n \"Chemical element\\n\\nGeneral properties\",\n \"Chemical element\\n\\nSeveral terms are commonly used to characterize the general physical and chemical properties of the chemical elements. A first distinction is between metals, which readily conduct electricity, nonmetals, which do not, and a small group, (the metalloids), having intermediate properties and often behaving as semiconductors.\",\n \"Chemical element\\n\\nA more refined classification is often shown in colored presentations of the periodic table. This system restricts the terms \\\"metal\\\" and \\\"nonmetal\\\" to only certain of the more broadly defined metals and nonmetals, adding additional terms for certain sets of the more broadly viewed metals and nonmetals. The version of this classification used in the periodic tables presented here includes: actinides, alkali metals, alkaline earth metals, halogens, lanthanides, transition metals, post-transition metals, metalloids, polyatomic nonmetals, diatomic nonmetals, and noble gases. In this system, the alkali metals, alkaline earth metals, and transition metals, as well as the lanthanides and the actinides, are special groups of the metals viewed in a broader sense. Similarly, the polyatomic nonmetals, diatomic nonmetals and the noble gases are nonmetals viewed in the broader sense. In some presentations, the halogens are not distinguished, with astatine identified as a metalloid and the others identified as nonmetals.\",\n \"Chemical element\\n\\nStates of matter\",\n \"Chemical element\\n\\nAnother commonly used basic distinction among the elements is their state of matter (phase), whether solid, liquid, or gas, at a selected standard temperature and pressure (STP). Most of the elements are solids at conventional temperatures and atmospheric pressure, while several are gases. Only bromine and mercury are liquids at 0 degrees Celsius (32 degrees Fahrenheit) and normal atmospheric pressure; caesium and gallium are solids at that temperature, but melt at 28.4 °C (83.2 °F) and 29.8 °C (85.6 °F), respectively.\",\n \"Chemical element\\n\\nMelting and boiling points\",\n \"Chemical element\\n\\nMelting and boiling points, typically expressed in degrees Celsius at a pressure of one atmosphere, are commonly used in characterizing the various elements. While known for most elements, either or both of these measurements is still undetermined for some of the radioactive elements available in only tiny quantities. Since helium remains a liquid even at absolute zero at atmospheric pressure, it has only a boiling point, and not a melting point, in conventional presentations.\",\n \"Chemical element\\n\\nDensities\",\n \"Chemical element\\n\\nThe density at a selected standard temperature and pressure (STP) is frequently used in characterizing the elements. Density is often expressed in grams per cubic centimeter (g/cm3). Since several elements are gases at commonly encountered temperatures, their densities are usually stated for their gaseous forms; when liquefied or solidified, the gaseous elements have densities similar to those of the other elements.\",\n \"Chemical element\\n\\nWhen an element has allotropes with different densities, one representative allotrope is typically selected in summary presentations, while densities for each allotrope can be stated where more detail is provided. For example, the three familiar allotropes of carbon (amorphous carbon, graphite, and diamond) have densities of 1.8–2.1, 2.267, and 3.515 g/cm3, respectively.\",\n \"Chemical element\\n\\nCrystal structures\",\n \"Chemical element\\n\\nThe elements studied to date as solid samples have eight kinds of crystal structures: cubic, body-centered cubic, face-centered cubic, hexagonal, monoclinic, orthorhombic, rhombohedral, and tetragonal. For some of the synthetically produced transuranic elements, available samples have been too small to determine crystal structures.\",\n \"Chemical element\\n\\nOccurrence and origin on Earth\",\n \"Chemical element\\n\\nChemical elements may also be categorized by their origin on Earth, with the first 94 considered naturally occurring, while those with atomic numbers beyond 94 have only been produced artificially as the synthetic products of man-made nuclear reactions.\",\n \"Chemical element\\n\\nOf the 94 naturally occurring elements, 84 are considered primordial and either stable or weakly radioactive. The remaining 10 naturally occurring elements possess half lives too short for them to have been present at the beginning of the Solar System, and are therefore considered transient elements. (Plutonium is sometimes also considered a transient element because primordial plutonium has by now decayed to almost undetectable traces.) Of these 10 transient elements, 5 (polonium, radon, radium, actinium, and protactinium) are relatively common decay products of thorium, uranium, and plutonium. The remaining 5 transient elements (technetium, promethium, astatine, francium, and neptunium) occur only rarely, as products of rare decay modes or nuclear reaction processes involving uranium or other heavy elements.\",\n \"Chemical element\\n\\nElements with atomic numbers 1 through 40 are all stable, while those with atomic numbers 41 through 82 (except technetium and promethium) are metastable. The half-lives of these metastable \\\"theoretical radionuclides\\\" are so long (at least 100 million times longer than the estimated age of the universe) that their radioactive decay has yet to be detected by experiment. Elements with atomic numbers 83 through 94 are unstable to the point that their radioactive decay can be detected. Four of these elements, bismuth (element 83), thorium (element 90), uranium (element 92), and plutonium (element 94), have one or more isotopes with half-lives long enough to survive as remnants of the explosive stellar nucleosynthesis that produced the heavy elements before the formation of our solar system. For example, at over 1.9 years, over a billion times longer than the current estimated age of the universe, bismuth-209 has the longest known alpha decay half-life of any naturally occurring element. The very heaviest elements (those beyond plutonium, element 94) undergo radioactive decay with short half-lives and do not occur in nature.\",\n \"Chemical element\\n\\nThe periodic table\",\n \"Chemical element\\n\\nThe properties of the chemical elements are often summarized using the periodic table, which powerfully and elegantly organizes the elements by increasing atomic number into rows (\\\"periods\\\") in which the columns (\\\"groups\\\") share recurring (\\\"periodic\\\") physical and chemical properties. The current standard table contains 118 confirmed elements as of 10 April 2010.\",\n \"Chemical element\\n\\nAlthough earlier precursors to this presentation exist, its invention is generally credited to the Russian chemist Dmitri Mendeleev in 1869, who intended the table to illustrate recurring trends in the properties of the elements. The layout of the table has been refined and extended over time as new elements have been discovered and new theoretical models have been developed to explain chemical behavior.\",\n \"Chemical element\\n\\nUse of the periodic table is now ubiquitous within the academic discipline of chemistry, providing an extremely useful framework to classify, systematize and compare all the many different forms of chemical behavior. The table has also found wide application in physics, geology, biology, materials science, engineering, agriculture, medicine, nutrition, environmental health, and astronomy. Its principles are especially important in chemical engineering.\",\n \"Chemical element\\n\\nNomenclature and symbols\",\n \"Chemical element\\n\\nThe various chemical elements are formally identified by their unique atomic numbers, by their accepted names, and by their symbols.\",\n \"Chemical element\\n\\nAtomic numbers\",\n \"Chemical element\\n\\nThe known elements have atomic numbers from 1 through 118, conventionally presented as Arabic numerals. Since the elements can be uniquely sequenced by atomic number, conventionally from lowest to highest (as in a periodic table), sets of elements are sometimes specified by such notation as \\\"through\\\", \\\"beyond\\\", or \\\"from ... through\\\", as in \\\"through iron\\\", \\\"beyond uranium\\\", or \\\"from lanthanum through lutetium\\\". The terms \\\"light\\\" and \\\"heavy\\\" are sometimes also used informally to indicate relative atomic numbers (not densities), as in \\\"lighter than carbon\\\" or \\\"heavier than lead\\\", although technically the weight or mass of atoms of an element (their atomic weights or atomic masses) do not always increase monotonically with their atomic numbers.\",\n \"Chemical element\\n\\nElement names\",\n \"Chemical element\\n\\nThe naming of various substances now known as elements precedes the atomic theory of matter, as names were given locally by various cultures to various minerals, metals, compounds, alloys, mixtures, and other materials, although at the time it was not known which chemicals were elements and which compounds. As they were identified as elements, the existing names for anciently-known elements (e.g., gold, mercury, iron) were kept in most countries. National differences emerged over the names of elements either for convenience, linguistic niceties, or nationalism. For a few illustrative examples: German speakers use \\\"Wasserstoff\\\" (water substance) for \\\"hydrogen\\\", \\\"Sauerstoff\\\" (acid substance) for \\\"oxygen\\\" and \\\"Stickstoff\\\" (smothering substance) for \\\"nitrogen\\\", while English and some romance languages use \\\"sodium\\\" for \\\"natrium\\\" and \\\"potassium\\\" for \\\"kalium\\\", and the French, Italians, Greeks, Portuguese and Poles prefer \\\"azote/azot/azoto\\\" (from roots meaning \\\"no life\\\") for \\\"nitrogen\\\".\",\n \"Chemical element\\n\\nFor purposes of international communication and trade, the official names of the chemical elements both ancient and more recently recognized are decided by the International Union of Pure and Applied Chemistry (IUPAC), which has decided on a sort of international English language, drawing on traditional English names even when an element's chemical symbol is based on a Latin or other traditional word, for example adopting \\\"gold\\\" rather than \\\"aurum\\\" as the name for the 79th element (Au). IUPAC prefers the British spellings \\\"aluminium\\\" and \\\"caesium\\\" over the U.S. spellings \\\"aluminum\\\" and \\\"cesium\\\", and the U.S. \\\"sulfur\\\" over the British \\\"sulphur\\\". However, elements that are practical to sell in bulk in many countries often still have locally used national names, and countries whose national language does not use the Latin alphabet are likely to use the IUPAC element names.\",\n \"Chemical element\\n\\nAccording to IUPAC, chemical elements are not proper nouns in English; consequently, the full name of an element is not routinely capitalized in English, even if derived from a proper noun, as in californium and einsteinium. Isotope names of chemical elements are also uncapitalized if written out, e.g., carbon-12 or uranium-235. Chemical element symbols (such as Cf for californium and Es for einsteinium), are always capitalized (see below).\",\n \"Chemical element\\n\\nIn the second half of the twentieth century, physics laboratories became able to produce nuclei of chemical elements with half-lives too short for an appreciable amount of them to exist at any time. These are also named by IUPAC, which generally adopts the name chosen by the discoverer. This practice can lead to the controversial question of which research group actually discovered an element, a question that delayed the naming of elements with atomic number of 104 and higher for a considerable amount of time. (See element naming controversy).\",\n \"Chemical element\\n\\nPrecursors of such controversies involved the nationalistic namings of elements in the late 19th century. For example, lutetium was named in reference to Paris, France. The Germans were reluctant to relinquish naming rights to the French, often calling it cassiopeium. Similarly, the British discoverer of niobium originally named it columbium, in reference to the New World. It was used extensively as such by American publications prior to the international standardization.\",\n \"Chemical element\\n\\nChemical symbols\",\n \"Chemical element\\n\\nSpecific chemical elements\",\n \"Chemical element\\n\\nBefore chemistry became a science, alchemists had designed arcane symbols for both metals and common compounds. These were however used as abbreviations in diagrams or procedures; there was no concept of atoms combining to form molecules. With his advances in the atomic theory of matter, John Dalton devised his own simpler symbols, based on circles, to depict molecules.\",\n \"Chemical element\\n\\nThe current system of chemical notation was invented by Berzelius. In this typographical system, chemical symbols are not mere abbreviations—though each consists of letters of the Latin alphabet. They are intended as universal symbols for people of all languages and alphabets.\",\n \"Chemical element\\n\\nThe first of these symbols were intended to be fully universal. Since Latin was the common language of science at that time, they were abbreviations based on the Latin names of metals. Cu comes from Cuprum, Fe comes from Ferrum, Ag from Argentum. The symbols were not followed by a period (full stop) as with abbreviations. Later chemical elements were also assigned unique chemical symbols, based on the name of the element, but not necessarily in English. For example, sodium has the chemical symbol 'Na' after the Latin natrium. The same applies to \\\"W\\\" (wolfram) for tungsten, \\\"Fe\\\" (ferrum) for iron, \\\"Hg\\\" (hydrargyrum) for mercury, \\\"Sn\\\" (stannum) for tin, \\\"K\\\" (kalium) for potassium, \\\"Au\\\" (aurum) for gold, \\\"Ag\\\" (argentum) for silver, \\\"Pb\\\" (plumbum) for lead, \\\"Cu\\\" (cuprum) for copper, and \\\"Sb\\\" (stibium) for antimony.\",\n \"Chemical element\\n\\nChemical symbols are understood internationally when element names might require translation. There have sometimes been differences in the past. For example, Germans in the past have used \\\"J\\\" (for the alternate name Jod) for iodine, but now use \\\"I\\\" and \\\"Iod\\\".\",\n \"Chemical element\\n\\nThe first letter of a chemical symbol is always capitalized, as in the preceding examples, and the subsequent letters, if any, are always lower case (small letters). Thus, the symbols for californium or einsteinium are Cf and Es.\",\n \"Chemical element\\n\\nGeneral chemical symbols\",\n \"Chemical element\\n\\nThere are also symbols in chemical equations for groups of chemical elements, for example in comparative formulas. These are often a single capital letter, and the letters are reserved and not used for names of specific elements. For example, an \\\"X\\\" indicates a variable group (usually a halogen) in a class of compounds, while \\\"R\\\" is a radical, meaning a compound structure such as a hydrocarbon chain. The letter \\\"Q\\\" is reserved for \\\"heat\\\" in a chemical reaction. \\\"Y\\\" is also often used as a general chemical symbol, although it is also the symbol of yttrium. \\\"Z\\\" is also frequently used as a general variable group. \\\"E\\\" is used in organic chemistry to denote an electron-withdrawing group. \\\"L\\\" is used to represent a general ligand in inorganic and organometallic chemistry. \\\"M\\\" is also often used in place of a general metal.\",\n \"Chemical element\\n\\nAt least two additional, two-letter generic chemical symbols are also in informal usage, \\\"Ln\\\" for any lanthanide element and \\\"An\\\" for any actinide element. \\\"Rg\\\" was formerly used for any rare gas element, but the group of rare gases has now been renamed noble gases and the symbol \\\"Rg\\\" has now been assigned to the element roentgenium.\",\n \"Chemical element\\n\\nIsotope symbols\",\n \"Chemical element\\n\\nIsotopes are distinguished by the atomic mass number (total protons and neutrons) for a particular isotope of an element, with this number combined with the pertinent element's symbol. IUPAC prefers that isotope symbols be written in superscript notation when practical, for example 12C and 235U. However, other notations, such as carbon-12 and uranium-235, or C-12 and U-235, are also used.\",\n \"Chemical element\\n\\nAs a special case, the three naturally occurring isotopes of the element hydrogen are often specified as H for 1H (protium), D for 2H (deuterium), and T for 3H (tritium). This convention is easier to use in chemical equations, replacing the need to write out the mass number for each atom. For example, the formula for heavy water may be written D2O instead of 2H2O.\",\n \"Chemical element\\n\\nOrigin of the elements\",\n \"Chemical element\\n\\nOnly about 4% of the total mass of the universe is made of atoms or ions, and thus represented by chemical elements. This fraction is about 15% of the total matter, with the remainder of the matter (85%) being dark matter. The nature of dark matter is unknown, but it is not composed of atoms of chemical elements because it contains no protons, neutrons, or electrons. (The remaining non-matter part of the mass of the universe is composed of the even more mysterious dark energy).\",\n \"Chemical element\\n\\nThe universe's 94 naturally occurring chemical elements are thought to have been produced by at least four cosmic processes. Most of the hydrogen and helium in the universe was produced primordially in the first few minutes of the Big Bang. Three recurrently occurring later processes are thought to have produced the remaining elements. Stellar nucleosynthesis, an ongoing process, produces all elements from carbon through iron in atomic number, but little lithium, beryllium, or boron. Elements heavier in atomic number than iron, as heavy as uranium and plutonium, are produced by explosive nucleosynthesis in supernovas and other cataclysmic cosmic events. Cosmic ray spallation (fragmentation) of carbon, nitrogen, and oxygen is important to the production of lithium, beryllium and boron.\",\n \"Chemical element\\n\\nDuring the early phases of the Big Bang, nucleosynthesis of hydrogen nuclei resulted in the production of hydrogen-1 (protium, 1H) and helium-4 (4He), as well as a smaller amount of deuterium (2H) and very minuscule amounts (on the order of 10−10) of lithium and beryllium. Even smaller amounts of boron may have been produced in the Big Bang, since it has been observed in some very old stars, while carbon has not. It is generally agreed that no heavier elements than boron were produced in the Big Bang. As a result, the primordial abundance of atoms (or ions) consisted of roughly 75% 1H, 25% 4He, and 0.01% deuterium, with only tiny traces of lithium, beryllium, and perhaps boron. Subsequent enrichment of galactic halos occurred due to stellar nucleosynthesis and supernova nucleosynthesis. However, the element abundance in intergalactic space can still closely resemble primordial conditions, unless it has been enriched by some means.\",\n \"Chemical element\\n\\nOn Earth (and elsewhere), trace amounts of various elements continue to be produced from other elements as products of natural transmutation processes. These include some produced by cosmic rays or other nuclear reactions (see cosmogenic and nucleogenic nuclides), and others produced as decay products of long-lived primordial nuclides. For example, trace (but detectable) amounts of carbon-14 (14C) are continually produced in the atmosphere by cosmic rays impacting nitrogen atoms, and argon-40 (40Ar) is continually produced by the decay of primordially occurring but unstable potassium-40 (40K). Also, three primordially occurring but radioactive actinides, thorium, uranium, and plutonium, decay through a series of recurrently produced but unstable radioactive elements such as radium and radon, which are transiently present in any sample of these metals or their ores or compounds. Three other radioactive elements, technetium, promethium, and neptunium, occur only incidentally in natural materials, produced as individual atoms by natural fission of the nuclei of various heavy elements or in other rare nuclear processes.\",\n \"Chemical element\\n\\nHuman technology has produced various additional elements beyond these first 94, with those through atomic number 118 now known.\",\n \"Chemical element\\n\\nAbundance\",\n \"Chemical element\\n\\nThe following graph (note log scale) shows the abundance of elements in our solar system. The table shows the twelve most common elements in our galaxy (estimated spectroscopically), as measured in parts per million, by mass. Nearby galaxies that have evolved along similar lines have a corresponding enrichment of elements heavier than hydrogen and helium. The more distant galaxies are being viewed as they appeared in the past, so their abundances of elements appear closer to the primordial mixture. As physical laws and processes appear common throughout the visible universe, however, scientist expect that these galaxies evolved elements in similar abundance.\",\n \"Chemical element\\n\\nThe abundance of elements in the Solar System is in keeping with their origin from nucleosynthesis in the Big Bang and a number of progenitor supernova stars. Very abundant hydrogen and helium are products of the Big Bang, but the next three elements are rare since they had little time to form in the Big Bang and are not made in stars (they are, however, produced in small quantities by the breakup of heavier elements in interstellar dust, as a result of impact by cosmic rays). Beginning with carbon, elements are produced in stars by buildup from alpha particles (helium nuclei), resulting in an alternatingly larger abundance of elements with even atomic numbers (these are also more stable). In general, such elements up to iron are made in large stars in the process of becoming supernovas. Iron-56 is particularly common, since it is the most stable element that can easily be made from alpha particles (being a product of decay of radioactive nickel-56, ultimately made from 14 helium nuclei). Elements heavier than iron are made in energy-absorbing processes in large stars, and their abundance in the universe (and on Earth) generally decreases with their atomic number.\",\n \"Chemical element\\n\\nThe abundance of the chemical elements on Earth varies from air to crust to ocean, and in various types of life. The abundance of elements in Earth's crust differs from that in the Solar system (as seen in the Sun and heavy planets like Jupiter) mainly in selective loss of the very lightest elements (hydrogen and helium) and also volatile neon, carbon (as hydrocarbons), nitrogen and sulfur, as a result of solar heating in the early formation of the solar system. Oxygen, the most abundant Earth element by mass, is retained on Earth by combination with silicon. Aluminum at 8% by mass is more common in the Earth's crust than in the universe and solar system, but the composition of the far more bulky mantle, which has magnesium and iron in place of aluminum (which occurs there only at 2% of mass) more closely mirrors the elemental composition of the solar system, save for the noted loss of volatile elements to space, and loss of iron which has migrated to the Earth's core.\",\n \"Chemical element\\n\\nThe composition of the human body, by contrast, more closely follows the composition of seawater—save that the human body has additional stores of carbon and nitrogen necessary to form the proteins and nucleic acids, together with phosphorus in the nucleic acids and energy transfer molecule adenosine triphosphate (ATP) that occurs in the cells of all living organisms. Certain kinds of organisms require particular additional elements, for example the magnesium in chlorophyll in green plants, the calcium in mollusc shells, or the iron in the hemoglobin in vertebrate animals' red blood cells.\",\n \"Chemical element\\n\\nHistory\",\n \"Chemical element\\n\\nEvolving definitions\",\n \"Chemical element\\n\\nThe concept of an \\\"element\\\" as an undivisible substance has developed through three major historical phases: Classical definitions (such as those of the ancient Greeks), chemical definitions, and atomic definitions.\",\n \"Chemical element\\n\\nClassical definitions\",\n \"Chemical element\\n\\nAncient philosophy posited a set of classical elements to explain observed patterns in nature. These elements originally referred to earth, water, air and fire rather than the chemical elements of modern science.\",\n \"Chemical element\\n\\nThe term 'elements' (stoicheia) was first used by the Greek philosopher Plato in about 360 BCE in his dialogue Timaeus, which includes a discussion of the composition of inorganic and organic bodies and is a speculative treatise on chemistry. Plato believed the elements introduced a century earlier by Empedocles were composed of small polyhedral forms: tetrahedron (fire), octahedron (air), icosahedron (water), and cube (earth).\",\n \"Chemical element\\n\\nAristotle, c. 350 BCE, also used the term stoicheia and added a fifth element called aether, which formed the heavens. Aristotle defined an element as:\",\n \"Chemical element\\n\\nChemical definitions\",\n \"Chemical element\\n\\nIn 1661, Robert Boyle proposed his theory of corpuscularism which favoured the analysis of matter as constituted by irreducible units of matter (atoms) and, choosing to side with neither Aristotle's view of the four elements nor Paracelsus' view of three fundamental elements, left open the question of the number of elements. The first modern list of chemical elements was given in Antoine Lavoisier's 1789 Elements of Chemistry, which contained thirty-three elements, including light and caloric. By 1818, Jöns Jakob Berzelius had determined atomic weights for forty-five of the forty-nine then-accepted elements. Dmitri Mendeleev had sixty-six elements in his periodic table of 1869.\",\n \"Chemical element\\n\\nFrom Boyle until the early 20th century, an element was defined as a pure substance that could not be decomposed into any simpler substance. Put another way, a chemical element cannot be transformed into other chemical elements by chemical processes. Elements during this time were generally distinguished by their atomic weights, a property measurable with fair accuracy by available analytical techniques.\",\n \"Chemical element\\n\\nAtomic definitions\",\n \"Chemical element\\n\\nThe 1913 discovery by English physicist Henry Moseley that the nuclear charge is the physical basis for an atom's atomic number, further refined when the nature of protons and neutrons became appreciated, eventually led to the current definition of an element based on atomic number (number of protons per atomic nucleus). The use of atomic numbers, rather than atomic weights, to distinguish elements has greater predictive value (since these numbers are integers), and also resolves some ambiguities in the chemistry-based view due to varying properties of isotopes and allotropes within the same element. Currently, IUPAC defines an element to exist if it has isotopes with a lifetime longer than the 10−14 seconds it takes the nucleus to form an electronic cloud.\",\n \"Chemical element\\n\\nBy 1914, seventy-two elements were known, all naturally occurring. The remaining naturally occurring elements were discovered or isolated in subsequent decades, and various additional elements have also been produced synthetically, with much of that work pioneered by Glenn T. Seaborg. In 1955, element 101 was discovered and named mendelevium in honor of D.I. Mendeleev, the first to arrange the elements in a periodic manner. Most recently, the synthesis of element 118 was reported in October 2006, and the synthesis of element 117 was reported in April 2010.\",\n \"Chemical element\\n\\nDiscovery and recognition of various elements\",\n \"Chemical element\\n\\nTen materials familiar to various prehistoric cultures are now known to be chemical elements: Carbon, copper, gold, iron, lead, mercury, silver, sulfur, tin, and zinc. Three additional materials now accepted as elements, arsenic, antimony, and bismuth, were recognized as distinct substances prior to 1500 AD. Phosphorus, cobalt, and platinum were isolated before 1750.\",\n \"Chemical element\\n\\nMost of the remaining naturally occurring chemical elements were identified and characterized by 1900, including:\\n* Such now-familiar industrial materials as aluminium, silicon, nickel, chromium, magnesium, and tungsten\\n* Reactive metals such as lithium, sodium, potassium, and calcium\\n* The halogens fluorine, chlorine, bromine, and iodine\\n* Gases such as hydrogen, oxygen, nitrogen, helium, argon, and neon\\n* Most of the rare-earth elements, including cerium, lanthanum, gadolinium, and neodymium.\\n* The more common radioactive elements, including uranium, thorium, radium, and radon\",\n \"Chemical element\\n\\nElements isolated or produced since 1900 include:\\n* The three remaining undiscovered regularly occurring stable natural elements: hafnium, lutetium, and rhenium\\n* Plutonium, which was first produced synthetically in 1940 by Glenn T. Seaborg, but is now also known from a few long-persisting natural occurrences\\n* The three incidentally occurring natural elements (neptunium, promethium, and technetium), which were all first produced synthetically but later discovered in trace amounts in certain geological samples\\n* Three scarce decay products of uranium or thorium, (astatine, francium, and protactinium), and\\n* Various synthetic transuranic elements, beginning with americium and curium\",\n \"Chemical element\\n\\nRecently discovered elements\",\n \"Chemical element\\n\\nThe first transuranium element (element with atomic number greater than 92) discovered was neptunium in 1940. Since 1999 claims for the discovery of new elements have been considered by the IUPAC/IUPAP Joint Working Party. As of January 2016, all 118 elements have been confirmed as discovered by IUPAC. The discovery of element 112 was acknowledged in 2009, and the name copernicium and the atomic symbol Cn were suggested for it. The name and symbol were officially endorsed by IUPAC on 19 February 2010. The heaviest element that is believed to have been synthesized to date is element 118, ununoctium, on 9 October 2006, by the Flerov Laboratory of Nuclear Reactions in Dubna, Russia. Element 117 was the latest element claimed to be discovered, in 2009. IUPAC officially recognized flerovium and livermorium, elements 114 and 116, in June 2011 and approved their names in May 2012. In December 2015, IUPAC recognized elements 113, 115, 117 and 118, and announced the elements' proposed final names on 8 June 2016. The names, nihonium (113, Nh), moscovium (115, Mc), tennessine (117, Ts), and oganesson (118, Og), are expected to be approved by the end of 2016.\",\n \"Chemical element\\n\\nList of the 118 known chemical elements\",\n \"Chemical element\\n\\nThe following sortable table includes the 118 known chemical elements, with the names linking to the Wikipedia articles on each.\\n* Atomic number, name, and symbol all serve independently as unique identifiers.\\n* Names are those accepted by IUPAC; provisional names for recently produced elements not yet formally named are in parentheses.\\n* Group, period, and block refer to an element's position in the periodic table. Group numbers here show the currently accepted numbering; for older alternate numberings, see Group (periodic table).\\n* State of matter (solid, liquid, or gas) applies at standard temperature and pressure conditions (STP).\\n* Occurrence distinguishes naturally occurring elements, categorized as either primordial or transient (from decay), and additional synthetic elements that have been produced technologically, but are not known to occur naturally.\\n* Description summarizes an element's properties using the broad categories commonly presented in periodic tables: Actinide, alkali metal, alkaline earth metal, lanthanide, post-transition metal, metalloid, noble gas, polyatomic or diatomic nonmetal, and transition metal.\"\n]","isConversational":false}}},{"rowIdx":1787,"cells":{"id":{"kind":"string","value":"tc_2760"},"question":{"kind":"string","value":"\"What are classified by their measurement in degrees as \"\"right\"\", \"\"reflex\"\", \"\"obtuse\"\", or \"\"acute\"\"?\""},"answer":{"kind":"string","value":"Angles"},"answer_aliases":{"kind":"list like","value":["angles","anglii","angles people","angle tribe","angili","angli","angles tribe"],"string":"[\n \"angles\",\n \"anglii\",\n \"angles people\",\n \"angle tribe\",\n \"angili\",\n \"angli\",\n \"angles tribe\"\n]","isConversational":false},"documents":{"kind":"list like","value":["Degree (angle)\n\nA degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of plane angle, defined by representing a full rotation as 360 degrees.","Degree (angle)\n\nIt is not an SI unit, as the SI unit for angles is radian, but it is mentioned in the SI brochure as an accepted unit. Because a full rotation equals 2 radians, one degree is equivalent to radians.","Degree (angle)\n\nHistory","Degree (angle)\n\nThe original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year. Ancient astronomers noticed that the sun, which follows through the ecliptic path over the course of the year, seems to advance in its path by approximately one degree each day. Some ancient calendars, such as the Persian calendar, used 360 days for a year. The use of a calendar with 360 days may be related to the use of sexagesimal numbers.","Degree (angle)\n\nAnother theory is that the Babylonians subdivided the circle using the angle of an equilateral triangle as the basic unit and further subdivided the latter into 60 parts following their sexagesimal numeric system. The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle. A chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree.","Degree (angle)\n\nAristarchus of Samos and Hipparchus seem to have been among the first Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically. Timocharis, Aristarchus, Aristillus, Archimedes, and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes. Eratosthenes used a simpler sexagesimal system dividing a circle into 60 parts.","Degree (angle)\n\nThe division of the circle into 360 parts also occurred in ancient India, as evidenced in the Rigveda:","Degree (angle)\n\nAnother motivation for choosing the number 360 may have been that it is readily divisible: 360 has 24 divisors,The divisors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360. making it one of only 7 numbers such that no number less than twice as much has more divisors . Furthermore, it is divisible by every number from 1 to 10 except 7.Contrast this with the relatively unwieldy 2520, which is the least common multiple for every number from 1 to 10. This property has many useful applications, such as dividing the world into 24 time zones, each of which is nominally 15° of longitude, to correlate with the established 24-hour day convention.","Degree (angle)\n\nFinally, it may be the case that more than one of these factors has come into play. According to that theory, the number is approximately 365 because of the apparent movement of the sun against the celestial sphere and that it was rounded to 360 for some of the mathematical reasons cited above.","Degree (angle)\n\nSubdivisions","Degree (angle)\n\nFor many practical purposes, a degree is a small enough angle that whole degrees provide sufficient precision. When this is not the case, as in astronomy or for geographic coordinates (latitude and longitude), degree measurements may be written using decimal degrees. For example, 40.1875°, with the degree symbol behind the decimals.","Degree (angle)\n\nAlternatively, the traditional sexagesimal unit subdivisions can be used. One degree is divided into 60 minutes (of arc), and one minute into 60 seconds (of arc). Use of degrees-minutes-seconds is also called DMS notation. These subdivisions, also called the arcminute and arcsecond, are respectively represented as a single and double prime. For example, 40.1875° = 40° 11′ 15″, or using quotation mark characters as 40° 11' 15\". Additional precision can be provided using decimals for the arcseconds component.","Degree (angle)\n\nThe older system of thirds, fourths, etc., which continues the sexagesimal unit subdivision, was used by al-Kashi and other ancient astronomers, but is rarely used today. These subdivisions were denoted by writing the Roman numeral for the number of sixtieths in superscript: 1I for a \"prime\" (minute of arc), 1II for a second, 1III for a third, 1IV for a fourth, etc. Hence the modern symbols for the minute and second of arc, and the word \"second\" also refer to this system.","Degree (angle)\n\nAlternative units","Degree (angle)\n\nIn most mathematical work beyond practical geometry, angles are typically measured in radians rather than degrees. This is for a variety of reasons; for example, the trigonometric functions have simpler and more \"natural\" properties when their arguments are expressed in radians. These considerations outweigh the convenient divisibility of the number 360. One complete turn (360°) is equal to 2Pi| radians, so 180° is equal to radians, or equivalently, the degree is a mathematical constant: 1° = .","Degree (angle)\n\nThe turn (or revolution, full circle, full rotation, cycle) is used in technology and science. 1 turn = 360°.","Degree (angle)\n\nWith the invention of the metric system, based on powers of ten, there was an attempt to replace degrees by decimal \"degrees\"These new and decimal \"degrees\" must not be confused with decimal degrees. called grad or gon, where the number in a right angle is equal to 100 gon with 400 gon in a full circle (1° \n gon). Although that idea was abandoned by Napoleon, grades continued to be used in several fields and many scientific calculators support them. Decigrades were used with French artillery sights in World War I.","Degree (angle)\n\nAn angular mil, which is most used in military applications, has at least three specific variants, ranging from to , each approximately equal to one milliradian. However, used by the Russian Army originated in Imperial Russia, where an equilateral chord was divided into tenths to give a circle of 600 units (this may be seen on a lining plane, an early device for aiming indirect fire artillery, dating from about 1900, in the St Petersberg Museum of Artillery).","Angle\n\nIn planar geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. \nAngles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. These are called dihedral angles. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles.","Angle\n\nAngle is also used to designate the measure of an angle or of a rotation. This measure is the ratio of the length of a circular arc to its radius. In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation.","Angle\n\nThe word angle comes from the Latin word angulus, meaning \"corner\"; cognate words are the Greek (ankylοs), meaning \"crooked, curved,\" and the English word \"ankle\". Both are connected with the Proto-Indo-European root *ank-, meaning \"to bend\" or \"bow\".","Angle\n\nEuclid defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other. According to Proclus an angle must be either a quality or a quantity, or a relationship. The first concept was used by Eudemus, who regarded an angle as a deviation from a straight line; the second by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines; Euclid adopted the third concept, although his definitions of right, acute, and obtuse angles are certainly quantitative.","Angle\n\nIdentifying angles","Angle\n\nIn mathematical expressions, it is common to use Greek letters (α, β, γ, θ, φ, . . . ) to serve as variables standing for the size of some angle. (To avoid confusion with its other meaning, the symbol Pi| is typically not used for this purpose.) Lower case Roman letters (a, b, c, . . . ) are also used, as are upper case Roman letters in the context of polygons. See the figures in this article for examples.","Angle\n\nIn geometric figures, angles may also be identified by the labels attached to the three points that define them. For example, the angle at vertex A enclosed by the rays AB and AC (i.e. the lines from point A to point B and point A to point C) is denoted ∠BAC or \\widehat{\\rm BAC}. Sometimes, where there is no risk of confusion, the angle may be referred to simply by its vertex (\"angle A\").","Angle\n\nPotentially, an angle denoted, say, ∠BAC might refer to any of four angles: the clockwise angle from B to C, the anticlockwise angle from B to C, the clockwise angle from C to B, or the anticlockwise angle from C to B, where the direction in which the angle is measured determines its sign (see Positive and negative angles). However, in many geometrical situations it is obvious from context that the positive angle less than or equal to 180 degrees is meant, and no ambiguity arises. Otherwise, a convention may be adopted so that ∠BAC always refers to the anticlockwise (positive) angle from B to C, and ∠CAB to the anticlockwise (positive) angle from C to B.","Angle\n\nTypes of angles","Angle\n\nIndividual angles","Angle\n\n*Angles smaller than a right angle (less than 90°) are called acute angles (\"acute\" meaning \"sharp\").\n*An angle equal to turn (90° or radians) is called a right angle. Two lines that form a right angle are said to be normal, orthogonal, or perpendicular.\n*Angles larger than a right angle and smaller than a straight angle (between 90° and 180°) are called obtuse angles (\"obtuse\" meaning \"blunt\").\n*An angle equal to turn (180° or radians) is called a straight angle.\n*Angles larger than a straight angle but less than 1 turn (between 180° and 360°) are called reflex angles.\n*An angle equal to 1 turn (360° or 2 radians) is called a full angle, complete angle, or a perigon.\n*Angles that are not right angles or a multiple of a right angle are called oblique angles.","Angle\n\nThe names, intervals, and measured units are shown in a table below:","Angle\n\nEquivalence angle pairs","Angle\n\n*Angles that have the same measure (i.e. the same magnitude) are said to be equal or congruent. An angle is defined by its measure and is not dependent upon the lengths of the sides of the angle (e.g. all right angles are equal in measure).\n*Two angles which share terminal sides, but differ in size by an integer multiple of a turn, are called coterminal angles.\n*A reference angle is the acute version of any angle determined by repeatedly subtracting or adding straight angle ( turn, 180°, or radians), to the results as necessary, until the magnitude of result is an acute angle, a value between 0 and turn, 90°, or radians. For example, an angle of 30 degrees has a reference angle of 30 degrees, and an angle of 150 degrees also has a reference angle of 30 degrees (180 – 150). An angle of 750 degrees has a reference angle of 30 degrees (750 – 720).","Angle\n\nVertical and adjacent angle pairs","Angle\n\nWhen two straight lines intersect at a point, four angles are formed. Pairwise these angles are named according to their location relative to each other.\n*A pair of angles opposite each other, formed by two intersecting straight lines that form an \"X\"-like shape, are called vertical angles or opposite angles or vertically opposite angles. They are abbreviated as vert. opp. ∠s.","Angle\n\nThe equality of vertically opposite angles is called the vertical angle theorem. Eudemus of Rhodes attributed the proof to Thales of Miletus. The proposition showed that since both of a pair of vertical angles are supplementary to both of the adjacent angles, the vertical angles are equal in measure. According to a historical Note, when Thales visited Egypt, he observed that whenever the Egyptians drew two intersecting lines, they would measure the vertical angles to make sure that they were equal. Thales concluded that one could prove that all vertical angles are equal if one accepted some general notions such as: all straight angles are equal, equals added to equals are equal, and equals subtracted from equals are equal.","Angle\n\nIn the figure, assume the measure of Angle A x. When two adjacent angles form a straight line, they are supplementary. Therefore, the measure of Angle C \n 180 − x. Similarly, the measure of Angle D 180 − x. Both Angle C and Angle D have measures equal to 180 − x and are congruent. Since Angle B is supplementary to both Angles C and D, either of these angle measures may be used to determine the measure of Angle B. Using the measure of either Angle C or Angle D we find the measure of Angle B \n 180 − (180 − x) 180 − 180 + x \n x. Therefore, both Angle A and Angle B have measures equal to x and are equal in measure.","Angle\n\n*Adjacent angles, often abbreviated as adj. ∠s, are angles that share a common vertex and edge but do not share any interior points. In other words, they are angles that are side by side, or adjacent, sharing an \"arm\". Adjacent angles which sum to a right angle, straight angle or full angle are special and are respectively called complementary, supplementary and explementary angles (see \"Combine angle pairs\" below).","Angle\n\nA transversal is a line that intersects a pair of (often parallel) lines and is associated with alternate interior angles, corresponding angles, interior angles, and exterior angles.","Angle\n\nCombining angle pairs","Angle\n\nThere are three special angle pairs which involve the summation of angles:","Angle\n\n*Complementary angles are angle pairs whose measures sum to one right angle ( turn, 90°, or radians). If the two complementary angles are adjacent their non-shared sides form a right angle. In Euclidean geometry, the two acute angles in a right triangle are complementary, because the sum of internal angles of a triangle is 180 degrees, and the right angle itself accounts for ninety degrees.\nThe adjective complementary is from Latin complementum, associated with the verb complere, \"to fill up\". An acute angle is \"filled up\" by its complement to form a right angle.\nThe difference between an angle and a right angle is termed the complement of the angle.\nIf angles A and B are complementary, the following relationships hold:\n: \\sin^2A + \\sin^2B 1. \\quad \\cos^2A + \\cos^2B \n 1.\n: \\tan A \\cot B. \\quad \\quad \\quad \\sec A \n \\csc B.\n(The tangent of an angle equals the cotangent of its complement and its secant equals the cosecant of its complement.)\nThe prefix \"co-\" in the names of some trigonometric ratios refers to the word \"complementary\".","Angle\n\n*Two angles that sum to a straight angle ( turn, 180°, or radians) are called supplementary angles.\nIf the two supplementary angles are adjacent (i.e. have a common vertex and share just one side), their non-shared sides form a straight line. Such angles are called a linear pair of angles. However, supplementary angles do not have to be on the same line, and can be separated in space. For example, adjacent angles of a parallelogram are supplementary, and opposite angles of a cyclic quadrilateral (one whose vertices all fall on a single circle) are supplementary.\nIf a point P is exterior to a circle with center O, and if the tangent lines from P touch the circle at points T and Q, then ∠TPQ and ∠TOQ are supplementary.\nThe sines of supplementary angles are equal. Their cosines and tangents (unless undefined) are equal in magnitude but have opposite signs.\nIn Euclidean geometry, any sum of two angles in a triangle is supplementary to the third, because the sum of internal angles of a triangle is a straight angle.","Angle\n\n*Two angles that sum to a complete angle (1 turn, 360°, or 2 radians) are called explementary angles or conjugate angles.\n*:The difference between an angle and a complete angle is termed the explement of the angle or conjugate of an angle.","Angle\n\nPolygon related angles","Angle\n\n*An angle that is part of a simple polygon is called an interior angle if it lies on the inside of that simple polygon. A simple concave polygon has at least one interior angle that is a reflex angle. *:In Euclidean geometry, the measures of the interior angles of a triangle add up to radians, 180°, or turn; the measures of the interior angles of a simple convex quadrilateral add up to 2 radians, 360°, or 1 turn. In general, the measures of the interior angles of a simple convex polygon with n sides add up to (n − 2) radians, or 180(n − 2) degrees, (2n − 4) right angles, or ( − 1) turn. *The supplement of an interior angle is called an exterior angle, that is, an interior angle and an exterior angle form a linear pair of angles. There are two exterior angles at each vertex of the polygon, each determined by extending one of the two sides of the polygon that meet at the vertex; these two angles are vertical angles and hence are equal.","Angle\n\nAn exterior angle measures the amount of rotation one has to make at a vertex to trace out the polygon. If the corresponding interior angle is a reflex angle, the exterior angle should be considered negative. Even in a non-simple polygon it may be possible to define the exterior angle, but one will have to pick an orientation of the plane (or surface) to decide the sign of the exterior angle measure. *:In Euclidean geometry, the sum of the exterior angles of a simple convex polygon will be one full turn (360°). The exterior angle here could be called a supplementary exterior angle. Exterior angles are commonly used in Logo Turtle Geometry when drawing regular polygons. *In a triangle, the bisectors of two exterior angles and the bisector of the other interior angle are concurrent (meet at a single point).Johnson, Roger A. Advanced Euclidean Geometry, Dover Publications, 2007. *In a triangle, three intersection points, each of an external angle bisector with the opposite extended side, are collinear.","Angle\n\n* In a triangle, three intersection points, two of them between an interior angle bisector and the opposite side, and the third between the other exterior angle bisector and the opposite side extended, are collinear. *Some authors use the name exterior angle of a simple polygon to simply mean the explement exterior angle (not supplement!) of the interior angle. This conflicts with the above usage.","Angle\n\nPlane related angles","Angle\n\n*The angle between two planes (such as two adjacent faces of a polyhedron) is called a dihedral angle. It may be defined as the acute angle between two lines normal to the planes.\n*The angle between a plane and an intersecting straight line is equal to ninety degrees minus the angle between the intersecting line and the line that goes through the point of intersection and is normal to the plane.","Angle\n\nMeasuring angles","Angle\n\nThe size of a geometric angle is usually characterized by the magnitude of the smallest rotation that maps one of the rays into the other. Angles that have the same size are said to be equal or congruent or equal in measure.","Angle\n\nIn some contexts, such as identifying a point on a circle or describing the orientation of an object in two dimensions relative to a reference orientation, angles that differ by an exact multiple of a full turn are effectively equivalent. In other contexts, such as identifying a point on a spiral curve or describing the cumulative rotation of an object in two dimensions relative to a reference orientation, angles that differ by a non-zero multiple of a full turn are not equivalent.","Angle\n\nIn order to measure an angle θ, a circular arc centered at the vertex of the angle is drawn, e.g. with a pair of compasses. The ratio of the length s of the arc by the radius r of the circle is the measure of the angle in radians.","Angle\n\nThe measure of the angle in another angular unit is then obtained by multiplying its measure in radians by the scaling factor , where k is the measure of a complete turn in the chosen unit (for example 360 for degrees or 400 for gradians):","Angle\n\n\\theta = k \\frac{s}{2\\pi r}.","Angle\n\nThe value of θ thus defined is independent of the size of the circle: if the length of the radius is changed then the arc length changes in the same proportion, so the ratio s/r is unaltered. (Proof. The formula above can be rewritten as One turn, for which units, corresponds to an arc equal in length to the circle's circumference, which is 2r, so . Substituting n for θ and 2r for s in the formula, results in )","Angle\n\nAngle addition postulate","Angle\n\nThe angle addition postulate states that if B is in the interior of angle AOC, then","Angle\n\nm\\angle AOC = m\\angle AOB + m\\angle BOC","Angle\n\nThe measure of the angle AOC is the sum of the measure of angle AOB and the measure of angle BOC.\nIn this postulate it does not matter in which unit the angle is measured as long as each angle is measured in the same unit.","Angle\n\nUnits","Angle\n\nUnits used to represent angles are listed below in descending magnitude order. Of these units, the degree and the radian are by far the most commonly used. Angles expressed in radians are dimensionless for the purposes of dimensional analysis.","Angle\n\nMost units of angular measurement are defined such that one turn (i.e. one full circle) is equal to n units, for some whole number n. The two exceptions are the radian and the diameter part.","Angle\n\n;Turn (n = 1): The turn, also cycle, full circle, revolution, and rotation, is complete circular movement or measure (as to return to the same point) with circle or ellipse. A turn is abbreviated , cyc, rev, or rot depending on the application, but in the acronym rpm (revolutions per minute), just r is used. A turn of n units is obtained by setting in the formula above. The equivalence of 1 turn is 360°, 2 rad, 400 grad, and 4 right angles. The symbol can also be used as a mathematical constant to represent 2 radians. Used in this way () allows for radians to be expressed as a fraction of a turn. For example, half a turn is .","Angle\n\n;Quadrant (n 4): The quadrant is of a turn, i.e. a right angle. It is the unit used in Euclid's Elements. 1 quad. \n 90° rad \n turn = 100 grad. In German the symbol ∟ has been used to denote a quadrant.","Angle\n\n;Sextant (n 6): The sextant (angle of the equilateral triangle) is of a turn. It was the unit used by the Babylonians, and is especially easy to construct with ruler and compasses. The degree, minute of arc and second of arc are sexagesimal subunits of the Babylonian unit. 1 Babylonian unit \n 60° = /3 rad ≈ 1.047197551 rad.","Angle\n\n;Radian (n 2 \n 6.283 . . . ): The radian is the angle subtended by an arc of a circle that has the same length as the circle's radius. The case of radian for the formula given earlier, a radian of n 2 units is obtained by setting k \n = 1. One turn is 2 radians, and one radian is degrees, or about 57.2958 degrees. The radian is abbreviated rad, though this symbol is often omitted in mathematical texts, where radians are assumed unless specified otherwise. When radians are used angles are considered as dimensionless. The radian is used in virtually all mathematical work beyond simple practical geometry, due, for example, to the pleasing and \"natural\" properties that the trigonometric functions display when their arguments are in radians. The radian is the (derived) unit of angular measurement in the SI system.","Angle\n\n;Clock position (n = 12): A clock position is the relative direction of an object described using the analogy of a 12-hour clock. One imagines a clock face lying either upright or flat in front of oneself, and identifies the twelve hour markings with the directions in which they point.","Angle\n\n;Hour angle (n 24): The astronomical hour angle is of a turn. Since this system is amenable to measuring objects that cycle once per day (such as the relative position of stars), the sexagesimal subunits are called minute of time and second of time. Note that these are distinct from, and 15 times larger than, minutes and seconds of arc. 1 hour \n 15° rad \n quad. turn \n grad.","Angle\n\n;(Compass) point or wind (n 32): The point, used in navigation, is of a turn. 1 point \n of a right angle 11.25° \n 12.5 grad. Each point is subdivided in four quarter-points so that 1 turn equals 128 quarter-points.","Angle\n\n;Hexacontade (n = 60): The hexacontade is a unit of 6° that Eratosthenes used, so that a whole turn was divided into 60 units.","Angle\n\n;Pechus (n = 144–180): –The pechus was a Babylonian unit equal to about 2° or °.","Angle\n\n;Binary degree (n = 256): The binary degree, also known as the binary radian (or brad), is of a turn. The binary degree is used in computing so that an angle can be efficiently represented in a single byte (albeit to limited precision). Other measures of angle used in computing may be based on dividing one whole turn into 2n equal parts for other values of n.","Angle\n\n;Degree (n 360): The degree, denoted by a small superscript circle (°), is 1/360 of a turn, so one turn is 360°. The case of degrees for the formula given earlier, a degree of n \n 360° units is obtained by setting k = . One advantage of this old sexagesimal subunit is that many angles common in simple geometry are measured as a whole number of degrees. Fractions of a degree may be written in normal decimal notation (e.g. 3.5° for three and a half degrees), but the \"minute\" and \"second\" sexagesimal subunits of the \"degree-minute-second\" system are also in use, especially for geographical coordinates and in astronomy and ballistics:","Angle\n\n;Diameter part (n = 376.99 . . . ): The diameter part (occasionally used in Islamic mathematics) is radian. One \"diameter part\" is approximately 0.95493°. There are about 376.991 diameter parts per turn.","Angle\n\n;Grad (n = 400): The grad, also called grade, gradian, or gon, is of a turn, so a right angle is 100 grads. It is a decimal subunit of the quadrant. A kilometre was historically defined as a centi-grad of arc along a great circle of the Earth, so the kilometer is the decimal analog to the sexagesimal nautical mile. The grad is used mostly in triangulation.","Angle\n\n;Mil (n 6000–6400): The mil is any of several units that are approximately equal to a milliradian. There are several definitions ranging from 0.05625 to 0.06 degrees (3.375 to 3.6 minutes), with the milliradian being approximately 0.05729578 degrees (3.43775 minutes). In NATO countries, it is defined as of a circle. Its value is approximately equal to the angle subtended by a width of 1 metre as seen from 1 km away ( \n 0.0009817 . . . ≈ ).","Angle\n\n;Minute of arc (n 21,600): The minute of arc (or MOA, arcminute, or just minute) is of a degree \n turn. It is denoted by a single prime ( ′ ). For example, 3° 30′ is equal to 3 × 60 + 30 210 minutes or 3 + \n 3.5 degrees. A mixed format with decimal fractions is also sometimes used, e.g. 3° 5.72′ = 3 + degrees. A nautical mile was historically defined as a minute of arc along a great circle of the Earth.","Angle\n\n;Second of arc (n = 1,296,000): The second of arc (or arcsecond, or just second) is of a minute of arc and of a degree. It is denoted by a double prime ( ″ ). For example, 3° 7′ 30″ is equal to 3 + + degrees, or 3.125 degrees.","Angle\n\nPositive and negative angles","Angle\n\nAlthough the definition of the measurement of an angle does not support the concept of a negative angle, it is frequently useful to impose a convention that allows positive and negative angular values to represent orientations and/or rotations in opposite directions relative to some reference.","Angle\n\nIn a two-dimensional Cartesian coordinate system, an angle is typically defined by its two sides, with its vertex at the origin. The initial side is on the positive x-axis, while the other side or terminal side is defined by the measure from the initial side in radians, degrees, or turns. With positive angles representing rotations toward the positive y-axis and negative angles representing rotations toward the negative y-axis. When Cartesian coordinates are represented by standard position, defined by the x-axis rightward and the y-axis upward, positive rotations are anticlockwise and negative rotations are clockwise.","Angle\n\nIn many contexts, an angle of −θ is effectively equivalent to an angle of \"one full turn minus θ\". For example, an orientation represented as −45° is effectively equivalent to an orientation represented as 360° − 45° or 315°. However, a rotation of −45° would not be the same as a rotation of 315°.","Angle\n\nIn three-dimensional geometry, \"clockwise\" and \"anticlockwise\" have no absolute meaning, so the direction of positive and negative angles must be defined relative to some reference, which is typically a vector passing through the angle's vertex and perpendicular to the plane in which the rays of the angle lie.","Angle\n\nIn navigation, bearings are measured relative to north. By convention, viewed from above, bearing angle are positive clockwise, so a bearing of 45° corresponds to a north-east orientation. Negative bearings are not used in navigation, so a north-west orientation corresponds to a bearing of 315°.","Angle\n\nAlternative ways of measuring the size of an angle","Angle\n\nThere are several alternatives to measuring the size of an angle by the angle of rotation.\nThe grade of a slope, or gradient is equal to the tangent of the angle, or sometimes (rarely) the sine. A gradient is often expressed as a percentage. For very small values (less than 5%), the grade of a slope is approximately the measure of the angle in radians.","Angle\n\nIn rational geometry the spread between two lines is defined at the square of the sine of the angle between the lines. Since the sine of an angle and the sine of its supplementary angle are the same, any angle of rotation that maps one of the lines into the other leads to the same value for the spread between the lines.","Angle\n\nAstronomical approximations","Angle\n\nAstronomers measure angular separation of objects in degrees from their point of observation.\n* 0.5° is approximately the width of the sun or moon.\n* 1° is approximately the width of a little finger at arm's length.\n* 10° is approximately the width of a closed fist at arm's length.\n* 20° is approximately the width of a handspan at arm's length.","Angle\n\nThese measurements clearly depend on the individual subject, and the above should be treated as rough rule of thumb approximations only.","Angle\n\nAngles between curves","Angle\n\nThe angle between a line and a curve (mixed angle) or between two intersecting curves (curvilinear angle) is defined to be the angle between the tangents at the point of intersection. Various names (now rarely, if ever, used) have been given to particular cases:—amphicyrtic (Gr. , on both sides, κυρτός, convex) or cissoidal (Gr. κισσός, ivy), biconvex; xystroidal or sistroidal (Gr. ξυστρίς, a tool for scraping), concavo-convex; amphicoelic (Gr. κοίλη, a hollow) or angulus lunularis, biconcave.","Angle\n\nBisecting and trisecting angles","Angle\n\nThe ancient Greek mathematicians knew how to bisect an angle (divide it into two angles of equal measure) using only a compass and straightedge, but could only trisect certain angles. In 1837 Pierre Wantzel showed that for most angles this construction cannot be performed.","Angle\n\nDot product and generalisations","Angle\n\nIn the Euclidean space, the angle θ between two Euclidean vectors u and v is related to their dot product and their lengths by the formula","Angle\n\n\\mathbf{u} \\cdot \\mathbf{v} = \\cos(\\theta) \\left\\| \\mathbf{u} \\right\\| \\left\\| \\mathbf{v} \\right\\| .","Angle\n\nThis formula supplies an easy method to find the angle between two planes (or curved surfaces) from their normal vectors and between skew lines from their vector equations.","Angle\n\nInner product","Angle\n\nTo define angles in an abstract real inner product space, we replace the Euclidean dot product ( · ) by the inner product \\langle \\cdot , \\cdot \\rangle , i.e.","Angle\n\n\\langle \\mathbf{u} , \\mathbf{v} \\rangle = \\cos(\\theta)\\ \\left\\| \\mathbf{u} \\right\\|\\ \\left\\| \\mathbf{v} \\right\\| .","Angle\n\nIn a complex inner product space, the expression for the cosine above may give non-real values, so it is replaced with","Angle\n\n\\operatorname{Re} \\left( \\langle \\mathbf{u} , \\mathbf{v} \\rangle \\right) = \\cos(\\theta)\\ \\left\\| \\mathbf{u} \\right\\| \\ \\left\\| \\mathbf{v} \\right\\| .","Angle\n\nor, more commonly, using the absolute value, with","Angle\n\n\\left| \\langle \\mathbf{u} , \\mathbf{v} \\rangle \\right| = | \\cos(\\theta) | \\ \\left\\| \\mathbf{u} \\right\\| \\ \\left\\| \\mathbf{v} \\right\\| .","Angle\n\nThe latter definition ignores the direction of the vectors and thus describes the angle between one-dimensional subspaces \\operatorname{span}(\\mathbf{u}) and \\operatorname{span}(\\mathbf{v}) spanned by the vectors \\mathbf{u} and \\mathbf{v} correspondingly.","Angle\n\nAngles between subspaces","Angle\n\nThe definition of the angle between one-dimensional subspaces \\operatorname{span}(\\mathbf{u}) and \\operatorname{span}(\\mathbf{v}) given by","Angle\n\n\\left| \\langle \\mathbf{u} , \\mathbf{v} \\rangle \\right| = | \\cos(\\theta) | \\ \\left\\| \\mathbf{u} \\right\\| \\ \\left\\| \\mathbf{v} \\right\\|","Angle\n\nin a Hilbert space can be extended to subspaces of any finite dimensions. Given two subspaces \\mathcal{U} , \\mathcal{W} with \\dim ( \\mathcal{U}) :k \\leq \\dim ( \\mathcal{W}) :\n l , this leads to a definition of k angles called canonical or principal angles between subspaces.","Angle\n\nAngles in Riemannian geometry","Angle\n\nIn Riemannian geometry, the metric tensor is used to define the angle between two tangents. Where U and V are tangent vectors and gij are the components of the metric tensor G,","Angle\n\n\\cos \\theta = \\frac{g_{ij}U^iV^j}\n{\\sqrt{ \\left| g_{ij}U^iU^j \\right| \\left| g_{ij}V^iV^j \\right|}}.","Angle\n\nAngles in geography and astronomy","Angle\n\nIn geography, the location of any point on the Earth can be identified using a geographic coordinate system. This system specifies the latitude and longitude of any location in terms of angles subtended at the centre of the Earth, using the equator and (usually) the Greenwich meridian as references.","Angle\n\nIn astronomy, a given point on the celestial sphere (that is, the apparent position of an astronomical object) can be identified using any of several astronomical coordinate systems, where the references vary according to the particular system. Astronomers measure the angular separation of two stars by imagining two lines through the centre of the Earth, each intersecting one of the stars. The angle between those lines can be measured, and is the angular separation between the two stars.","Angle\n\nIn both geography and astronomy, a sighting direction can be specified in terms of a vertical angle such as altitude /elevation with respect to the horizon as well as the azimuth with respect to north.","Angle\n\nAstronomers also measure the apparent size of objects as an angular diameter. For example, the full moon has an angular diameter of approximately 0.5°, when viewed from Earth. One could say, \"The Moon's diameter subtends an angle of half a degree.\" The small-angle formula can be used to convert such an angular measurement into a distance/size ratio."],"string":"[\n \"Degree (angle)\\n\\nA degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of plane angle, defined by representing a full rotation as 360 degrees.\",\n \"Degree (angle)\\n\\nIt is not an SI unit, as the SI unit for angles is radian, but it is mentioned in the SI brochure as an accepted unit. Because a full rotation equals 2 radians, one degree is equivalent to radians.\",\n \"Degree (angle)\\n\\nHistory\",\n \"Degree (angle)\\n\\nThe original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year. Ancient astronomers noticed that the sun, which follows through the ecliptic path over the course of the year, seems to advance in its path by approximately one degree each day. Some ancient calendars, such as the Persian calendar, used 360 days for a year. The use of a calendar with 360 days may be related to the use of sexagesimal numbers.\",\n \"Degree (angle)\\n\\nAnother theory is that the Babylonians subdivided the circle using the angle of an equilateral triangle as the basic unit and further subdivided the latter into 60 parts following their sexagesimal numeric system. The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle. A chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree.\",\n \"Degree (angle)\\n\\nAristarchus of Samos and Hipparchus seem to have been among the first Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically. Timocharis, Aristarchus, Aristillus, Archimedes, and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes. Eratosthenes used a simpler sexagesimal system dividing a circle into 60 parts.\",\n \"Degree (angle)\\n\\nThe division of the circle into 360 parts also occurred in ancient India, as evidenced in the Rigveda:\",\n \"Degree (angle)\\n\\nAnother motivation for choosing the number 360 may have been that it is readily divisible: 360 has 24 divisors,The divisors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360. making it one of only 7 numbers such that no number less than twice as much has more divisors . Furthermore, it is divisible by every number from 1 to 10 except 7.Contrast this with the relatively unwieldy 2520, which is the least common multiple for every number from 1 to 10. This property has many useful applications, such as dividing the world into 24 time zones, each of which is nominally 15° of longitude, to correlate with the established 24-hour day convention.\",\n \"Degree (angle)\\n\\nFinally, it may be the case that more than one of these factors has come into play. According to that theory, the number is approximately 365 because of the apparent movement of the sun against the celestial sphere and that it was rounded to 360 for some of the mathematical reasons cited above.\",\n \"Degree (angle)\\n\\nSubdivisions\",\n \"Degree (angle)\\n\\nFor many practical purposes, a degree is a small enough angle that whole degrees provide sufficient precision. When this is not the case, as in astronomy or for geographic coordinates (latitude and longitude), degree measurements may be written using decimal degrees. For example, 40.1875°, with the degree symbol behind the decimals.\",\n \"Degree (angle)\\n\\nAlternatively, the traditional sexagesimal unit subdivisions can be used. One degree is divided into 60 minutes (of arc), and one minute into 60 seconds (of arc). Use of degrees-minutes-seconds is also called DMS notation. These subdivisions, also called the arcminute and arcsecond, are respectively represented as a single and double prime. For example, 40.1875° = 40° 11′ 15″, or using quotation mark characters as 40° 11' 15\\\". Additional precision can be provided using decimals for the arcseconds component.\",\n \"Degree (angle)\\n\\nThe older system of thirds, fourths, etc., which continues the sexagesimal unit subdivision, was used by al-Kashi and other ancient astronomers, but is rarely used today. These subdivisions were denoted by writing the Roman numeral for the number of sixtieths in superscript: 1I for a \\\"prime\\\" (minute of arc), 1II for a second, 1III for a third, 1IV for a fourth, etc. Hence the modern symbols for the minute and second of arc, and the word \\\"second\\\" also refer to this system.\",\n \"Degree (angle)\\n\\nAlternative units\",\n \"Degree (angle)\\n\\nIn most mathematical work beyond practical geometry, angles are typically measured in radians rather than degrees. This is for a variety of reasons; for example, the trigonometric functions have simpler and more \\\"natural\\\" properties when their arguments are expressed in radians. These considerations outweigh the convenient divisibility of the number 360. One complete turn (360°) is equal to 2Pi| radians, so 180° is equal to radians, or equivalently, the degree is a mathematical constant: 1° = .\",\n \"Degree (angle)\\n\\nThe turn (or revolution, full circle, full rotation, cycle) is used in technology and science. 1 turn = 360°.\",\n \"Degree (angle)\\n\\nWith the invention of the metric system, based on powers of ten, there was an attempt to replace degrees by decimal \\\"degrees\\\"These new and decimal \\\"degrees\\\" must not be confused with decimal degrees. called grad or gon, where the number in a right angle is equal to 100 gon with 400 gon in a full circle (1° \\n gon). Although that idea was abandoned by Napoleon, grades continued to be used in several fields and many scientific calculators support them. Decigrades were used with French artillery sights in World War I.\",\n \"Degree (angle)\\n\\nAn angular mil, which is most used in military applications, has at least three specific variants, ranging from to , each approximately equal to one milliradian. However, used by the Russian Army originated in Imperial Russia, where an equilateral chord was divided into tenths to give a circle of 600 units (this may be seen on a lining plane, an early device for aiming indirect fire artillery, dating from about 1900, in the St Petersberg Museum of Artillery).\",\n \"Angle\\n\\nIn planar geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. \\nAngles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. These are called dihedral angles. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles.\",\n \"Angle\\n\\nAngle is also used to designate the measure of an angle or of a rotation. This measure is the ratio of the length of a circular arc to its radius. In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation.\",\n \"Angle\\n\\nThe word angle comes from the Latin word angulus, meaning \\\"corner\\\"; cognate words are the Greek (ankylοs), meaning \\\"crooked, curved,\\\" and the English word \\\"ankle\\\". Both are connected with the Proto-Indo-European root *ank-, meaning \\\"to bend\\\" or \\\"bow\\\".\",\n \"Angle\\n\\nEuclid defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other. According to Proclus an angle must be either a quality or a quantity, or a relationship. The first concept was used by Eudemus, who regarded an angle as a deviation from a straight line; the second by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines; Euclid adopted the third concept, although his definitions of right, acute, and obtuse angles are certainly quantitative.\",\n \"Angle\\n\\nIdentifying angles\",\n \"Angle\\n\\nIn mathematical expressions, it is common to use Greek letters (α, β, γ, θ, φ, . . . ) to serve as variables standing for the size of some angle. (To avoid confusion with its other meaning, the symbol Pi| is typically not used for this purpose.) Lower case Roman letters (a, b, c, . . . ) are also used, as are upper case Roman letters in the context of polygons. See the figures in this article for examples.\",\n \"Angle\\n\\nIn geometric figures, angles may also be identified by the labels attached to the three points that define them. For example, the angle at vertex A enclosed by the rays AB and AC (i.e. the lines from point A to point B and point A to point C) is denoted ∠BAC or \\\\widehat{\\\\rm BAC}. Sometimes, where there is no risk of confusion, the angle may be referred to simply by its vertex (\\\"angle A\\\").\",\n \"Angle\\n\\nPotentially, an angle denoted, say, ∠BAC might refer to any of four angles: the clockwise angle from B to C, the anticlockwise angle from B to C, the clockwise angle from C to B, or the anticlockwise angle from C to B, where the direction in which the angle is measured determines its sign (see Positive and negative angles). However, in many geometrical situations it is obvious from context that the positive angle less than or equal to 180 degrees is meant, and no ambiguity arises. Otherwise, a convention may be adopted so that ∠BAC always refers to the anticlockwise (positive) angle from B to C, and ∠CAB to the anticlockwise (positive) angle from C to B.\",\n \"Angle\\n\\nTypes of angles\",\n \"Angle\\n\\nIndividual angles\",\n \"Angle\\n\\n*Angles smaller than a right angle (less than 90°) are called acute angles (\\\"acute\\\" meaning \\\"sharp\\\").\\n*An angle equal to turn (90° or radians) is called a right angle. Two lines that form a right angle are said to be normal, orthogonal, or perpendicular.\\n*Angles larger than a right angle and smaller than a straight angle (between 90° and 180°) are called obtuse angles (\\\"obtuse\\\" meaning \\\"blunt\\\").\\n*An angle equal to turn (180° or radians) is called a straight angle.\\n*Angles larger than a straight angle but less than 1 turn (between 180° and 360°) are called reflex angles.\\n*An angle equal to 1 turn (360° or 2 radians) is called a full angle, complete angle, or a perigon.\\n*Angles that are not right angles or a multiple of a right angle are called oblique angles.\",\n \"Angle\\n\\nThe names, intervals, and measured units are shown in a table below:\",\n \"Angle\\n\\nEquivalence angle pairs\",\n \"Angle\\n\\n*Angles that have the same measure (i.e. the same magnitude) are said to be equal or congruent. An angle is defined by its measure and is not dependent upon the lengths of the sides of the angle (e.g. all right angles are equal in measure).\\n*Two angles which share terminal sides, but differ in size by an integer multiple of a turn, are called coterminal angles.\\n*A reference angle is the acute version of any angle determined by repeatedly subtracting or adding straight angle ( turn, 180°, or radians), to the results as necessary, until the magnitude of result is an acute angle, a value between 0 and turn, 90°, or radians. For example, an angle of 30 degrees has a reference angle of 30 degrees, and an angle of 150 degrees also has a reference angle of 30 degrees (180 – 150). An angle of 750 degrees has a reference angle of 30 degrees (750 – 720).\",\n \"Angle\\n\\nVertical and adjacent angle pairs\",\n \"Angle\\n\\nWhen two straight lines intersect at a point, four angles are formed. Pairwise these angles are named according to their location relative to each other.\\n*A pair of angles opposite each other, formed by two intersecting straight lines that form an \\\"X\\\"-like shape, are called vertical angles or opposite angles or vertically opposite angles. They are abbreviated as vert. opp. ∠s.\",\n \"Angle\\n\\nThe equality of vertically opposite angles is called the vertical angle theorem. Eudemus of Rhodes attributed the proof to Thales of Miletus. The proposition showed that since both of a pair of vertical angles are supplementary to both of the adjacent angles, the vertical angles are equal in measure. According to a historical Note, when Thales visited Egypt, he observed that whenever the Egyptians drew two intersecting lines, they would measure the vertical angles to make sure that they were equal. Thales concluded that one could prove that all vertical angles are equal if one accepted some general notions such as: all straight angles are equal, equals added to equals are equal, and equals subtracted from equals are equal.\",\n \"Angle\\n\\nIn the figure, assume the measure of Angle A x. When two adjacent angles form a straight line, they are supplementary. Therefore, the measure of Angle C \\n 180 − x. Similarly, the measure of Angle D 180 − x. Both Angle C and Angle D have measures equal to 180 − x and are congruent. Since Angle B is supplementary to both Angles C and D, either of these angle measures may be used to determine the measure of Angle B. Using the measure of either Angle C or Angle D we find the measure of Angle B \\n 180 − (180 − x) 180 − 180 + x \\n x. Therefore, both Angle A and Angle B have measures equal to x and are equal in measure.\",\n \"Angle\\n\\n*Adjacent angles, often abbreviated as adj. ∠s, are angles that share a common vertex and edge but do not share any interior points. In other words, they are angles that are side by side, or adjacent, sharing an \\\"arm\\\". Adjacent angles which sum to a right angle, straight angle or full angle are special and are respectively called complementary, supplementary and explementary angles (see \\\"Combine angle pairs\\\" below).\",\n \"Angle\\n\\nA transversal is a line that intersects a pair of (often parallel) lines and is associated with alternate interior angles, corresponding angles, interior angles, and exterior angles.\",\n \"Angle\\n\\nCombining angle pairs\",\n \"Angle\\n\\nThere are three special angle pairs which involve the summation of angles:\",\n \"Angle\\n\\n*Complementary angles are angle pairs whose measures sum to one right angle ( turn, 90°, or radians). If the two complementary angles are adjacent their non-shared sides form a right angle. In Euclidean geometry, the two acute angles in a right triangle are complementary, because the sum of internal angles of a triangle is 180 degrees, and the right angle itself accounts for ninety degrees.\\nThe adjective complementary is from Latin complementum, associated with the verb complere, \\\"to fill up\\\". An acute angle is \\\"filled up\\\" by its complement to form a right angle.\\nThe difference between an angle and a right angle is termed the complement of the angle.\\nIf angles A and B are complementary, the following relationships hold:\\n: \\\\sin^2A + \\\\sin^2B 1. \\\\quad \\\\cos^2A + \\\\cos^2B \\n 1.\\n: \\\\tan A \\\\cot B. \\\\quad \\\\quad \\\\quad \\\\sec A \\n \\\\csc B.\\n(The tangent of an angle equals the cotangent of its complement and its secant equals the cosecant of its complement.)\\nThe prefix \\\"co-\\\" in the names of some trigonometric ratios refers to the word \\\"complementary\\\".\",\n \"Angle\\n\\n*Two angles that sum to a straight angle ( turn, 180°, or radians) are called supplementary angles.\\nIf the two supplementary angles are adjacent (i.e. have a common vertex and share just one side), their non-shared sides form a straight line. Such angles are called a linear pair of angles. However, supplementary angles do not have to be on the same line, and can be separated in space. For example, adjacent angles of a parallelogram are supplementary, and opposite angles of a cyclic quadrilateral (one whose vertices all fall on a single circle) are supplementary.\\nIf a point P is exterior to a circle with center O, and if the tangent lines from P touch the circle at points T and Q, then ∠TPQ and ∠TOQ are supplementary.\\nThe sines of supplementary angles are equal. Their cosines and tangents (unless undefined) are equal in magnitude but have opposite signs.\\nIn Euclidean geometry, any sum of two angles in a triangle is supplementary to the third, because the sum of internal angles of a triangle is a straight angle.\",\n \"Angle\\n\\n*Two angles that sum to a complete angle (1 turn, 360°, or 2 radians) are called explementary angles or conjugate angles.\\n*:The difference between an angle and a complete angle is termed the explement of the angle or conjugate of an angle.\",\n \"Angle\\n\\nPolygon related angles\",\n \"Angle\\n\\n*An angle that is part of a simple polygon is called an interior angle if it lies on the inside of that simple polygon. A simple concave polygon has at least one interior angle that is a reflex angle. *:In Euclidean geometry, the measures of the interior angles of a triangle add up to radians, 180°, or turn; the measures of the interior angles of a simple convex quadrilateral add up to 2 radians, 360°, or 1 turn. In general, the measures of the interior angles of a simple convex polygon with n sides add up to (n − 2) radians, or 180(n − 2) degrees, (2n − 4) right angles, or ( − 1) turn. *The supplement of an interior angle is called an exterior angle, that is, an interior angle and an exterior angle form a linear pair of angles. There are two exterior angles at each vertex of the polygon, each determined by extending one of the two sides of the polygon that meet at the vertex; these two angles are vertical angles and hence are equal.\",\n \"Angle\\n\\nAn exterior angle measures the amount of rotation one has to make at a vertex to trace out the polygon. If the corresponding interior angle is a reflex angle, the exterior angle should be considered negative. Even in a non-simple polygon it may be possible to define the exterior angle, but one will have to pick an orientation of the plane (or surface) to decide the sign of the exterior angle measure. *:In Euclidean geometry, the sum of the exterior angles of a simple convex polygon will be one full turn (360°). The exterior angle here could be called a supplementary exterior angle. Exterior angles are commonly used in Logo Turtle Geometry when drawing regular polygons. *In a triangle, the bisectors of two exterior angles and the bisector of the other interior angle are concurrent (meet at a single point).Johnson, Roger A. Advanced Euclidean Geometry, Dover Publications, 2007. *In a triangle, three intersection points, each of an external angle bisector with the opposite extended side, are collinear.\",\n \"Angle\\n\\n* In a triangle, three intersection points, two of them between an interior angle bisector and the opposite side, and the third between the other exterior angle bisector and the opposite side extended, are collinear. *Some authors use the name exterior angle of a simple polygon to simply mean the explement exterior angle (not supplement!) of the interior angle. This conflicts with the above usage.\",\n \"Angle\\n\\nPlane related angles\",\n \"Angle\\n\\n*The angle between two planes (such as two adjacent faces of a polyhedron) is called a dihedral angle. It may be defined as the acute angle between two lines normal to the planes.\\n*The angle between a plane and an intersecting straight line is equal to ninety degrees minus the angle between the intersecting line and the line that goes through the point of intersection and is normal to the plane.\",\n \"Angle\\n\\nMeasuring angles\",\n \"Angle\\n\\nThe size of a geometric angle is usually characterized by the magnitude of the smallest rotation that maps one of the rays into the other. Angles that have the same size are said to be equal or congruent or equal in measure.\",\n \"Angle\\n\\nIn some contexts, such as identifying a point on a circle or describing the orientation of an object in two dimensions relative to a reference orientation, angles that differ by an exact multiple of a full turn are effectively equivalent. In other contexts, such as identifying a point on a spiral curve or describing the cumulative rotation of an object in two dimensions relative to a reference orientation, angles that differ by a non-zero multiple of a full turn are not equivalent.\",\n \"Angle\\n\\nIn order to measure an angle θ, a circular arc centered at the vertex of the angle is drawn, e.g. with a pair of compasses. The ratio of the length s of the arc by the radius r of the circle is the measure of the angle in radians.\",\n \"Angle\\n\\nThe measure of the angle in another angular unit is then obtained by multiplying its measure in radians by the scaling factor , where k is the measure of a complete turn in the chosen unit (for example 360 for degrees or 400 for gradians):\",\n \"Angle\\n\\n\\\\theta = k \\\\frac{s}{2\\\\pi r}.\",\n \"Angle\\n\\nThe value of θ thus defined is independent of the size of the circle: if the length of the radius is changed then the arc length changes in the same proportion, so the ratio s/r is unaltered. (Proof. The formula above can be rewritten as One turn, for which units, corresponds to an arc equal in length to the circle's circumference, which is 2r, so . Substituting n for θ and 2r for s in the formula, results in )\",\n \"Angle\\n\\nAngle addition postulate\",\n \"Angle\\n\\nThe angle addition postulate states that if B is in the interior of angle AOC, then\",\n \"Angle\\n\\nm\\\\angle AOC = m\\\\angle AOB + m\\\\angle BOC\",\n \"Angle\\n\\nThe measure of the angle AOC is the sum of the measure of angle AOB and the measure of angle BOC.\\nIn this postulate it does not matter in which unit the angle is measured as long as each angle is measured in the same unit.\",\n \"Angle\\n\\nUnits\",\n \"Angle\\n\\nUnits used to represent angles are listed below in descending magnitude order. Of these units, the degree and the radian are by far the most commonly used. Angles expressed in radians are dimensionless for the purposes of dimensional analysis.\",\n \"Angle\\n\\nMost units of angular measurement are defined such that one turn (i.e. one full circle) is equal to n units, for some whole number n. The two exceptions are the radian and the diameter part.\",\n \"Angle\\n\\n;Turn (n = 1): The turn, also cycle, full circle, revolution, and rotation, is complete circular movement or measure (as to return to the same point) with circle or ellipse. A turn is abbreviated , cyc, rev, or rot depending on the application, but in the acronym rpm (revolutions per minute), just r is used. A turn of n units is obtained by setting in the formula above. The equivalence of 1 turn is 360°, 2 rad, 400 grad, and 4 right angles. The symbol can also be used as a mathematical constant to represent 2 radians. Used in this way () allows for radians to be expressed as a fraction of a turn. For example, half a turn is .\",\n \"Angle\\n\\n;Quadrant (n 4): The quadrant is of a turn, i.e. a right angle. It is the unit used in Euclid's Elements. 1 quad. \\n 90° rad \\n turn = 100 grad. In German the symbol ∟ has been used to denote a quadrant.\",\n \"Angle\\n\\n;Sextant (n 6): The sextant (angle of the equilateral triangle) is of a turn. It was the unit used by the Babylonians, and is especially easy to construct with ruler and compasses. The degree, minute of arc and second of arc are sexagesimal subunits of the Babylonian unit. 1 Babylonian unit \\n 60° = /3 rad ≈ 1.047197551 rad.\",\n \"Angle\\n\\n;Radian (n 2 \\n 6.283 . . . ): The radian is the angle subtended by an arc of a circle that has the same length as the circle's radius. The case of radian for the formula given earlier, a radian of n 2 units is obtained by setting k \\n = 1. One turn is 2 radians, and one radian is degrees, or about 57.2958 degrees. The radian is abbreviated rad, though this symbol is often omitted in mathematical texts, where radians are assumed unless specified otherwise. When radians are used angles are considered as dimensionless. The radian is used in virtually all mathematical work beyond simple practical geometry, due, for example, to the pleasing and \\\"natural\\\" properties that the trigonometric functions display when their arguments are in radians. The radian is the (derived) unit of angular measurement in the SI system.\",\n \"Angle\\n\\n;Clock position (n = 12): A clock position is the relative direction of an object described using the analogy of a 12-hour clock. One imagines a clock face lying either upright or flat in front of oneself, and identifies the twelve hour markings with the directions in which they point.\",\n \"Angle\\n\\n;Hour angle (n 24): The astronomical hour angle is of a turn. Since this system is amenable to measuring objects that cycle once per day (such as the relative position of stars), the sexagesimal subunits are called minute of time and second of time. Note that these are distinct from, and 15 times larger than, minutes and seconds of arc. 1 hour \\n 15° rad \\n quad. turn \\n grad.\",\n \"Angle\\n\\n;(Compass) point or wind (n 32): The point, used in navigation, is of a turn. 1 point \\n of a right angle 11.25° \\n 12.5 grad. Each point is subdivided in four quarter-points so that 1 turn equals 128 quarter-points.\",\n \"Angle\\n\\n;Hexacontade (n = 60): The hexacontade is a unit of 6° that Eratosthenes used, so that a whole turn was divided into 60 units.\",\n \"Angle\\n\\n;Pechus (n = 144–180): –The pechus was a Babylonian unit equal to about 2° or °.\",\n \"Angle\\n\\n;Binary degree (n = 256): The binary degree, also known as the binary radian (or brad), is of a turn. The binary degree is used in computing so that an angle can be efficiently represented in a single byte (albeit to limited precision). Other measures of angle used in computing may be based on dividing one whole turn into 2n equal parts for other values of n.\",\n \"Angle\\n\\n;Degree (n 360): The degree, denoted by a small superscript circle (°), is 1/360 of a turn, so one turn is 360°. The case of degrees for the formula given earlier, a degree of n \\n 360° units is obtained by setting k = . One advantage of this old sexagesimal subunit is that many angles common in simple geometry are measured as a whole number of degrees. Fractions of a degree may be written in normal decimal notation (e.g. 3.5° for three and a half degrees), but the \\\"minute\\\" and \\\"second\\\" sexagesimal subunits of the \\\"degree-minute-second\\\" system are also in use, especially for geographical coordinates and in astronomy and ballistics:\",\n \"Angle\\n\\n;Diameter part (n = 376.99 . . . ): The diameter part (occasionally used in Islamic mathematics) is radian. One \\\"diameter part\\\" is approximately 0.95493°. There are about 376.991 diameter parts per turn.\",\n \"Angle\\n\\n;Grad (n = 400): The grad, also called grade, gradian, or gon, is of a turn, so a right angle is 100 grads. It is a decimal subunit of the quadrant. A kilometre was historically defined as a centi-grad of arc along a great circle of the Earth, so the kilometer is the decimal analog to the sexagesimal nautical mile. The grad is used mostly in triangulation.\",\n \"Angle\\n\\n;Mil (n 6000–6400): The mil is any of several units that are approximately equal to a milliradian. There are several definitions ranging from 0.05625 to 0.06 degrees (3.375 to 3.6 minutes), with the milliradian being approximately 0.05729578 degrees (3.43775 minutes). In NATO countries, it is defined as of a circle. Its value is approximately equal to the angle subtended by a width of 1 metre as seen from 1 km away ( \\n 0.0009817 . . . ≈ ).\",\n \"Angle\\n\\n;Minute of arc (n 21,600): The minute of arc (or MOA, arcminute, or just minute) is of a degree \\n turn. It is denoted by a single prime ( ′ ). For example, 3° 30′ is equal to 3 × 60 + 30 210 minutes or 3 + \\n 3.5 degrees. A mixed format with decimal fractions is also sometimes used, e.g. 3° 5.72′ = 3 + degrees. A nautical mile was historically defined as a minute of arc along a great circle of the Earth.\",\n \"Angle\\n\\n;Second of arc (n = 1,296,000): The second of arc (or arcsecond, or just second) is of a minute of arc and of a degree. It is denoted by a double prime ( ″ ). For example, 3° 7′ 30″ is equal to 3 + + degrees, or 3.125 degrees.\",\n \"Angle\\n\\nPositive and negative angles\",\n \"Angle\\n\\nAlthough the definition of the measurement of an angle does not support the concept of a negative angle, it is frequently useful to impose a convention that allows positive and negative angular values to represent orientations and/or rotations in opposite directions relative to some reference.\",\n \"Angle\\n\\nIn a two-dimensional Cartesian coordinate system, an angle is typically defined by its two sides, with its vertex at the origin. The initial side is on the positive x-axis, while the other side or terminal side is defined by the measure from the initial side in radians, degrees, or turns. With positive angles representing rotations toward the positive y-axis and negative angles representing rotations toward the negative y-axis. When Cartesian coordinates are represented by standard position, defined by the x-axis rightward and the y-axis upward, positive rotations are anticlockwise and negative rotations are clockwise.\",\n \"Angle\\n\\nIn many contexts, an angle of −θ is effectively equivalent to an angle of \\\"one full turn minus θ\\\". For example, an orientation represented as −45° is effectively equivalent to an orientation represented as 360° − 45° or 315°. However, a rotation of −45° would not be the same as a rotation of 315°.\",\n \"Angle\\n\\nIn three-dimensional geometry, \\\"clockwise\\\" and \\\"anticlockwise\\\" have no absolute meaning, so the direction of positive and negative angles must be defined relative to some reference, which is typically a vector passing through the angle's vertex and perpendicular to the plane in which the rays of the angle lie.\",\n \"Angle\\n\\nIn navigation, bearings are measured relative to north. By convention, viewed from above, bearing angle are positive clockwise, so a bearing of 45° corresponds to a north-east orientation. Negative bearings are not used in navigation, so a north-west orientation corresponds to a bearing of 315°.\",\n \"Angle\\n\\nAlternative ways of measuring the size of an angle\",\n \"Angle\\n\\nThere are several alternatives to measuring the size of an angle by the angle of rotation.\\nThe grade of a slope, or gradient is equal to the tangent of the angle, or sometimes (rarely) the sine. A gradient is often expressed as a percentage. For very small values (less than 5%), the grade of a slope is approximately the measure of the angle in radians.\",\n \"Angle\\n\\nIn rational geometry the spread between two lines is defined at the square of the sine of the angle between the lines. Since the sine of an angle and the sine of its supplementary angle are the same, any angle of rotation that maps one of the lines into the other leads to the same value for the spread between the lines.\",\n \"Angle\\n\\nAstronomical approximations\",\n \"Angle\\n\\nAstronomers measure angular separation of objects in degrees from their point of observation.\\n* 0.5° is approximately the width of the sun or moon.\\n* 1° is approximately the width of a little finger at arm's length.\\n* 10° is approximately the width of a closed fist at arm's length.\\n* 20° is approximately the width of a handspan at arm's length.\",\n \"Angle\\n\\nThese measurements clearly depend on the individual subject, and the above should be treated as rough rule of thumb approximations only.\",\n \"Angle\\n\\nAngles between curves\",\n \"Angle\\n\\nThe angle between a line and a curve (mixed angle) or between two intersecting curves (curvilinear angle) is defined to be the angle between the tangents at the point of intersection. Various names (now rarely, if ever, used) have been given to particular cases:—amphicyrtic (Gr. , on both sides, κυρτός, convex) or cissoidal (Gr. κισσός, ivy), biconvex; xystroidal or sistroidal (Gr. ξυστρίς, a tool for scraping), concavo-convex; amphicoelic (Gr. κοίλη, a hollow) or angulus lunularis, biconcave.\",\n \"Angle\\n\\nBisecting and trisecting angles\",\n \"Angle\\n\\nThe ancient Greek mathematicians knew how to bisect an angle (divide it into two angles of equal measure) using only a compass and straightedge, but could only trisect certain angles. In 1837 Pierre Wantzel showed that for most angles this construction cannot be performed.\",\n \"Angle\\n\\nDot product and generalisations\",\n \"Angle\\n\\nIn the Euclidean space, the angle θ between two Euclidean vectors u and v is related to their dot product and their lengths by the formula\",\n \"Angle\\n\\n\\\\mathbf{u} \\\\cdot \\\\mathbf{v} = \\\\cos(\\\\theta) \\\\left\\\\| \\\\mathbf{u} \\\\right\\\\| \\\\left\\\\| \\\\mathbf{v} \\\\right\\\\| .\",\n \"Angle\\n\\nThis formula supplies an easy method to find the angle between two planes (or curved surfaces) from their normal vectors and between skew lines from their vector equations.\",\n \"Angle\\n\\nInner product\",\n \"Angle\\n\\nTo define angles in an abstract real inner product space, we replace the Euclidean dot product ( · ) by the inner product \\\\langle \\\\cdot , \\\\cdot \\\\rangle , i.e.\",\n \"Angle\\n\\n\\\\langle \\\\mathbf{u} , \\\\mathbf{v} \\\\rangle = \\\\cos(\\\\theta)\\\\ \\\\left\\\\| \\\\mathbf{u} \\\\right\\\\|\\\\ \\\\left\\\\| \\\\mathbf{v} \\\\right\\\\| .\",\n \"Angle\\n\\nIn a complex inner product space, the expression for the cosine above may give non-real values, so it is replaced with\",\n \"Angle\\n\\n\\\\operatorname{Re} \\\\left( \\\\langle \\\\mathbf{u} , \\\\mathbf{v} \\\\rangle \\\\right) = \\\\cos(\\\\theta)\\\\ \\\\left\\\\| \\\\mathbf{u} \\\\right\\\\| \\\\ \\\\left\\\\| \\\\mathbf{v} \\\\right\\\\| .\",\n \"Angle\\n\\nor, more commonly, using the absolute value, with\",\n \"Angle\\n\\n\\\\left| \\\\langle \\\\mathbf{u} , \\\\mathbf{v} \\\\rangle \\\\right| = | \\\\cos(\\\\theta) | \\\\ \\\\left\\\\| \\\\mathbf{u} \\\\right\\\\| \\\\ \\\\left\\\\| \\\\mathbf{v} \\\\right\\\\| .\",\n \"Angle\\n\\nThe latter definition ignores the direction of the vectors and thus describes the angle between one-dimensional subspaces \\\\operatorname{span}(\\\\mathbf{u}) and \\\\operatorname{span}(\\\\mathbf{v}) spanned by the vectors \\\\mathbf{u} and \\\\mathbf{v} correspondingly.\",\n \"Angle\\n\\nAngles between subspaces\",\n \"Angle\\n\\nThe definition of the angle between one-dimensional subspaces \\\\operatorname{span}(\\\\mathbf{u}) and \\\\operatorname{span}(\\\\mathbf{v}) given by\",\n \"Angle\\n\\n\\\\left| \\\\langle \\\\mathbf{u} , \\\\mathbf{v} \\\\rangle \\\\right| = | \\\\cos(\\\\theta) | \\\\ \\\\left\\\\| \\\\mathbf{u} \\\\right\\\\| \\\\ \\\\left\\\\| \\\\mathbf{v} \\\\right\\\\|\",\n \"Angle\\n\\nin a Hilbert space can be extended to subspaces of any finite dimensions. Given two subspaces \\\\mathcal{U} , \\\\mathcal{W} with \\\\dim ( \\\\mathcal{U}) :k \\\\leq \\\\dim ( \\\\mathcal{W}) :\\n l , this leads to a definition of k angles called canonical or principal angles between subspaces.\",\n \"Angle\\n\\nAngles in Riemannian geometry\",\n \"Angle\\n\\nIn Riemannian geometry, the metric tensor is used to define the angle between two tangents. Where U and V are tangent vectors and gij are the components of the metric tensor G,\",\n \"Angle\\n\\n\\\\cos \\\\theta = \\\\frac{g_{ij}U^iV^j}\\n{\\\\sqrt{ \\\\left| g_{ij}U^iU^j \\\\right| \\\\left| g_{ij}V^iV^j \\\\right|}}.\",\n \"Angle\\n\\nAngles in geography and astronomy\",\n \"Angle\\n\\nIn geography, the location of any point on the Earth can be identified using a geographic coordinate system. This system specifies the latitude and longitude of any location in terms of angles subtended at the centre of the Earth, using the equator and (usually) the Greenwich meridian as references.\",\n \"Angle\\n\\nIn astronomy, a given point on the celestial sphere (that is, the apparent position of an astronomical object) can be identified using any of several astronomical coordinate systems, where the references vary according to the particular system. Astronomers measure the angular separation of two stars by imagining two lines through the centre of the Earth, each intersecting one of the stars. The angle between those lines can be measured, and is the angular separation between the two stars.\",\n \"Angle\\n\\nIn both geography and astronomy, a sighting direction can be specified in terms of a vertical angle such as altitude /elevation with respect to the horizon as well as the azimuth with respect to north.\",\n \"Angle\\n\\nAstronomers also measure the apparent size of objects as an angular diameter. For example, the full moon has an angular diameter of approximately 0.5°, when viewed from Earth. One could say, \\\"The Moon's diameter subtends an angle of half a degree.\\\" The small-angle formula can be used to convert such an angular measurement into a distance/size ratio.\"\n]","isConversational":false}}},{"rowIdx":1788,"cells":{"id":{"kind":"string","value":"tc_2761"},"question":{"kind":"string","value":"What is the name given to the longest side of a right-angled triangle?"},"answer":{"kind":"string","value":"Hypotenuse"},"answer_aliases":{"kind":"list like","value":["hypothenuse","hypotenuse","hypoteneuse","hypotenus"],"string":"[\n \"hypothenuse\",\n \"hypotenuse\",\n \"hypoteneuse\",\n \"hypotenus\"\n]","isConversational":false},"documents":{"kind":"list like","value":["Right triangle\n\nA right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry.","Right triangle\n\nThe side opposite the right angle is called the hypotenuse (side c in the figure). The sides adjacent to the right angle are called legs (or catheti, singular: cathetus). Side a may be identified as the side adjacent to angle B and opposed to (or opposite) angle A, while side b is the side adjacent to angle A and opposed to angle B.","Right triangle\n\nIf the lengths of all three sides of a right triangle are integers, the triangle is said to be a Pythagorean triangle and its side lengths are collectively known as a Pythagorean triple.","Right triangle\n\nPrincipal properties","Right triangle\n\nArea","Right triangle\n\nAs with any triangle, the area is equal to one half the base multiplied by the corresponding height. In a right triangle, if one leg is taken as the base then the other is height, so the area of a right triangle is one half the product of the two legs. As a formula the area T is\nT=\\tfrac{1}{2}ab","Right triangle\n\nwhere a and b are the legs of the triangle.","Right triangle\n\nIf the incircle is tangent to the hypotenuse AB at point P, then denoting the semi-perimeter as s, we have and , and the area is given by\nT\\text{PA} \\cdot \\text{PB} \n (s-a)(s-b).","Right triangle\n\nThis formula only applies to right triangles.","Right triangle\n\nAltitudes","Right triangle\n\nIf an altitude is drawn from the vertex with the right angle to the hypotenuse then the triangle is divided into two smaller triangles which are both similar to the original and therefore similar to each other. From this:\n* The altitude to the hypotenuse is the geometric mean (mean proportional) of the two segments of the hypotenuse.\n* Each leg of the triangle is the mean proportional of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.\nIn equations,\n\\displaystyle f^2=de, (this is sometimes known as the right triangle altitude theorem)\n\\displaystyle b^2=ce,\n\\displaystyle a^2=cd","Right triangle\n\nwhere a, b, c, d, e, f are as shown in the diagram. Thus\nf=\\frac{ab}{c}.","Right triangle\n\nMoreover, the altitude to the hypotenuse is related to the legs of the right triangle byVoles, Roger, \"Integer solutions of a^{-2} + b^{-2} = d^{-2},\" Mathematical Gazette 83, July 1999, 269–271. \n\\frac{1}{a^2} + \\frac{1}{b^2} = \\frac{1}{f^2}.","Right triangle\n\nFor solutions of this equation in integer values of a, b, f, and c, see here.","Right triangle\n\nThe altitude from either leg coincides with the other leg. Since these intersect at the right-angled vertex, the right triangle's orthocenter—the intersection of its three altitudes—coincides with the right-angled vertex.","Right triangle\n\nPythagorean theorem","Right triangle\n\nThe Pythagorean theorem states that:\nIn any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).","Right triangle\n\nThis can be stated in equation form as\n\\displaystyle a^2+b^2=c^2","Right triangle\n\nwhere c is the length of the hypotenuse, and a and b are the lengths of the remaining two sides.","Right triangle\n\nPythagorean triples are integer values of a, b, c satisfying this equation.","Right triangle\n\nInradius and circumradius","Right triangle\n\nThe radius of the incircle of a right triangle with legs a and b and hypotenuse c is\nr \\frac{a+b-c}{2} \n \\frac{ab}{a+b+c}.","Right triangle\n\nThe radius of the circumcircle is half the length of the hypotenuse,\nR = \\frac{c}{2}.","Right triangle\n\nThus the sum of the circumradius and the inradius is half the sum of the legs:Inequalities proposed in “Crux Mathematicorum”, [http://www.imomath.com/othercomp/Journ/ineq.pdf].","Right triangle\n\nR+r = \\frac{a+b}{2}.","Right triangle\n\nOne of the legs can be expressed in terms of the inradius and the other leg as\n\\displaystyle a=\\frac{2r(b-r)}{b-2r}.","Right triangle\n\nCharacterizations","Right triangle\n\nA triangle ABC with sides a \\le b , semiperimeter s, area T, altitude h opposite the longest side, circumradius R, inradius r, exradii ra, rb, rc (tangent to a, b, c respectively), and medians ma, mb, mc is a right triangle if and only if any one of the statements in the following six categories is true. All of them are of course also properties of a right triangle, since characterizations are equivalences.","Right triangle\n\nSides and semiperimeter","Right triangle\n\n* \\displaystyle a^2+b^2=c^2\\quad (\\text{Pythagorean theorem})\n* \\displaystyle (s-a)(s-b)=s(s-c)\n* \\displaystyle s=2R+r. \n* \\displaystyle a^2+b^2+c^28R^2.","Right triangle\n\nAngles","Right triangle\n\n* A and B are complementary. \n* \\displaystyle \\cos{A}\\cos{B}\\cos{C}0.CTK Wiki Math, A Variant of the Pythagorean Theorem, 2011, [http://www.cut-the-knot.org/wiki-math/index.php?n\nTrigonometry.AVariantOfPythagoreanTheorem].\n* \\displaystyle \\sin^2{A}+\\sin^2{B}+\\sin^2{C}2.\n* \\displaystyle \\cos^2{A}+\\cos^2{B}+\\cos^2{C}1.\n* \\displaystyle \\sin{2A}\\sin{2B}\n2\\sin{A}\\sin{B}.","Right triangle\n\nArea","Right triangle\n\n* \\displaystyle T=\\frac{ab}{2}\n* \\displaystyle Tr_ar_b\nrr_c\n* \\displaystyle T=r(2R+r)\n* T=PA\\cdot PB, where P is the tangency point of the incircle at the longest side AB.","Right triangle\n\nInradius and exradii* \\displaystyle r\ns-c=(a+b-c)/2\n* \\displaystyle r_as-b\n(a-b+c)/2\n* \\displaystyle r_bs-a\n(-a+b+c)/2\n* \\displaystyle r_cs\n(a+b+c)/2\n* \\displaystyle r_a+r_b+r_c+r=a+b+c\n* \\displaystyle r_a^2+r_b^2+r_c^2+r^2=a^2+b^2+c^2\n* \\displaystyle r=\\frac{r_ar_b}{r_c}","Right triangle\n\nAltitude and medians","Right triangle\n\n* \\displaystyle h=\\frac{ab}{c}\n* \\displaystyle m_a^2+m_b^2+m_c^26R^2.\n* The length of one median is equal to the circumradius.\n* The shortest altitude (the one from the vertex with the biggest angle) is the geometric mean of the line segments it divides the opposite (longest) side into. This is the right triangle altitude theorem.","Right triangle\n\nCircumcircle and incircle","Right triangle\n\n* The triangle can be inscribed in a semicircle, with one side coinciding with the entirety of the diameter (Thales' theorem).\n* The circumcenter is the midpoint of the longest side.\n* The longest side is a diameter of the circumcircle \\displaystyle (c=2R).\n* The circumcircle is tangent to the nine-point circle.Andreescu, Titu and Andrica, Dorian, \"Complex Numbers from A to...Z\", Birkhäuser, 2006, pp. 109-110.\n* The orthocenter lies on the circumcircle.\n* The distance between the incenter and the orthocenter is equal to \\sqrt{2}r.","Right triangle\n\nTrigonometric ratios","Right triangle\n\nThe trigonometric functions for acute angles can be defined as ratios of the sides of a right triangle. For a given angle, a right triangle may be constructed with this angle, and the sides labeled opposite, adjacent and hypotenuse with reference to this angle according to the definitions above. These ratios of the sides do not depend on the particular right triangle chosen, but only on the given angle, since all triangles constructed this way are similar. If, for a given angle α, the opposite side, adjacent side and hypotenuse are labeled O, A and H respectively, then the trigonometric functions are\n\\sin\\alpha \\frac {O}{H},\\,\\cos\\alpha \n\\frac {A}{H},\\,\\tan\\alpha \\frac {O}{A},\\,\\sec\\alpha \n\\frac {H}{A},\\,\\cot\\alpha \\frac {A}{O},\\,\\csc\\alpha \n\\frac {H}{O}.","Right triangle\n\nFor the expression of hyperbolic functions as ratio of the sides of a right triangle, see the hyperbolic triangle of a hyperbolic sector.","Right triangle\n\nSpecial right triangles","Right triangle\n\nThe values of the trigonometric functions can be evaluated exactly for certain angles using right triangles with special angles. These include the 30-60-90 triangle which can be used to evaluate the trigonometric functions for any multiple of π/6, and the 45-45-90 triangle which can be used to evaluate the trigonometric functions for any multiple of π/4.","Right triangle\n\nKepler triangle","Right triangle\n\nLet H, G, and A be the harmonic mean, the geometric mean, and the arithmetic mean of two positive numbers a and b with a > b. If a right triangle has legs H and G and hypotenuse A, then \n\\frac{A}{H} \\frac{A^{2}}{G^{2}} \n \\frac{G^{2}}{H^{2}} = \\phi \\,","Right triangle\n\nand\n\\frac{a}{b} = \\phi^{3}, \\,","Right triangle\n\nwhere \\phi is the golden ratio \\tfrac{1+ \\sqrt{5}}{2}. \\, Since the sides of this right triangle are in geometric progression, this is the Kepler triangle.","Right triangle\n\nThales' theorem","Right triangle\n\nThales' theorem states that if A is any point of the circle with diameter BC (except B or C themselves) ABC is a right triangle where A is the right angle. The converse states that if a right triangle is inscribed in a circle then the hypotenuse will be a diameter of the circle. A corollary is that the length of the hypotenuse is twice the distance from the right angle vertex to the midpoint of the hypotenuse. Also, the center of the circle that circumscribes a right triangle is the midpoint of the hypotenuse and its radius is one half the length of the hypotenuse.","Right triangle\n\nMedians","Right triangle\n\nThe following formulas hold for the medians of a right triangle:\nm_a^2 + m_b^2 5m_c^2 \n \\frac{5}{4}c^2.","Right triangle\n\nThe median on the hypotenuse of a right triangle divides the triangle into two isosceles triangles, because the median equals one-half the hypotenuse.","Right triangle\n\nThe medians ma and mb from the legs satisfy","Right triangle\n\n4c^4+9a^2b^2=16m_a^2m_b^2.","Right triangle\n\nEuler line","Right triangle\n\nIn a right triangle, the Euler line contains the median on the hypotenuse—that is, it goes through both the right-angled vertex and the midpoint of the side opposite that vertex. This is because the right triangle's orthocenter, the intersection of its altitudes, falls on the right-angled vertex while its circumcenter, the intersection of its perpendicular bisectors of sides, falls on the midpoint of the hypotenuse.","Right triangle\n\nInequalities","Right triangle\n\nIn any right triangle the diameter of the incircle is less than half the hypotenuse, and more strongly it is less than or equal to the hypotenuse times (\\sqrt{2}-1).Posamentier, Alfred S., and Lehmann, Ingmar. The Secrets of Triangles. Prometheus Books, 2012.","Right triangle\n\nIn a right triangle with legs a, b and hypotenuse c,","Right triangle\n\nc \\geq \\frac{\\sqrt{2}}{2}(a+b)","Right triangle\n\nwith equality only in the isosceles case.","Right triangle\n\nIf the altitude from the hypotenuse is denoted hc, then","Right triangle\n\nh_c \\leq \\frac{\\sqrt {2}}{4}(a+b)","Right triangle\n\nwith equality only in the isosceles case.","Right triangle\n\nOther properties","Right triangle\n\nIf segments of lengths p and q emanating from vertex C trisect the hypotenuse into segments of length c/3, thenPosamentier, Alfred S., and Salkind, Charles T. Challenging Problems in Geometry, Dover, 1996.\np^2 + q^2 = 5\\left(\\frac{c}{3}\\right)^2.","Right triangle\n\nThe right triangle is the only triangle having two, rather than one or three, distinct inscribed squares.","Right triangle\n\nLet h and k (h > k) be the sides of the two inscribed squares in a right triangle with hypotenuse c. Then\n\\frac{1}{c^2} + \\frac{1}{h^2} = \\frac{1}{k^2}.","Right triangle\n\nThese sides and the incircle radius r are related by a similar formula:","Right triangle\n\n\\displaystyle \\frac{1}{r}=-{\\frac{1}{c}}+\\frac{1}{h}+\\frac{1}{k}.","Right triangle\n\nThe perimeter of a right triangle equals the sum of the radii of the incircle and the three excircles:","Right triangle\n\na+b+c=r+r_a+r_b+r_c.","Triangle\n\nA triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \\triangle ABC.","Triangle\n\nIn Euclidean geometry any three points, when non-collinear, determine a unique triangle and a unique plane (i.e. a two-dimensional Euclidean space). This article is about triangles in Euclidean geometry except where otherwise noted.","Triangle\n\nTypes of triangle","Triangle\n\nBy lengths of sides","Triangle\n\nTriangles can be classified according to the lengths of their sides:\n*An equilateral triangle has all sides the same length. An equilateral triangle is also a regular polygon with all angles measuring 60°. *An isosceles triangle has two sides of equal length.Euclid defines isosceles triangles based on the number of equal sides, i.e. only two equal sides. An alternative approach defines isosceles triangles based on shared properties, i.e. equilateral triangles are a special case of isosceles triangles. An isosceles triangle also has two angles of the same measure; namely, the angles opposite to the two sides of the same length; this fact is the content of the isosceles triangle theorem, which was known by Euclid. Some mathematicians define an isosceles triangle to have exactly two equal sides, whereas others define an isosceles triangle as one with at least two equal sides. The latter definition would make all equilateral triangles isosceles triangles. The 45–45–90 right triangle, which appears in the tetrakis square tiling, is isosceles. *A scalene triangle has all its sides of different lengths. Equivalently, it has all angles of different measure. A right triangle is also a scalene triangle if and only if it is not isosceles.","Triangle\n\nHatch marks, also called tick marks, are used in diagrams of triangles and other geometric figures to identify sides of equal lengths. A side can be marked with a pattern of \"ticks\", short line segments in the form of tally marks; two sides have equal lengths if they are both marked with the same pattern. In a triangle, the pattern is usually no more than 3 ticks. An equilateral triangle has the same pattern on all 3 sides, an isosceles triangle has the same pattern on just 2 sides, and a scalene triangle has different patterns on all sides since no sides are equal. Similarly, patterns of 1, 2, or 3 concentric arcs inside the angles are used to indicate equal angles. An equilateral triangle has the same pattern on all 3 angles, an isosceles triangle has the same pattern on just 2 angles, and a scalene triangle has different patterns on all angles since no angles are equal.","Triangle\n\nBy internal angles","Triangle\n\nTriangles can also be classified according to their internal angles, measured here in degrees. *A right triangle (or right-angled triangle, formerly called a rectangled triangle) has one of its interior angles measuring 90° (a right angle). The side opposite to the right angle is the hypotenuse, the longest side of the triangle. The other two sides are called the legs or catheti (singular: cathetus) of the triangle. Right triangles obey the Pythagorean theorem: the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse: , where a and b are the lengths of the legs and c is the length of the hypotenuse. Special right triangles are right triangles with additional properties that make calculations involving them easier. One of the two most famous is the 3–4–5 right triangle, where . In this situation, 3, 4, and 5 are a Pythagorean triple. The other one is an isosceles triangle that has 2 angles that each measure 45 degrees. *Triangles that do not have an angle measuring 90° are called oblique triangles. *A triangle with all interior angles measuring less than 90° is an acute triangle or acute-angled triangle.","Triangle\n\nIf c is the length of the longest side, then , where a and b are the lengths of the other sides. *A triangle with one interior angle measuring more than 90° is an obtuse triangle or obtuse-angled triangle. If c is the length of the longest side, then , where a and b are the lengths of the other sides. *A triangle with an interior angle of 180° (and collinear vertices) is degenerate. *A right degenerate triangle has collinear vertices, two of which are coincident.","Triangle\n\nA triangle that has two angles with the same measure also has two sides with the same length, and therefore it is an isosceles triangle. It follows that in a triangle where all angles have the same measure, all three sides have the same length, and such a triangle is therefore equilateral.","Triangle\n\nBasic facts","Triangle\n\nTriangles are assumed to be two-dimensional plane figures, unless the context provides otherwise (see Non-planar triangles, below). In rigorous treatments, a triangle is therefore called a 2-simplex (see also Polytope). Elementary facts about triangles were presented by Euclid in books 1–4 of his Elements, around 300 BC.","Triangle\n\nThe sum of the measures of the interior angles of a triangle in Euclidean space is always 180 degrees. This fact is equivalent to Euclid's parallel postulate. This allows determination of the measure of the third angle of any triangle given the measure of two angles. An exterior angle of a triangle is an angle that is a linear pair (and hence supplementary) to an interior angle. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it; this is the exterior angle theorem. The sum of the measures of the three exterior angles (one for each vertex) of any triangle is 360 degrees.The n external angles of any n-sided convex polygon add up to 360 degrees.","Triangle\n\nSimilarity and congruence","Triangle\n\nTwo triangles are said to be similar if every angle of one triangle has the same measure as the corresponding angle in the other triangle. The corresponding sides of similar triangles have lengths that are in the same proportion, and this property is also sufficient to establish similarity.","Triangle\n\nSome basic theorems about similar triangles are:\n*If and only if one pair of internal angles of two triangles have the same measure as each other, and another pair also have the same measure as each other, the triangles are similar.\n*If and only if one pair of corresponding sides of two triangles are in the same proportion as are another pair of corresponding sides, and their included angles have the same measure, then the triangles are similar. (The included angle for any two sides of a polygon is the internal angle between those two sides.)\n*If and only if three pairs of corresponding sides of two triangles are all in the same proportion, then the triangles are similar.Again, in all cases \"mirror images\" are also similar.","Triangle\n\nTwo triangles that are congruent have exactly the same size and shape:All pairs of congruent triangles are also similar; but not all pairs of similar triangles are congruent. all pairs of corresponding interior angles are equal in measure, and all pairs of corresponding sides have the same length. (This is a total of six equalities, but three are often sufficient to prove congruence.)","Triangle\n\nSome individually necessary and sufficient conditions for a pair of triangles to be congruent are:\n*SAS Postulate: Two sides in a triangle have the same length as two sides in the other triangle, and the included angles have the same measure.\n*ASA: Two interior angles and the included side in a triangle have the same measure and length, respectively, as those in the other triangle. (The included side for a pair of angles is the side that is common to them.)\n*SSS: Each side of a triangle has the same length as a corresponding side of the other triangle.\n*AAS: Two angles and a corresponding (non-included) side in a triangle have the same measure and length, respectively, as those in the other triangle. (This is sometimes referred to as AAcorrS and then includes ASA above.)","Triangle\n\nSome individually sufficient conditions are:","Triangle\n\n*Hypotenuse-Leg (HL) Theorem: The hypotenuse and a leg in a right triangle have the same length as those in another right triangle. This is also called RHS (right-angle, hypotenuse, side).\n*Hypotenuse-Angle Theorem: The hypotenuse and an acute angle in one right triangle have the same length and measure, respectively, as those in the other right triangle. This is just a particular case of the AAS theorem.\nAn important condition is:\n*Side-Side-Angle (or Angle-Side-Side) condition: If two sides and a corresponding non-included angle of a triangle have the same length and measure, respectively, as those in another triangle, then this is not sufficient to prove congruence; but if the angle given is opposite to the longer side of the two sides, then the triangles are congruent. The Hypotenuse-Leg Theorem is a particular case of this criterion. The Side-Side-Angle condition does not by itself guarantee that the triangles are congruent because one triangle could be obtuse-angled and the other acute-angled.","Triangle\n\nUsing right triangles and the concept of similarity, the trigonometric functions sine and cosine can be defined. These are functions of an angle which are investigated in trigonometry.","Triangle\n\nRight triangles","Triangle\n\nA central theorem is the Pythagorean theorem, which states in any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the two other sides. If the hypotenuse has length c, and the legs have lengths a and b, then the theorem states that\na^2 + b^2 = c^2.\\,","Triangle\n\nThe converse is true: if the lengths of the sides of a triangle satisfy the above equation, then the triangle has a right angle opposite side c.","Triangle\n\nSome other facts about right triangles:\n*The acute angles of a right triangle are complementary.\na + b + 90^{\\circ} 180^{\\circ} \\Rightarrow a + b \n 90^{\\circ} \\Rightarrow a = 90^{\\circ} - b\n*If the legs of a right triangle have the same length, then the angles opposite those legs have the same measure. Since these angles are complementary, it follows that each measures 45 degrees. By the Pythagorean theorem, the length of the hypotenuse is the length of a leg times √2.\n*In a right triangle with acute angles measuring 30 and 60 degrees, the hypotenuse is twice the length of the shorter side, and the longer side is equal to the length of the shorter side times √3:\n:c = 2a\\,\n:b = a\\times\\sqrt{3}.","Triangle\n\nFor all triangles, angles and sides are related by the law of cosines and law of sines (also called the cosine rule and sine rule).","Triangle\n\nExistence of a triangle","Triangle\n\nCondition on the sides","Triangle\n\nThe triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. That sum can equal the length of the third side only in the case of a degenerate triangle, one with collinear vertices. It is not possible for that sum to be less than the length of the third side. A triangle with three given positive side lengths exists if and only if those side lengths satisfy the triangle inequality.","Triangle\n\nConditions on the angles","Triangle\n\nThree given angles form a non-degenerate triangle (and indeed an infinitude of them) if and only if both of these conditions hold: (a) each of the angles is positive, and (b) the angles sum to 180°. If degenerate triangles are permitted, angles of 0° are permitted.","Triangle\n\nTrigonometric conditions","Triangle\n\nThree positive angles α, β, and γ, each of them less than 180°, are the angles of a triangle if and only if any one of the following conditions holds:\n\\tan{\\frac{\\alpha}{2}}\\tan{\\frac{\\beta}{2}}+\\tan{\\frac{\\beta}{2}}\\tan{\\frac{\\gamma}{2}}+\\tan{\\frac{\\gamma}{2}}\\tan{\\frac{\\alpha}{2}}1,Vardan Verdiyan & Daniel Campos Salas, \"Simple trigonometric substitutions with broad results\", Mathematical Reflections no 6, 2007.","Triangle\n\n\\sin^2{\\frac{\\alpha}{2}}+\\sin^2{\\frac{\\beta}{2}}+\\sin^2{\\frac{\\gamma}{2}}+2\\sin{\\frac{\\alpha}{2}}\\sin{\\frac{\\beta}{2}}\\sin{\\frac{\\gamma}{2}}1,","Triangle\n\n\\sin(2\\alpha) + \\sin(2\\beta) + \\sin(2\\gamma) = 4\\sin(\\alpha)\\sin(\\beta)\\sin(\\gamma),","Triangle\n\n\\cos^2\\alpha+\\cos^2\\beta+\\cos^2\\gamma+2\\cos(\\alpha)\\cos(\\beta)\\cos(\\gamma)1,","Triangle\n\n\\tan(\\alpha) + \\tan(\\beta) + \\tan(\\gamma) = \\tan(\\alpha)\\tan(\\beta)\\tan(\\gamma),","Triangle\n\nthe latter equality applying only if none of the angles is 90° (so the tangent function's value is always finite).","Triangle\n\nPoints, lines, and circles associated with a triangle","Triangle\n\nThere are thousands of different constructions that find a special point associated with (and often inside) a triangle, satisfying some unique property: see the article Encyclopedia of Triangle Centers for a catalogue of them. Often they are constructed by finding three lines associated in a symmetrical way with the three sides (or vertices) and then proving that the three lines meet in a single point: an important tool for proving the existence of these is Ceva's theorem, which gives a criterion for determining when three such lines are concurrent. Similarly, lines associated with a triangle are often constructed by proving that three symmetrically constructed points are collinear: here Menelaus' theorem gives a useful general criterion. In this section just a few of the most commonly encountered constructions are explained.","Triangle\n\nA perpendicular bisector of a side of a triangle is a straight line passing through the midpoint of the side and being perpendicular to it, i.e. forming a right angle with it. The three perpendicular bisectors meet in a single point, the triangle's circumcenter, usually denoted by O; this point is the center of the circumcircle, the circle passing through all three vertices. The diameter of this circle, called the circumdiameter, can be found from the law of sines stated above. The circumcircle's radius is called the circumradius.","Triangle\n\nThales' theorem implies that if the circumcenter is located on one side of the triangle, then the opposite angle is a right one. If the circumcenter is located inside the triangle, then the triangle is acute; if the circumcenter is located outside the triangle, then the triangle is obtuse.","Triangle\n\nAn altitude of a triangle is a straight line through a vertex and perpendicular to (i.e. forming a right angle with) the opposite side. This opposite side is called the base of the altitude, and the point where the altitude intersects the base (or its extension) is called the foot of the altitude. The length of the altitude is the distance between the base and the vertex. The three altitudes intersect in a single point, called the orthocenter of the triangle, usually denoted by H. The orthocenter lies inside the triangle if and only if the triangle is acute.","Triangle\n\nAn angle bisector of a triangle is a straight line through a vertex which cuts the corresponding angle in half. The three angle bisectors intersect in a single point, the incenter, usually denoted by I, the center of the triangle's incircle. The incircle is the circle which lies inside the triangle and touches all three sides. Its radius is called the inradius. There are three other important circles, the excircles; they lie outside the triangle and touch one side as well as the extensions of the other two. The centers of the in- and excircles form an orthocentric system.","Triangle\n\nA median of a triangle is a straight line through a vertex and the midpoint of the opposite side, and divides the triangle into two equal areas. The three medians intersect in a single point, the triangle's centroid or geometric barycenter, usually denoted by G. The centroid of a rigid triangular object (cut out of a thin sheet of uniform density) is also its center of mass: the object can be balanced on its centroid in a uniform gravitational field. The centroid cuts every median in the ratio 2:1, i.e. the distance between a vertex and the centroid is twice the distance between the centroid and the midpoint of the opposite side.","Triangle\n\nThe midpoints of the three sides and the feet of the three altitudes all lie on a single circle, the triangle's nine-point circle. The remaining three points for which it is named are the midpoints of the portion of altitude between the vertices and the orthocenter. The radius of the nine-point circle is half that of the circumcircle. It touches the incircle (at the Feuerbach point) and the three excircles.","Triangle\n\nThe centroid (yellow), orthocenter (blue), circumcenter (green) and center of the nine-point circle (red point) all lie on a single line, known as Euler's line (red line). The center of the nine-point circle lies at the midpoint between the orthocenter and the circumcenter, and the distance between the centroid and the circumcenter is half that between the centroid and the orthocenter.","Triangle\n\nThe center of the incircle is not in general located on Euler's line.","Triangle\n\nIf one reflects a median in the angle bisector that passes through the same vertex, one obtains a symmedian. The three symmedians intersect in a single point, the symmedian point of the triangle.","Triangle\n\nComputing the sides and angles","Triangle\n\nThere are various standard methods for calculating the length of a side or the measure of an angle. Certain methods are suited to calculating values in a right-angled triangle; more complex methods may be required in other situations.","Triangle\n\nTrigonometric ratios in right triangles","Triangle\n\nIn right triangles, the trigonometric ratios of sine, cosine and tangent can be used to find unknown angles and the lengths of unknown sides. The sides of the triangle are known as follows:\n*The hypotenuse is the side opposite the right angle, or defined as the longest side of a right-angled triangle, in this case h.\n*The opposite side is the side opposite to the angle we are interested in, in this case a.\n*The adjacent side is the side that is in contact with the angle we are interested in and the right angle, hence its name. In this case the adjacent side is b.","Triangle\n\nSine, cosine and tangent","Triangle\n\nThe sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. In our case\n\\sin A \\frac {\\text{opposite side}}{\\text{hypotenuse}} \n \\frac {a}{h}\\,.","Triangle\n\nNote that this ratio does not depend on the particular right triangle chosen, as long as it contains the angle A, since all those triangles are similar.","Triangle\n\nThe cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. In our case\n\\cos A \\frac {\\text{adjacent side}}{\\text{hypotenuse}} \n \\frac {b}{h}\\,.","Triangle\n\nThe tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. In our case\n\\tan A \\frac {\\text{opposite side}}{\\text{adjacent side}} \n \\frac {a}{b} =\\frac {\\sin A}{\\cos A}\\,.","Triangle\n\nThe acronym \"SOH-CAH-TOA\" is a useful mnemonic for these ratios.","Triangle\n\nInverse functions","Triangle\n\nThe inverse trigonometric functions can be used to calculate the internal angles for a right angled triangle with the length of any two sides.","Triangle\n\nArcsin can be used to calculate an angle from the length of the opposite side and the length of the hypotenuse.\n\\theta = \\arcsin \\left( \\frac{\\text{opposite side}}{\\text{hypotenuse}} \\right)","Triangle\n\nArccos can be used to calculate an angle from the length of the adjacent side and the length of the hypotenuse.\n\\theta = \\arccos \\left( \\frac{\\text{adjacent side}}{\\text{hypotenuse}} \\right)","Triangle\n\nArctan can be used to calculate an angle from the length of the opposite side and the length of the adjacent side.\n\\theta = \\arctan \\left( \\frac{\\text{opposite side}}{\\text{adjacent side}} \\right)","Triangle\n\nIn introductory geometry and trigonometry courses, the notation sin−1, cos−1, etc., are often used in place of arcsin, arccos, etc. However, the arcsin, arccos, etc., notation is standard in higher mathematics where trigonometric functions are commonly raised to powers, as this avoids confusion between multiplicative inverse and compositional inverse.","Triangle\n\nSine, cosine and tangent rules","Triangle\n\nThe law of sines, or sine rule, states that the ratio of the length of a side to the sine of its corresponding opposite angle is constant, that is\n\\frac{a}{\\sin \\alpha} \\frac{b}{\\sin \\beta} \n \\frac{c}{\\sin \\gamma}.","Triangle\n\nThis ratio is equal to the diameter of the circumscribed circle of the given triangle. Another interpretation of this theorem is that every triangle with angles α, β and γ is similar to a triangle with side lengths equal to sin α, sin β and sin γ. This triangle can be constructed by first constructing a circle of diameter 1, and inscribing in it two of the angles of the triangle. The length of the sides of that triangle will be sin α, sin β and sin γ. The side whose length is sin α is opposite to the angle whose measure is α, etc.","Triangle\n\nThe law of cosines, or cosine rule, connects the length of an unknown side of a triangle to the length of the other sides and the angle opposite to the unknown side. As per the law:","Triangle\n\nFor a triangle with length of sides a, b, c and angles of α, β, γ respectively, given two known lengths of a triangle a and b, and the angle between the two known sides γ (or the angle opposite to the unknown side c), to calculate the third side c, the following formula can be used:\nc^2\\ = a^2 + b^2 - 2ab\\cos(\\gamma)\nb^2\\ = a^2 + c^2 - 2ac\\cos(\\beta)\na^2\\ = b^2 + c^2 - 2bc\\cos(\\alpha)","Triangle\n\nIf the lengths of all three sides of any triangle are known the three angles can be calculated:\n\\alpha=\\arccos\\left(\\frac{b^2+c^2-a^2}{2bc}\\right)\n\\beta=\\arccos\\left(\\frac{a^2+c^2-b^2}{2ac}\\right)\n\\gamma=\\arccos\\left(\\frac{a^2+b^2-c^2}{2ab}\\right)","Triangle\n\nThe law of tangents or tangent rule, can be used to find a side or an angle when you know two sides and an angle or two angles and a side. It states that: \n\\frac{a-b}{a+b} = \\frac{\\tan[\\frac{1}{2}(\\alpha-\\beta)]}{\\tan[\\frac{1}{2}(\\alpha+\\beta)]}.","Triangle\n\nSolution of triangles","Triangle\n\n\"Solution of triangles\" is the main trigonometric problem: to find missing characteristics of a triangle (three angles, the lengths of the three sides etc.) when at least three of these characteristics are given. The triangle can be located on a plane or on a sphere. This problem often occurs in various trigonometric applications, such as geodesy, astronomy, construction, navigation etc.","Triangle\n\nComputing the area of a triangle","Triangle\n\nCalculating the area T of a triangle is an elementary problem encountered often in many different situations. The best known and simplest formula is:\nT=\\frac{1}{2}bh\nwhere b is the length of the base of the triangle, and h is the height or altitude of the triangle. The term \"base\" denotes any side, and \"height\" denotes the length of a perpendicular from the vertex opposite the side onto the line containing the side itself. In 499 CE Aryabhata, a great mathematician-astronomer from the classical age of Indian mathematics and Indian astronomy, used this method in the Aryabhatiya (section 2.6).","Triangle\n\nAlthough simple, this formula is only useful if the height can be readily found, which is not always the case. For example, the surveyor of a triangular field might find it relatively easy to measure the length of each side, but relatively difficult to construct a 'height'. Various methods may be used in practice, depending on what is known about the triangle. The following is a selection of frequently used formulae for the area of a triangle.","Triangle\n\nUsing trigonometry","Triangle\n\nThe height of a triangle can be found through the application of trigonometry.","Triangle\n\nKnowing SAS: Using the labels in the image on the right, the altitude is . Substituting this in the formula T=\\frac{1}{2}bh derived above, the area of the triangle can be expressed as:\nT \\frac{1}{2}ab\\sin \\gamma \n \\frac{1}{2}bc\\sin \\alpha = \\frac{1}{2}ca\\sin \\beta","Triangle\n\n(where α is the interior angle at A, β is the interior angle at B, \\gamma is the interior angle at C and c is the line AB).","Triangle\n\nFurthermore, since sin α sin (π − α) \n sin (β + \\gamma), and similarly for the other two angles:\nT \\frac{1}{2}ab\\sin (\\alpha+\\beta) \n \\frac{1}{2}bc\\sin (\\beta+\\gamma) = \\frac{1}{2}ca\\sin (\\gamma+\\alpha).","Triangle\n\nKnowing AAS:\nT = \\frac {b^{2}(\\sin \\alpha)(\\sin (\\alpha + \\beta))}{2\\sin \\beta},","Triangle\n\nand analogously if the known side is a or c.","Triangle\n\nKnowing ASA: \nT \\frac{a^{2}}{2(\\cot \\beta + \\cot \\gamma)} \n \\frac{a^{2} (\\sin \\beta)(\\sin \\gamma)}{2\\sin(\\beta + \\gamma)},","Triangle\n\nand analogously if the known side is b or c.","Triangle\n\nUsing Heron's formula","Triangle\n\nThe shape of the triangle is determined by the lengths of the sides. Therefore, the area can also be derived from the lengths of the sides. By Heron's formula:\nT = \\sqrt{s(s-a)(s-b)(s-c)}","Triangle\n\nwhere s= \\tfrac{a+b+c}{2} is the semiperimeter, or half of the triangle's perimeter.","Triangle\n\nThree other equivalent ways of writing Heron's formula are\nT = \\frac{1}{4} \\sqrt{(a^2+b^2+c^2)^2-2(a^4+b^4+c^4)}\nT = \\frac{1}{4} \\sqrt{2(a^2b^2+a^2c^2+b^2c^2)-(a^4+b^4+c^4)}\nT = \\frac{1}{4} \\sqrt{(a+b-c) (a-b+c) (-a+b+c) (a+b+c)}.","Triangle\n\nUsing vectors","Triangle\n\nThe area of a parallelogram embedded in a three-dimensional Euclidean space can be calculated using vectors. Let vectors AB and AC point respectively from A to B and from A to C. The area of parallelogram ABDC is then\n|\\mathbf{AB}\\times\\mathbf{AC}|,","Triangle\n\nwhich is the magnitude of the cross product of vectors AB and AC. The area of triangle ABC is half of this,\n\\frac{1}{2}|\\mathbf{AB}\\times\\mathbf{AC}|.","Triangle\n\nThe area of triangle ABC can also be expressed in terms of dot products as follows:\n\\frac{1}{2} \\sqrt{(\\mathbf{AB} \\cdot \\mathbf{AB})(\\mathbf{AC} \\cdot \\mathbf{AC}) -(\\mathbf{AB} \\cdot \\mathbf{AC})^2} =\\frac{1}{2} \\sqrt{ |\\mathbf{AB}|^2 |\\mathbf{AC}|^2 -(\\mathbf{AB} \\cdot \\mathbf{AC})^2}.\\,","Triangle\n\nIn two-dimensional Euclidean space, expressing vector AB as a free vector in Cartesian space equal to (x1,y1) and AC as (x2,y2), this can be rewritten as:\n\\frac{1}{2}\\,|x_1 y_2 - x_2 y_1|.\\,","Triangle\n\nUsing coordinates","Triangle\n\nIf vertex A is located at the origin (0, 0) of a Cartesian coordinate system and the coordinates of the other two vertices are given by and , then the area can be computed as times the absolute value of the determinant\nT \\frac{1}{2}\\left|\\det\\begin{pmatrix}x_B & x_C \\\\ y_B & y_C \\end{pmatrix}\\right| \n \\frac{1}{2}|x_B y_C - x_C y_B|.","Triangle\n\nFor three general vertices, the equation is:\nT \\frac{1}{2} \\left| \\det\\begin{pmatrix}x_A & x_B & x_C \\\\ y_A & y_B & y_C \\\\ 1 & 1 & 1\\end{pmatrix} \\right| \n \\frac{1}{2} \\big| x_A y_B - x_A y_C + x_B y_C - x_B y_A + x_C y_A - x_C y_B \\big|,","Triangle\n\nwhich can be written as\nT = \\frac{1}{2} \\big| (x_A - x_C) (y_B - y_A) - (x_A - x_B) (y_C - y_A) \\big|.","Triangle\n\nIf the points are labeled sequentially in the counterclockwise direction, the above determinant expressions are positive and the absolute value signs can be omitted. The above formula is known as the shoelace formula or the surveyor's formula.","Triangle\n\nIf we locate the vertices in the complex plane and denote them in counterclockwise sequence as , , and , and denote their complex conjugates as \\bar a, \\bar b, and \\bar c, then the formula\nT=\\frac{i}{4}\\begin{vmatrix}a & \\bar a & 1 \\\\ b & \\bar b & 1 \\\\ c & \\bar c & 1 \\end{vmatrix}","Triangle\n\nis equivalent to the shoelace formula.","Triangle\n\nIn three dimensions, the area of a general triangle , and ) is the Pythagorean sum of the areas of the respective projections on the three principal planes (i.e. x 0, y \n 0 and z = 0):\nT = \\frac{1}{2} \\sqrt{\\begin{vmatrix} x_A & x_B & x_C \\\\ y_A & y_B & y_C \\\\ 1 & 1 & 1 \\end{vmatrix}^2 +\n\\begin{vmatrix} y_A & y_B & y_C \\\\ z_A & z_B & z_C \\\\ 1 & 1 & 1 \\end{vmatrix}^2 +\n\\begin{vmatrix} z_A & z_B & z_C \\\\ x_A & x_B & x_C \\\\ 1 & 1 & 1 \\end{vmatrix}^2 }.","Triangle\n\nUsing line integrals","Triangle\n\nThe area within any closed curve, such as a triangle, is given by the line integral around the curve of the algebraic or signed distance of a point on the curve from an arbitrary oriented straight line L. Points to the right of L as oriented are taken to be at negative distance from L, while the weight for the integral is taken to be the component of arc length parallel to L rather than arc length itself.","Triangle\n\nThis method is well suited to computation of the area of an arbitrary polygon. Taking L to be the x-axis, the line integral between consecutive vertices (xi,yi) and (xi+1,yi+1) is given by the base times the mean height, namely . The sign of the area is an overall indicator of the direction of traversal, with negative area indicating counterclockwise traversal. The area of a triangle then falls out as the case of a polygon with three sides.","Triangle\n\nWhile the line integral method has in common with other coordinate-based methods the arbitrary choice of a coordinate system, unlike the others it makes no arbitrary choice of vertex of the triangle as origin or of side as base. Furthermore, the choice of coordinate system defined by L commits to only two degrees of freedom rather than the usual three, since the weight is a local distance (e.g. in the above) whence the method does not require choosing an axis normal to L.","Triangle\n\nWhen working in polar coordinates it is not necessary to convert to Cartesian coordinates to use line integration, since the line integral between consecutive vertices (ri,θi) and (ri+1,θi+1) of a polygon is given directly by . This is valid for all values of θ, with some decrease in numerical accuracy when |θ| is many orders of magnitude greater than π. With this formulation negative area indicates clockwise traversal, which should be kept in mind when mixing polar and cartesian coordinates. Just as the choice of y-axis () is immaterial for line integration in cartesian coordinates, so is the choice of zero heading () immaterial here.","Triangle\n\nFormulas resembling Heron's formula","Triangle\n\nThree formulas have the same structure as Heron's formula but are expressed in terms of different variables. First, denoting the medians from sides a, b, and c respectively as ma, mb, and mc and their semi-sum as σ, we have \nT = \\frac{4}{3} \\sqrt{\\sigma (\\sigma - m_a)(\\sigma - m_b)(\\sigma - m_c)}.","Triangle\n\nNext, denoting the altitudes from sides a, b, and c respectively as ha, hb, and hc, and denoting the semi-sum of the reciprocals of the altitudes as H = (h_a^{-1} + h_b^{-1} + h_c^{-1})/2 we have \nT^{-1} = 4 \\sqrt{H(H-h_a^{-1})(H-h_b^{-1})(H-h_c^{-1})}.","Triangle\n\nAnd denoting the semi-sum of the angles' sines as , we have \nT = D^{2} \\sqrt{S(S-\\sin \\alpha)(S-\\sin \\beta)(S-\\sin \\gamma)}","Triangle\n\nwhere D is the diameter of the circumcircle: D\\tfrac{a}{\\sin \\alpha} \n \\tfrac{b}{\\sin \\beta} = \\tfrac{c}{\\sin \\gamma}.","Triangle\n\nUsing Pick's theorem","Triangle\n\nSee Pick's theorem for a technique for finding the area of any arbitrary lattice polygon (one drawn on a grid with vertically and horizontally adjacent lattice points at equal distances, and with vertices on lattice points).","Triangle\n\nThe theorem states:\nT = I + \\frac{1}{2}B - 1","Triangle\n\nwhere I is the number of internal lattice points and B is the number of lattice points lying on the border of the polygon.","Triangle\n\nOther area formulas","Triangle\n\nNumerous other area formulas exist, such as\nT = r \\cdot s,","Triangle\n\nwhere r is the inradius, and s is the semiperimeter (in fact this formula holds for all tangential polygons), andSa ́ndor Nagydobai Kiss, \"A Distance Property of the Feuerbach Point and Its Extension\", Forum Geometricorum 16, 2016, 283–290. http://forumgeom.fau.edu/FG2016volume16/FG201634.pdf","Triangle\n\nTr_a(s-a)\nr_b(s-b)=r_c(s-c)","Triangle\n\nwhere r_a, \\, r_b,\\, r_c are the radii of the excircles tangent to sides a, b, c respectively.","Triangle\n\nWe also have","Triangle\n\nT = \\frac{1}{2}D^{2}(\\sin \\alpha)(\\sin \\beta)(\\sin \\gamma)","Triangle\n\nand \nT \\frac{abc}{2D} \n \\frac{abc}{4R}","Triangle\n\nfor circumdiameter D; and \nT = \\frac{\\tan \\alpha}{4}(b^{2}+c^{2}-a^{2})","Triangle\n\nfor angle α ≠ 90°.","Triangle\n\nThe area can also be expressed as \nT = \\sqrt{rr_ar_br_c}.","Triangle\n\nIn 1885, Baker gave a collection of over a hundred distinct area formulas for the triangle. These include:\nT = \\frac{1}{2}[abch_ah_bh_c]^{1/3},\nT = \\frac{1}{2} \\sqrt{abh_ah_b},\nT = \\frac{a+b}{2(h_a^{-1} + h_b^{-1})},\nT = \\frac{Rh_bh_c}{a}","Triangle\n\nfor circumradius (radius of the circumcircle) R, and\nT = \\frac{h_ah_b}{2 \\sin \\gamma}.","Triangle\n\nUpper bound on the area","Triangle\n\nThe area T of any triangle with perimeter p satisfies","Triangle\n\nT\\le \\tfrac{p^2}{12\\sqrt{3}},","Triangle\n\nwith equality holding if and only if the triangle is equilateral.","Triangle\n\nOther upper bounds on the area T are given by","Triangle\n\n4\\sqrt{3}T \\leq a^2+b^2+c^2","Triangle\n\nand","Triangle\n\n4\\sqrt{3}T \\leq \\frac{9abc}{a+b+c},","Triangle\n\nboth again holding if and only if the triangle is equilateral.","Triangle\n\nBisecting the area","Triangle\n\nThere are infinitely many lines that bisect the area of a triangle.Dunn, J.A., and Pretty, J.E., \"Halving a triangle,\" Mathematical Gazette 56, May 1972, 105–108. Three of them are the medians, which are the only area bisectors that go through the centroid. Three other area bisectors are parallel to the triangle's sides.","Triangle\n\nAny line through a triangle that splits both the triangle's area and its perimeter in half goes through the triangle's incenter. There can be one, two, or three of these for any given triangle.","Triangle\n\nFurther formulas for general Euclidean triangles","Triangle\n\nThe formulas in this section are true for all Euclidean triangles.","Triangle\n\nMedians, angle bisectors, perpendicular side bisectors, and altitudes","Triangle\n\nThe medians and the sides are related by\n\\frac{3}{4}(a^{2}+b^{2}+c^{2})=m_a^{2}+m_b^{2}+m_c^{2}","Triangle\n\nand\nm_a\\frac{1}{2} \\sqrt{2b^{2}+2c^{2}-a^{2}}\n \\sqrt{\\frac{1}{2}(a^{2}+b^{2}+c^{2})- \\frac{3}{4}a^{2}},","Triangle\n\nand equivalently for mb and mc.","Triangle\n\nFor angle A opposite side a, the length of the internal angle bisector is given by \nw_A \\frac{2 \\sqrt{bcs(s-a)}}{b+c} \n \\sqrt{bc\\left[1- \\frac{a^{2}}{(b+c)^{2}}\\right]} = \\frac{2bc}{b+c}\\cos \\frac{A}{2},","Triangle\n\nfor semiperimeter s, where the bisector length is measured from the vertex to where it meets the opposite side.","Triangle\n\nThe interior perpendicular bisectors are given by","Triangle\n\np_a=\\frac{2aT}{a^2+b^2-c^2}, \np_b=\\frac{2bT}{a^2+b^2-c^2}, \np_c=\\frac{2cT}{a^2-b^2+c^2},","Triangle\n\nwhere the sides are a \\ge b \\ge c and the area is T.","Triangle\n\nThe altitude from, for example, the side of length a is","Triangle\n\nh_a = \\frac{2T}{a}.","Triangle\n\nCircumradius and inradius","Triangle\n\nThe following formulas involve the circumradius R and the inradius r:\nR = \\sqrt{\\frac{a^2b^2c^2}{(a+b+c)(-a+b+c)(a-b+c)(a+b-c)}};\nr = \\sqrt{\\frac{(-a+b+c)(a-b+c)(a+b-c)}{4(a+b+c)}}; \n\\frac{1}{r} = \\frac{1}{h_a} + \\frac{1}{h_b} + \\frac{1}{h_c}","Triangle\n\nwhere ha etc. are the altitudes to the subscripted sides;\n\\frac{r}{R} \\frac{4 T^{2}}{sabc} \n \\cos \\alpha + \\cos \\beta + \\cos \\gamma -1;Longuet-Higgins, Michael S., \"On the ratio of the inradius to the circumradius of a triangle\", Mathematical Gazette 87, March 2003, 119–120.","Triangle\n\nand\n2Rr = \\frac{abc}{a+b+c}.","Triangle\n\nThe product of two sides of a triangle equals the altitude to the third side times the diameter of the circumcircle:Altshiller-Court, Nathan, College Geometry, Dover, 2007.","Triangle\n\nabh_cD, \\, \\, bc\nh_aD, \\, \\, ca=h_bD.","Triangle\n\nAdjacent triangles","Triangle\n\nSuppose two adjacent but non-overlapping triangles share the same side of length f and share the same circumcircle, so that the side of length f is a chord of the circumcircle and the triangles have side lengths (a, b, f) and (c, d, f), with the two triangles together forming a cyclic quadrilateral with side lengths in sequence (a, b, c, d). ThenJohnson, Roger A., Advanced Euclidean Geometry, Dover Publ. Co., 2007\nf^2 = \\frac{(ac+bd)(ad+bc)}{(ab+cd)}. \\,","Triangle\n\nCentroid","Triangle\n\nLet G be the centroid of a triangle with vertices A, B, and C, and let P be any interior point. Then the distances between the points are related by\n(PA)^2 + (PB)^2 +(PC)^2 =(GA)^2 + (GB)^2 + (GC)^2 +3(PG)^2. \\,","Triangle\n\nThe sum of the squares of the triangle's sides equals three times the sum of the squared distances of the centroid from the vertices:","Triangle\n\nAB^2+BC^2+CA^2=3(GA^2+GB^2+GC^2).","Triangle\n\nLet qa, qb, and qc be the distances from the centroid to the sides of lengths a, b, and c. Then\n \\frac{q_a}{q_b} \\frac{b}{a}, \\ \\ \\ \\ \\frac{q_b}{q_c} \n \\frac{c}{b}, \\ \\ \\ \\ \\frac{q_a}{q_c} = \\frac{c}{a} \\,","Triangle\n\nand\nq_a \\cdot a q_b \\cdot b \n q_c \\cdot c = \\frac{2}{3} T. \\,","Triangle\n\nCircumcenter, incenter, and orthocenter","Triangle\n\nCarnot's Theorem states that the sum of the distances from the circumcenter to the three sides equals the sum of the circumradius and the inradius. Here a segment's length is considered to be negative if and only if the segment lies entirely outside the triangle. This method is especially useful for deducing the properties of more abstract forms of triangles, such as the ones induced by Lie algebras, that otherwise have the same properties as usual triangles.","Triangle\n\nEuler's theorem states that the distance d between the circumcenter and the incenter is given by\n\\displaystyle d^2=R(R-2r)","Triangle\n\nor equivalently\n\\frac{1}{R-d} + \\frac{1}{R+d} = \\frac{1}{r},","Triangle\n\nwhere R is the circumradius and r is the inradius. Thus for all triangles R ≥ 2r, with equality holding for equilateral triangles.","Triangle\n\nIf we denote that the orthocenter divides one altitude into segments of lengths u and v, another altitude into segment lengths w and x, and the third altitude into segment lengths y and z, then uv wx \n yz.","Triangle\n\nThe distance from a side to the circumcenter equals half the distance from the opposite vertex to the orthocenter.","Triangle\n\nThe sum of the squares of the distances from the vertices to the orthocenter plus the sum of the squares of the sides equals twelve times the square of the circumradius.","Triangle\n\nAngles","Triangle\n\nFor any triangle,","Triangle\n\nab\\cos C+c\\cos B, \\quad b\nc\\cos A+a\\cos C, \\quad c=a\\cos B+b\\cos A.","Triangle\n\nMorley's trisector theorem","Triangle\n\nMorley's trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the Morley triangle.","Triangle\n\nFigures inscribed in a triangle","Triangle\n\nConics","Triangle\n\nAs discussed above, every triangle has a unique inscribed circle (incircle) that is interior to the triangle and tangent to all three sides.","Triangle\n\nEvery triangle has a unique Steiner inellipse which is interior to the triangle and tangent at the midpoints of the sides. Marden's theorem shows how to find the foci of this ellipse. This ellipse has the greatest area of any ellipse tangent to all three sides of the triangle.","Triangle\n\nThe Mandart inellipse of a triangle is the ellipse inscribed within the triangle tangent to its sides at the contact points of its excircles.","Triangle\n\nFor any ellipse inscribed in a triangle ABC, let the foci be P and Q. Then","Triangle\n\n\\frac{\\overline{PA} \\cdot \\overline{QA}}{\\overline{CA} \\cdot \\overline{AB}} + \\frac{\\overline{PB} \\cdot \\overline{QB}}{\\overline{AB} \\cdot \\overline{BC}} + \\frac{\\overline{PC} \\cdot \\overline{QC}}{\\overline{BC} \\cdot \\overline{CA}} = 1.","Triangle\n\nConvex polygon","Triangle\n\nEvery convex polygon with area T can be inscribed in a triangle of area at most equal to 2T. Equality holds (exclusively) for a parallelogram.","Triangle\n\nHexagon","Triangle\n\nThe Lemoine hexagon is a cyclic hexagon with vertices given by the six intersections of the sides of a triangle with the three lines that are parallel to the sides and that pass through its symmedian point. In either its simple form or its self-intersecting form, the Lemoine hexagon is interior to the triangle with two vertices on each side of the triangle.","Triangle\n\nSquares","Triangle\n\nEvery acute triangle has three inscribed squares (squares in its interior such that all four of a square's vertices lie on a side of the triangle, so two of them lie on the same side and hence one side of the square coincides with part of a side of the triangle). In a right triangle two of the squares coincide and have a vertex at the triangle's right angle, so a right triangle has only two distinct inscribed squares. An obtuse triangle has only one inscribed square, with a side coinciding with part of the triangle's longest side. Within a given triangle, a longer common side is associated with a smaller inscribed square. If an inscribed square has side of length qa and the triangle has a side of length a, part of which side coincides with a side of the square, then qa, a, the altitude ha from the side a, and the triangle's area T are related according to \nq_a\\frac{2Ta}{a^2+2T}\n\\frac{ah_a}{a+h_a}.","Triangle\n\nThe largest possible ratio of the area of the inscribed square to the area of the triangle is 1/2, which occurs when , , and the altitude of the triangle from the base of length a is equal to a. The smallest possible ratio of the side of one inscribed square to the side of another in the same non-obtuse triangle is 2\\sqrt{2}/3 0.94....Victor Oxman and Moshe Stupel, \"Why Are the Side Lengths of the Squares Inscribed in a Triangle so Close to Each Other?\", Forum Geometricorum 13 (2013) 113–115. http://forumgeom.fau.edu/FG2013volume13/FG201311index.html Both of these extreme cases occur for the isosceles right triangle.","Triangle\n\nTriangles","Triangle\n\nFrom an interior point in a reference triangle, the nearest points on the three sides serve as the vertices of the pedal triangle of that point. If the interior point is the circumcenter of the reference triangle, the vertices of the pedal triangle are the midpoints of the reference triangle's sides, and so the pedal triangle is called the midpoint triangle or medial triangle. The midpoint triangle subdivides the reference triangle into four congruent triangles which are similar to the reference triangle.","Triangle\n\nThe Gergonne triangle or intouch triangle of a reference triangle has its vertices at the three points of tangency of the reference triangle's sides with its incircle. The extouch triangle of a reference triangle has its vertices at the points of tangency of the reference triangle's excircles with its sides (not extended).","Triangle\n\nFigures circumscribed about a triangle","Triangle\n\nThe tangential triangle of a reference triangle (other than a right triangle) is the triangle whose sides are on the tangent lines to the reference triangle's circumcircle at its vertices.","Triangle\n\nAs mentioned above, every triangle has a unique circumcircle, a circle passing through all three vertices, whose center is the intersection of the perpendicular bisectors of the triangle's sides.","Triangle\n\nFurther, every triangle has a unique Steiner circumellipse, which passes through the triangle's vertices and has its center at the triangle's centroid. Of all ellipses going through the triangle's vertices, it has the smallest area.","Triangle\n\nThe Kiepert hyperbola is the unique conic which passes through the triangle's three vertices, its centroid, and its circumcenter.","Triangle\n\nOf all triangles contained in a given convex polygon, there exists a triangle with maximal area whose vertices are all vertices of the given polygon.","Triangle\n\nSpecifying the location of a point in a triangle","Triangle\n\nOne way to identify locations of points in (or outside) a triangle is to place the triangle in an arbitrary location and orientation in the Cartesian plane, and to use Cartesian coordinates. While convenient for many purposes, this approach has the disadvantage of all points' coordinate values being dependent on the arbitrary placement in the plane.","Triangle\n\nTwo systems avoid that feature, so that the coordinates of a point are not affected by moving the triangle, rotating it, or reflecting it as in a mirror, any of which give a congruent triangle, or even by rescaling it to give a similar triangle:","Triangle\n\n* Trilinear coordinates specify the relative distances of a point from the sides, so that coordinates x : y : z indicate that the ratio of the distance of the point from the first side to its distance from the second side is x : y , etc.\n* Barycentric coordinates of the form \\alpha :\\beta :\\gamma specify the point's location by the relative weights that would have to be put on the three vertices in order to balance the otherwise weightless triangle on the given point.","Triangle\n\nNon-planar triangles","Triangle\n\nA non-planar triangle is a triangle which is not contained in a (flat) plane. Some examples of non-planar triangles in non-Euclidean geometries are spherical triangles in spherical geometry and hyperbolic triangles in hyperbolic geometry.","Triangle\n\nWhile the measures of the internal angles in planar triangles always sum to 180°, a hyperbolic triangle has measures of angles that sum to less than 180°, and a spherical triangle has measures of angles that sum to more than 180°. A hyperbolic triangle can be obtained by drawing on a negatively curved surface, such as a saddle surface, and a spherical triangle can be obtained by drawing on a positively curved surface such as a sphere. Thus, if one draws a giant triangle on the surface of the Earth, one will find that the sum of the measures of its angles is greater than 180°; in fact it will be between 180° and 540°. In particular it is possible to draw a triangle on a sphere such that the measure of each of its internal angles is equal to 90°, adding up to a total of 270°.","Triangle\n\nSpecifically, on a sphere the sum of the angles of a triangle is\n180° × (1 + 4f),","Triangle\n\nwhere f is the fraction of the sphere's area which is enclosed by the triangle. For example, suppose that we draw a triangle on the Earth's surface with vertices at the North Pole, at a point on the equator at 0° longitude, and a point on the equator at 90° West longitude. The great circle line between the latter two points is the equator, and the great circle line between either of those points and the North Pole is a line of longitude; so there are right angles at the two points on the equator. Moreover, the angle at the North Pole is also 90° because the other two vertices differ by 90° of longitude. So the sum of the angles in this triangle is . The triangle encloses 1/4 of the northern hemisphere (90°/360° as viewed from the North Pole) and therefore 1/8 of the Earth's surface, so in the formula ; thus the formula correctly gives the sum of the triangle's angles as 270°.","Triangle\n\nFrom the above angle sum formula we can also see that the Earth's surface is locally flat: If we draw an arbitrarily small triangle in the neighborhood of one point on the Earth's surface, the fraction f of the Earth's surface which is enclosed by the triangle will be arbitrarily close to zero. In this case the angle sum formula simplifies to 180°, which we know is what Euclidean geometry tells us for triangles on a flat surface.","Triangle\n\nTriangles in construction","Triangle\n\nRectangles have been the most popular and common geometric form for buildings since the shape is easy to stack and organize; as a standard, it is easy to design furniture and fixtures to fit inside rectangularly shaped buildings. But triangles, while more difficult to use conceptually, provide a great deal of strength. As computer technology helps architects design creative new buildings, triangular shapes are becoming increasingly prevalent as parts of buildings and as the primary shape for some types of skyscrapers as well as building materials. In Tokyo in 1989, architects had wondered whether it was possible to build a 500-story tower to provide affordable office space for this densely packed city, but with the danger to buildings from earthquakes, architects considered that a triangular shape would have been necessary if such a building was ever to have been built (it hasn't by 2011).","Triangle\n\nIn New York City, as Broadway crisscrosses major avenues, the resulting blocks are cut like triangles, and buildings have been built on these shapes; one such building is the triangularly shaped Flatiron Building which real estate people admit has a \"warren of awkward spaces that do not easily accommodate modern office furniture\" but that has not prevented the structure from becoming a landmark icon. Designers have made houses in Norway using triangular themes. Triangle shapes have appeared in churches as well as public buildings including colleges as well as supports for innovative home designs.","Triangle\n\nTriangles are sturdy; while a rectangle can collapse into a parallelogram from pressure to one of its points, triangles have a natural strength which supports structures against lateral pressures. A triangle will not change shape unless its sides are bent or extended or broken or if its joints break; in essence, each of the three sides supports the other two. A rectangle, in contrast, is more dependent on the strength of its joints in a structural sense. Some innovative designers have proposed making bricks not out of rectangles, but with triangular shapes which can be combined in three dimensions. It is likely that triangles will be used increasingly in new ways as architecture increases in complexity. It is important to remember that triangles are strong in terms of rigidity, but while packed in a tessellating arrangement triangles are not as strong as hexagons under compression (hence the prevalence of hexagonal forms in nature). Tessellated triangles still maintain superior strength for cantilevering however, and this is the basis for one of the strongest man made structures, the tetrahedral truss."],"string":"[\n \"Right triangle\\n\\nA right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry.\",\n \"Right triangle\\n\\nThe side opposite the right angle is called the hypotenuse (side c in the figure). The sides adjacent to the right angle are called legs (or catheti, singular: cathetus). Side a may be identified as the side adjacent to angle B and opposed to (or opposite) angle A, while side b is the side adjacent to angle A and opposed to angle B.\",\n \"Right triangle\\n\\nIf the lengths of all three sides of a right triangle are integers, the triangle is said to be a Pythagorean triangle and its side lengths are collectively known as a Pythagorean triple.\",\n \"Right triangle\\n\\nPrincipal properties\",\n \"Right triangle\\n\\nArea\",\n \"Right triangle\\n\\nAs with any triangle, the area is equal to one half the base multiplied by the corresponding height. In a right triangle, if one leg is taken as the base then the other is height, so the area of a right triangle is one half the product of the two legs. As a formula the area T is\\nT=\\\\tfrac{1}{2}ab\",\n \"Right triangle\\n\\nwhere a and b are the legs of the triangle.\",\n \"Right triangle\\n\\nIf the incircle is tangent to the hypotenuse AB at point P, then denoting the semi-perimeter as s, we have and , and the area is given by\\nT\\\\text{PA} \\\\cdot \\\\text{PB} \\n (s-a)(s-b).\",\n \"Right triangle\\n\\nThis formula only applies to right triangles.\",\n \"Right triangle\\n\\nAltitudes\",\n \"Right triangle\\n\\nIf an altitude is drawn from the vertex with the right angle to the hypotenuse then the triangle is divided into two smaller triangles which are both similar to the original and therefore similar to each other. From this:\\n* The altitude to the hypotenuse is the geometric mean (mean proportional) of the two segments of the hypotenuse.\\n* Each leg of the triangle is the mean proportional of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.\\nIn equations,\\n\\\\displaystyle f^2=de, (this is sometimes known as the right triangle altitude theorem)\\n\\\\displaystyle b^2=ce,\\n\\\\displaystyle a^2=cd\",\n \"Right triangle\\n\\nwhere a, b, c, d, e, f are as shown in the diagram. Thus\\nf=\\\\frac{ab}{c}.\",\n \"Right triangle\\n\\nMoreover, the altitude to the hypotenuse is related to the legs of the right triangle byVoles, Roger, \\\"Integer solutions of a^{-2} + b^{-2} = d^{-2},\\\" Mathematical Gazette 83, July 1999, 269–271. \\n\\\\frac{1}{a^2} + \\\\frac{1}{b^2} = \\\\frac{1}{f^2}.\",\n \"Right triangle\\n\\nFor solutions of this equation in integer values of a, b, f, and c, see here.\",\n \"Right triangle\\n\\nThe altitude from either leg coincides with the other leg. Since these intersect at the right-angled vertex, the right triangle's orthocenter—the intersection of its three altitudes—coincides with the right-angled vertex.\",\n \"Right triangle\\n\\nPythagorean theorem\",\n \"Right triangle\\n\\nThe Pythagorean theorem states that:\\nIn any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).\",\n \"Right triangle\\n\\nThis can be stated in equation form as\\n\\\\displaystyle a^2+b^2=c^2\",\n \"Right triangle\\n\\nwhere c is the length of the hypotenuse, and a and b are the lengths of the remaining two sides.\",\n \"Right triangle\\n\\nPythagorean triples are integer values of a, b, c satisfying this equation.\",\n \"Right triangle\\n\\nInradius and circumradius\",\n \"Right triangle\\n\\nThe radius of the incircle of a right triangle with legs a and b and hypotenuse c is\\nr \\\\frac{a+b-c}{2} \\n \\\\frac{ab}{a+b+c}.\",\n \"Right triangle\\n\\nThe radius of the circumcircle is half the length of the hypotenuse,\\nR = \\\\frac{c}{2}.\",\n \"Right triangle\\n\\nThus the sum of the circumradius and the inradius is half the sum of the legs:Inequalities proposed in “Crux Mathematicorum”, [http://www.imomath.com/othercomp/Journ/ineq.pdf].\",\n \"Right triangle\\n\\nR+r = \\\\frac{a+b}{2}.\",\n \"Right triangle\\n\\nOne of the legs can be expressed in terms of the inradius and the other leg as\\n\\\\displaystyle a=\\\\frac{2r(b-r)}{b-2r}.\",\n \"Right triangle\\n\\nCharacterizations\",\n \"Right triangle\\n\\nA triangle ABC with sides a \\\\le b , semiperimeter s, area T, altitude h opposite the longest side, circumradius R, inradius r, exradii ra, rb, rc (tangent to a, b, c respectively), and medians ma, mb, mc is a right triangle if and only if any one of the statements in the following six categories is true. All of them are of course also properties of a right triangle, since characterizations are equivalences.\",\n \"Right triangle\\n\\nSides and semiperimeter\",\n \"Right triangle\\n\\n* \\\\displaystyle a^2+b^2=c^2\\\\quad (\\\\text{Pythagorean theorem})\\n* \\\\displaystyle (s-a)(s-b)=s(s-c)\\n* \\\\displaystyle s=2R+r. \\n* \\\\displaystyle a^2+b^2+c^28R^2.\",\n \"Right triangle\\n\\nAngles\",\n \"Right triangle\\n\\n* A and B are complementary. \\n* \\\\displaystyle \\\\cos{A}\\\\cos{B}\\\\cos{C}0.CTK Wiki Math, A Variant of the Pythagorean Theorem, 2011, [http://www.cut-the-knot.org/wiki-math/index.php?n\\nTrigonometry.AVariantOfPythagoreanTheorem].\\n* \\\\displaystyle \\\\sin^2{A}+\\\\sin^2{B}+\\\\sin^2{C}2.\\n* \\\\displaystyle \\\\cos^2{A}+\\\\cos^2{B}+\\\\cos^2{C}1.\\n* \\\\displaystyle \\\\sin{2A}\\\\sin{2B}\\n2\\\\sin{A}\\\\sin{B}.\",\n \"Right triangle\\n\\nArea\",\n \"Right triangle\\n\\n* \\\\displaystyle T=\\\\frac{ab}{2}\\n* \\\\displaystyle Tr_ar_b\\nrr_c\\n* \\\\displaystyle T=r(2R+r)\\n* T=PA\\\\cdot PB, where P is the tangency point of the incircle at the longest side AB.\",\n \"Right triangle\\n\\nInradius and exradii* \\\\displaystyle r\\ns-c=(a+b-c)/2\\n* \\\\displaystyle r_as-b\\n(a-b+c)/2\\n* \\\\displaystyle r_bs-a\\n(-a+b+c)/2\\n* \\\\displaystyle r_cs\\n(a+b+c)/2\\n* \\\\displaystyle r_a+r_b+r_c+r=a+b+c\\n* \\\\displaystyle r_a^2+r_b^2+r_c^2+r^2=a^2+b^2+c^2\\n* \\\\displaystyle r=\\\\frac{r_ar_b}{r_c}\",\n \"Right triangle\\n\\nAltitude and medians\",\n \"Right triangle\\n\\n* \\\\displaystyle h=\\\\frac{ab}{c}\\n* \\\\displaystyle m_a^2+m_b^2+m_c^26R^2.\\n* The length of one median is equal to the circumradius.\\n* The shortest altitude (the one from the vertex with the biggest angle) is the geometric mean of the line segments it divides the opposite (longest) side into. This is the right triangle altitude theorem.\",\n \"Right triangle\\n\\nCircumcircle and incircle\",\n \"Right triangle\\n\\n* The triangle can be inscribed in a semicircle, with one side coinciding with the entirety of the diameter (Thales' theorem).\\n* The circumcenter is the midpoint of the longest side.\\n* The longest side is a diameter of the circumcircle \\\\displaystyle (c=2R).\\n* The circumcircle is tangent to the nine-point circle.Andreescu, Titu and Andrica, Dorian, \\\"Complex Numbers from A to...Z\\\", Birkhäuser, 2006, pp. 109-110.\\n* The orthocenter lies on the circumcircle.\\n* The distance between the incenter and the orthocenter is equal to \\\\sqrt{2}r.\",\n \"Right triangle\\n\\nTrigonometric ratios\",\n \"Right triangle\\n\\nThe trigonometric functions for acute angles can be defined as ratios of the sides of a right triangle. For a given angle, a right triangle may be constructed with this angle, and the sides labeled opposite, adjacent and hypotenuse with reference to this angle according to the definitions above. These ratios of the sides do not depend on the particular right triangle chosen, but only on the given angle, since all triangles constructed this way are similar. If, for a given angle α, the opposite side, adjacent side and hypotenuse are labeled O, A and H respectively, then the trigonometric functions are\\n\\\\sin\\\\alpha \\\\frac {O}{H},\\\\,\\\\cos\\\\alpha \\n\\\\frac {A}{H},\\\\,\\\\tan\\\\alpha \\\\frac {O}{A},\\\\,\\\\sec\\\\alpha \\n\\\\frac {H}{A},\\\\,\\\\cot\\\\alpha \\\\frac {A}{O},\\\\,\\\\csc\\\\alpha \\n\\\\frac {H}{O}.\",\n \"Right triangle\\n\\nFor the expression of hyperbolic functions as ratio of the sides of a right triangle, see the hyperbolic triangle of a hyperbolic sector.\",\n \"Right triangle\\n\\nSpecial right triangles\",\n \"Right triangle\\n\\nThe values of the trigonometric functions can be evaluated exactly for certain angles using right triangles with special angles. These include the 30-60-90 triangle which can be used to evaluate the trigonometric functions for any multiple of π/6, and the 45-45-90 triangle which can be used to evaluate the trigonometric functions for any multiple of π/4.\",\n \"Right triangle\\n\\nKepler triangle\",\n \"Right triangle\\n\\nLet H, G, and A be the harmonic mean, the geometric mean, and the arithmetic mean of two positive numbers a and b with a > b. If a right triangle has legs H and G and hypotenuse A, then \\n\\\\frac{A}{H} \\\\frac{A^{2}}{G^{2}} \\n \\\\frac{G^{2}}{H^{2}} = \\\\phi \\\\,\",\n \"Right triangle\\n\\nand\\n\\\\frac{a}{b} = \\\\phi^{3}, \\\\,\",\n \"Right triangle\\n\\nwhere \\\\phi is the golden ratio \\\\tfrac{1+ \\\\sqrt{5}}{2}. \\\\, Since the sides of this right triangle are in geometric progression, this is the Kepler triangle.\",\n \"Right triangle\\n\\nThales' theorem\",\n \"Right triangle\\n\\nThales' theorem states that if A is any point of the circle with diameter BC (except B or C themselves) ABC is a right triangle where A is the right angle. The converse states that if a right triangle is inscribed in a circle then the hypotenuse will be a diameter of the circle. A corollary is that the length of the hypotenuse is twice the distance from the right angle vertex to the midpoint of the hypotenuse. Also, the center of the circle that circumscribes a right triangle is the midpoint of the hypotenuse and its radius is one half the length of the hypotenuse.\",\n \"Right triangle\\n\\nMedians\",\n \"Right triangle\\n\\nThe following formulas hold for the medians of a right triangle:\\nm_a^2 + m_b^2 5m_c^2 \\n \\\\frac{5}{4}c^2.\",\n \"Right triangle\\n\\nThe median on the hypotenuse of a right triangle divides the triangle into two isosceles triangles, because the median equals one-half the hypotenuse.\",\n \"Right triangle\\n\\nThe medians ma and mb from the legs satisfy\",\n \"Right triangle\\n\\n4c^4+9a^2b^2=16m_a^2m_b^2.\",\n \"Right triangle\\n\\nEuler line\",\n \"Right triangle\\n\\nIn a right triangle, the Euler line contains the median on the hypotenuse—that is, it goes through both the right-angled vertex and the midpoint of the side opposite that vertex. This is because the right triangle's orthocenter, the intersection of its altitudes, falls on the right-angled vertex while its circumcenter, the intersection of its perpendicular bisectors of sides, falls on the midpoint of the hypotenuse.\",\n \"Right triangle\\n\\nInequalities\",\n \"Right triangle\\n\\nIn any right triangle the diameter of the incircle is less than half the hypotenuse, and more strongly it is less than or equal to the hypotenuse times (\\\\sqrt{2}-1).Posamentier, Alfred S., and Lehmann, Ingmar. The Secrets of Triangles. Prometheus Books, 2012.\",\n \"Right triangle\\n\\nIn a right triangle with legs a, b and hypotenuse c,\",\n \"Right triangle\\n\\nc \\\\geq \\\\frac{\\\\sqrt{2}}{2}(a+b)\",\n \"Right triangle\\n\\nwith equality only in the isosceles case.\",\n \"Right triangle\\n\\nIf the altitude from the hypotenuse is denoted hc, then\",\n \"Right triangle\\n\\nh_c \\\\leq \\\\frac{\\\\sqrt {2}}{4}(a+b)\",\n \"Right triangle\\n\\nwith equality only in the isosceles case.\",\n \"Right triangle\\n\\nOther properties\",\n \"Right triangle\\n\\nIf segments of lengths p and q emanating from vertex C trisect the hypotenuse into segments of length c/3, thenPosamentier, Alfred S., and Salkind, Charles T. Challenging Problems in Geometry, Dover, 1996.\\np^2 + q^2 = 5\\\\left(\\\\frac{c}{3}\\\\right)^2.\",\n \"Right triangle\\n\\nThe right triangle is the only triangle having two, rather than one or three, distinct inscribed squares.\",\n \"Right triangle\\n\\nLet h and k (h > k) be the sides of the two inscribed squares in a right triangle with hypotenuse c. Then\\n\\\\frac{1}{c^2} + \\\\frac{1}{h^2} = \\\\frac{1}{k^2}.\",\n \"Right triangle\\n\\nThese sides and the incircle radius r are related by a similar formula:\",\n \"Right triangle\\n\\n\\\\displaystyle \\\\frac{1}{r}=-{\\\\frac{1}{c}}+\\\\frac{1}{h}+\\\\frac{1}{k}.\",\n \"Right triangle\\n\\nThe perimeter of a right triangle equals the sum of the radii of the incircle and the three excircles:\",\n \"Right triangle\\n\\na+b+c=r+r_a+r_b+r_c.\",\n \"Triangle\\n\\nA triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \\\\triangle ABC.\",\n \"Triangle\\n\\nIn Euclidean geometry any three points, when non-collinear, determine a unique triangle and a unique plane (i.e. a two-dimensional Euclidean space). This article is about triangles in Euclidean geometry except where otherwise noted.\",\n \"Triangle\\n\\nTypes of triangle\",\n \"Triangle\\n\\nBy lengths of sides\",\n \"Triangle\\n\\nTriangles can be classified according to the lengths of their sides:\\n*An equilateral triangle has all sides the same length. An equilateral triangle is also a regular polygon with all angles measuring 60°. *An isosceles triangle has two sides of equal length.Euclid defines isosceles triangles based on the number of equal sides, i.e. only two equal sides. An alternative approach defines isosceles triangles based on shared properties, i.e. equilateral triangles are a special case of isosceles triangles. An isosceles triangle also has two angles of the same measure; namely, the angles opposite to the two sides of the same length; this fact is the content of the isosceles triangle theorem, which was known by Euclid. Some mathematicians define an isosceles triangle to have exactly two equal sides, whereas others define an isosceles triangle as one with at least two equal sides. The latter definition would make all equilateral triangles isosceles triangles. The 45–45–90 right triangle, which appears in the tetrakis square tiling, is isosceles. *A scalene triangle has all its sides of different lengths. Equivalently, it has all angles of different measure. A right triangle is also a scalene triangle if and only if it is not isosceles.\",\n \"Triangle\\n\\nHatch marks, also called tick marks, are used in diagrams of triangles and other geometric figures to identify sides of equal lengths. A side can be marked with a pattern of \\\"ticks\\\", short line segments in the form of tally marks; two sides have equal lengths if they are both marked with the same pattern. In a triangle, the pattern is usually no more than 3 ticks. An equilateral triangle has the same pattern on all 3 sides, an isosceles triangle has the same pattern on just 2 sides, and a scalene triangle has different patterns on all sides since no sides are equal. Similarly, patterns of 1, 2, or 3 concentric arcs inside the angles are used to indicate equal angles. An equilateral triangle has the same pattern on all 3 angles, an isosceles triangle has the same pattern on just 2 angles, and a scalene triangle has different patterns on all angles since no angles are equal.\",\n \"Triangle\\n\\nBy internal angles\",\n \"Triangle\\n\\nTriangles can also be classified according to their internal angles, measured here in degrees. *A right triangle (or right-angled triangle, formerly called a rectangled triangle) has one of its interior angles measuring 90° (a right angle). The side opposite to the right angle is the hypotenuse, the longest side of the triangle. The other two sides are called the legs or catheti (singular: cathetus) of the triangle. Right triangles obey the Pythagorean theorem: the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse: , where a and b are the lengths of the legs and c is the length of the hypotenuse. Special right triangles are right triangles with additional properties that make calculations involving them easier. One of the two most famous is the 3–4–5 right triangle, where . In this situation, 3, 4, and 5 are a Pythagorean triple. The other one is an isosceles triangle that has 2 angles that each measure 45 degrees. *Triangles that do not have an angle measuring 90° are called oblique triangles. *A triangle with all interior angles measuring less than 90° is an acute triangle or acute-angled triangle.\",\n \"Triangle\\n\\nIf c is the length of the longest side, then , where a and b are the lengths of the other sides. *A triangle with one interior angle measuring more than 90° is an obtuse triangle or obtuse-angled triangle. If c is the length of the longest side, then , where a and b are the lengths of the other sides. *A triangle with an interior angle of 180° (and collinear vertices) is degenerate. *A right degenerate triangle has collinear vertices, two of which are coincident.\",\n \"Triangle\\n\\nA triangle that has two angles with the same measure also has two sides with the same length, and therefore it is an isosceles triangle. It follows that in a triangle where all angles have the same measure, all three sides have the same length, and such a triangle is therefore equilateral.\",\n \"Triangle\\n\\nBasic facts\",\n \"Triangle\\n\\nTriangles are assumed to be two-dimensional plane figures, unless the context provides otherwise (see Non-planar triangles, below). In rigorous treatments, a triangle is therefore called a 2-simplex (see also Polytope). Elementary facts about triangles were presented by Euclid in books 1–4 of his Elements, around 300 BC.\",\n \"Triangle\\n\\nThe sum of the measures of the interior angles of a triangle in Euclidean space is always 180 degrees. This fact is equivalent to Euclid's parallel postulate. This allows determination of the measure of the third angle of any triangle given the measure of two angles. An exterior angle of a triangle is an angle that is a linear pair (and hence supplementary) to an interior angle. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it; this is the exterior angle theorem. The sum of the measures of the three exterior angles (one for each vertex) of any triangle is 360 degrees.The n external angles of any n-sided convex polygon add up to 360 degrees.\",\n \"Triangle\\n\\nSimilarity and congruence\",\n \"Triangle\\n\\nTwo triangles are said to be similar if every angle of one triangle has the same measure as the corresponding angle in the other triangle. The corresponding sides of similar triangles have lengths that are in the same proportion, and this property is also sufficient to establish similarity.\",\n \"Triangle\\n\\nSome basic theorems about similar triangles are:\\n*If and only if one pair of internal angles of two triangles have the same measure as each other, and another pair also have the same measure as each other, the triangles are similar.\\n*If and only if one pair of corresponding sides of two triangles are in the same proportion as are another pair of corresponding sides, and their included angles have the same measure, then the triangles are similar. (The included angle for any two sides of a polygon is the internal angle between those two sides.)\\n*If and only if three pairs of corresponding sides of two triangles are all in the same proportion, then the triangles are similar.Again, in all cases \\\"mirror images\\\" are also similar.\",\n \"Triangle\\n\\nTwo triangles that are congruent have exactly the same size and shape:All pairs of congruent triangles are also similar; but not all pairs of similar triangles are congruent. all pairs of corresponding interior angles are equal in measure, and all pairs of corresponding sides have the same length. (This is a total of six equalities, but three are often sufficient to prove congruence.)\",\n \"Triangle\\n\\nSome individually necessary and sufficient conditions for a pair of triangles to be congruent are:\\n*SAS Postulate: Two sides in a triangle have the same length as two sides in the other triangle, and the included angles have the same measure.\\n*ASA: Two interior angles and the included side in a triangle have the same measure and length, respectively, as those in the other triangle. (The included side for a pair of angles is the side that is common to them.)\\n*SSS: Each side of a triangle has the same length as a corresponding side of the other triangle.\\n*AAS: Two angles and a corresponding (non-included) side in a triangle have the same measure and length, respectively, as those in the other triangle. (This is sometimes referred to as AAcorrS and then includes ASA above.)\",\n \"Triangle\\n\\nSome individually sufficient conditions are:\",\n \"Triangle\\n\\n*Hypotenuse-Leg (HL) Theorem: The hypotenuse and a leg in a right triangle have the same length as those in another right triangle. This is also called RHS (right-angle, hypotenuse, side).\\n*Hypotenuse-Angle Theorem: The hypotenuse and an acute angle in one right triangle have the same length and measure, respectively, as those in the other right triangle. This is just a particular case of the AAS theorem.\\nAn important condition is:\\n*Side-Side-Angle (or Angle-Side-Side) condition: If two sides and a corresponding non-included angle of a triangle have the same length and measure, respectively, as those in another triangle, then this is not sufficient to prove congruence; but if the angle given is opposite to the longer side of the two sides, then the triangles are congruent. The Hypotenuse-Leg Theorem is a particular case of this criterion. The Side-Side-Angle condition does not by itself guarantee that the triangles are congruent because one triangle could be obtuse-angled and the other acute-angled.\",\n \"Triangle\\n\\nUsing right triangles and the concept of similarity, the trigonometric functions sine and cosine can be defined. These are functions of an angle which are investigated in trigonometry.\",\n \"Triangle\\n\\nRight triangles\",\n \"Triangle\\n\\nA central theorem is the Pythagorean theorem, which states in any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the two other sides. If the hypotenuse has length c, and the legs have lengths a and b, then the theorem states that\\na^2 + b^2 = c^2.\\\\,\",\n \"Triangle\\n\\nThe converse is true: if the lengths of the sides of a triangle satisfy the above equation, then the triangle has a right angle opposite side c.\",\n \"Triangle\\n\\nSome other facts about right triangles:\\n*The acute angles of a right triangle are complementary.\\na + b + 90^{\\\\circ} 180^{\\\\circ} \\\\Rightarrow a + b \\n 90^{\\\\circ} \\\\Rightarrow a = 90^{\\\\circ} - b\\n*If the legs of a right triangle have the same length, then the angles opposite those legs have the same measure. Since these angles are complementary, it follows that each measures 45 degrees. By the Pythagorean theorem, the length of the hypotenuse is the length of a leg times √2.\\n*In a right triangle with acute angles measuring 30 and 60 degrees, the hypotenuse is twice the length of the shorter side, and the longer side is equal to the length of the shorter side times √3:\\n:c = 2a\\\\,\\n:b = a\\\\times\\\\sqrt{3}.\",\n \"Triangle\\n\\nFor all triangles, angles and sides are related by the law of cosines and law of sines (also called the cosine rule and sine rule).\",\n \"Triangle\\n\\nExistence of a triangle\",\n \"Triangle\\n\\nCondition on the sides\",\n \"Triangle\\n\\nThe triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. That sum can equal the length of the third side only in the case of a degenerate triangle, one with collinear vertices. It is not possible for that sum to be less than the length of the third side. A triangle with three given positive side lengths exists if and only if those side lengths satisfy the triangle inequality.\",\n \"Triangle\\n\\nConditions on the angles\",\n \"Triangle\\n\\nThree given angles form a non-degenerate triangle (and indeed an infinitude of them) if and only if both of these conditions hold: (a) each of the angles is positive, and (b) the angles sum to 180°. If degenerate triangles are permitted, angles of 0° are permitted.\",\n \"Triangle\\n\\nTrigonometric conditions\",\n \"Triangle\\n\\nThree positive angles α, β, and γ, each of them less than 180°, are the angles of a triangle if and only if any one of the following conditions holds:\\n\\\\tan{\\\\frac{\\\\alpha}{2}}\\\\tan{\\\\frac{\\\\beta}{2}}+\\\\tan{\\\\frac{\\\\beta}{2}}\\\\tan{\\\\frac{\\\\gamma}{2}}+\\\\tan{\\\\frac{\\\\gamma}{2}}\\\\tan{\\\\frac{\\\\alpha}{2}}1,Vardan Verdiyan & Daniel Campos Salas, \\\"Simple trigonometric substitutions with broad results\\\", Mathematical Reflections no 6, 2007.\",\n \"Triangle\\n\\n\\\\sin^2{\\\\frac{\\\\alpha}{2}}+\\\\sin^2{\\\\frac{\\\\beta}{2}}+\\\\sin^2{\\\\frac{\\\\gamma}{2}}+2\\\\sin{\\\\frac{\\\\alpha}{2}}\\\\sin{\\\\frac{\\\\beta}{2}}\\\\sin{\\\\frac{\\\\gamma}{2}}1,\",\n \"Triangle\\n\\n\\\\sin(2\\\\alpha) + \\\\sin(2\\\\beta) + \\\\sin(2\\\\gamma) = 4\\\\sin(\\\\alpha)\\\\sin(\\\\beta)\\\\sin(\\\\gamma),\",\n \"Triangle\\n\\n\\\\cos^2\\\\alpha+\\\\cos^2\\\\beta+\\\\cos^2\\\\gamma+2\\\\cos(\\\\alpha)\\\\cos(\\\\beta)\\\\cos(\\\\gamma)1,\",\n \"Triangle\\n\\n\\\\tan(\\\\alpha) + \\\\tan(\\\\beta) + \\\\tan(\\\\gamma) = \\\\tan(\\\\alpha)\\\\tan(\\\\beta)\\\\tan(\\\\gamma),\",\n \"Triangle\\n\\nthe latter equality applying only if none of the angles is 90° (so the tangent function's value is always finite).\",\n \"Triangle\\n\\nPoints, lines, and circles associated with a triangle\",\n \"Triangle\\n\\nThere are thousands of different constructions that find a special point associated with (and often inside) a triangle, satisfying some unique property: see the article Encyclopedia of Triangle Centers for a catalogue of them. Often they are constructed by finding three lines associated in a symmetrical way with the three sides (or vertices) and then proving that the three lines meet in a single point: an important tool for proving the existence of these is Ceva's theorem, which gives a criterion for determining when three such lines are concurrent. Similarly, lines associated with a triangle are often constructed by proving that three symmetrically constructed points are collinear: here Menelaus' theorem gives a useful general criterion. In this section just a few of the most commonly encountered constructions are explained.\",\n \"Triangle\\n\\nA perpendicular bisector of a side of a triangle is a straight line passing through the midpoint of the side and being perpendicular to it, i.e. forming a right angle with it. The three perpendicular bisectors meet in a single point, the triangle's circumcenter, usually denoted by O; this point is the center of the circumcircle, the circle passing through all three vertices. The diameter of this circle, called the circumdiameter, can be found from the law of sines stated above. The circumcircle's radius is called the circumradius.\",\n \"Triangle\\n\\nThales' theorem implies that if the circumcenter is located on one side of the triangle, then the opposite angle is a right one. If the circumcenter is located inside the triangle, then the triangle is acute; if the circumcenter is located outside the triangle, then the triangle is obtuse.\",\n \"Triangle\\n\\nAn altitude of a triangle is a straight line through a vertex and perpendicular to (i.e. forming a right angle with) the opposite side. This opposite side is called the base of the altitude, and the point where the altitude intersects the base (or its extension) is called the foot of the altitude. The length of the altitude is the distance between the base and the vertex. The three altitudes intersect in a single point, called the orthocenter of the triangle, usually denoted by H. The orthocenter lies inside the triangle if and only if the triangle is acute.\",\n \"Triangle\\n\\nAn angle bisector of a triangle is a straight line through a vertex which cuts the corresponding angle in half. The three angle bisectors intersect in a single point, the incenter, usually denoted by I, the center of the triangle's incircle. The incircle is the circle which lies inside the triangle and touches all three sides. Its radius is called the inradius. There are three other important circles, the excircles; they lie outside the triangle and touch one side as well as the extensions of the other two. The centers of the in- and excircles form an orthocentric system.\",\n \"Triangle\\n\\nA median of a triangle is a straight line through a vertex and the midpoint of the opposite side, and divides the triangle into two equal areas. The three medians intersect in a single point, the triangle's centroid or geometric barycenter, usually denoted by G. The centroid of a rigid triangular object (cut out of a thin sheet of uniform density) is also its center of mass: the object can be balanced on its centroid in a uniform gravitational field. The centroid cuts every median in the ratio 2:1, i.e. the distance between a vertex and the centroid is twice the distance between the centroid and the midpoint of the opposite side.\",\n \"Triangle\\n\\nThe midpoints of the three sides and the feet of the three altitudes all lie on a single circle, the triangle's nine-point circle. The remaining three points for which it is named are the midpoints of the portion of altitude between the vertices and the orthocenter. The radius of the nine-point circle is half that of the circumcircle. It touches the incircle (at the Feuerbach point) and the three excircles.\",\n \"Triangle\\n\\nThe centroid (yellow), orthocenter (blue), circumcenter (green) and center of the nine-point circle (red point) all lie on a single line, known as Euler's line (red line). The center of the nine-point circle lies at the midpoint between the orthocenter and the circumcenter, and the distance between the centroid and the circumcenter is half that between the centroid and the orthocenter.\",\n \"Triangle\\n\\nThe center of the incircle is not in general located on Euler's line.\",\n \"Triangle\\n\\nIf one reflects a median in the angle bisector that passes through the same vertex, one obtains a symmedian. The three symmedians intersect in a single point, the symmedian point of the triangle.\",\n \"Triangle\\n\\nComputing the sides and angles\",\n \"Triangle\\n\\nThere are various standard methods for calculating the length of a side or the measure of an angle. Certain methods are suited to calculating values in a right-angled triangle; more complex methods may be required in other situations.\",\n \"Triangle\\n\\nTrigonometric ratios in right triangles\",\n \"Triangle\\n\\nIn right triangles, the trigonometric ratios of sine, cosine and tangent can be used to find unknown angles and the lengths of unknown sides. The sides of the triangle are known as follows:\\n*The hypotenuse is the side opposite the right angle, or defined as the longest side of a right-angled triangle, in this case h.\\n*The opposite side is the side opposite to the angle we are interested in, in this case a.\\n*The adjacent side is the side that is in contact with the angle we are interested in and the right angle, hence its name. In this case the adjacent side is b.\",\n \"Triangle\\n\\nSine, cosine and tangent\",\n \"Triangle\\n\\nThe sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. In our case\\n\\\\sin A \\\\frac {\\\\text{opposite side}}{\\\\text{hypotenuse}} \\n \\\\frac {a}{h}\\\\,.\",\n \"Triangle\\n\\nNote that this ratio does not depend on the particular right triangle chosen, as long as it contains the angle A, since all those triangles are similar.\",\n \"Triangle\\n\\nThe cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. In our case\\n\\\\cos A \\\\frac {\\\\text{adjacent side}}{\\\\text{hypotenuse}} \\n \\\\frac {b}{h}\\\\,.\",\n \"Triangle\\n\\nThe tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. In our case\\n\\\\tan A \\\\frac {\\\\text{opposite side}}{\\\\text{adjacent side}} \\n \\\\frac {a}{b} =\\\\frac {\\\\sin A}{\\\\cos A}\\\\,.\",\n \"Triangle\\n\\nThe acronym \\\"SOH-CAH-TOA\\\" is a useful mnemonic for these ratios.\",\n \"Triangle\\n\\nInverse functions\",\n \"Triangle\\n\\nThe inverse trigonometric functions can be used to calculate the internal angles for a right angled triangle with the length of any two sides.\",\n \"Triangle\\n\\nArcsin can be used to calculate an angle from the length of the opposite side and the length of the hypotenuse.\\n\\\\theta = \\\\arcsin \\\\left( \\\\frac{\\\\text{opposite side}}{\\\\text{hypotenuse}} \\\\right)\",\n \"Triangle\\n\\nArccos can be used to calculate an angle from the length of the adjacent side and the length of the hypotenuse.\\n\\\\theta = \\\\arccos \\\\left( \\\\frac{\\\\text{adjacent side}}{\\\\text{hypotenuse}} \\\\right)\",\n \"Triangle\\n\\nArctan can be used to calculate an angle from the length of the opposite side and the length of the adjacent side.\\n\\\\theta = \\\\arctan \\\\left( \\\\frac{\\\\text{opposite side}}{\\\\text{adjacent side}} \\\\right)\",\n \"Triangle\\n\\nIn introductory geometry and trigonometry courses, the notation sin−1, cos−1, etc., are often used in place of arcsin, arccos, etc. However, the arcsin, arccos, etc., notation is standard in higher mathematics where trigonometric functions are commonly raised to powers, as this avoids confusion between multiplicative inverse and compositional inverse.\",\n \"Triangle\\n\\nSine, cosine and tangent rules\",\n \"Triangle\\n\\nThe law of sines, or sine rule, states that the ratio of the length of a side to the sine of its corresponding opposite angle is constant, that is\\n\\\\frac{a}{\\\\sin \\\\alpha} \\\\frac{b}{\\\\sin \\\\beta} \\n \\\\frac{c}{\\\\sin \\\\gamma}.\",\n \"Triangle\\n\\nThis ratio is equal to the diameter of the circumscribed circle of the given triangle. Another interpretation of this theorem is that every triangle with angles α, β and γ is similar to a triangle with side lengths equal to sin α, sin β and sin γ. This triangle can be constructed by first constructing a circle of diameter 1, and inscribing in it two of the angles of the triangle. The length of the sides of that triangle will be sin α, sin β and sin γ. The side whose length is sin α is opposite to the angle whose measure is α, etc.\",\n \"Triangle\\n\\nThe law of cosines, or cosine rule, connects the length of an unknown side of a triangle to the length of the other sides and the angle opposite to the unknown side. As per the law:\",\n \"Triangle\\n\\nFor a triangle with length of sides a, b, c and angles of α, β, γ respectively, given two known lengths of a triangle a and b, and the angle between the two known sides γ (or the angle opposite to the unknown side c), to calculate the third side c, the following formula can be used:\\nc^2\\\\ = a^2 + b^2 - 2ab\\\\cos(\\\\gamma)\\nb^2\\\\ = a^2 + c^2 - 2ac\\\\cos(\\\\beta)\\na^2\\\\ = b^2 + c^2 - 2bc\\\\cos(\\\\alpha)\",\n \"Triangle\\n\\nIf the lengths of all three sides of any triangle are known the three angles can be calculated:\\n\\\\alpha=\\\\arccos\\\\left(\\\\frac{b^2+c^2-a^2}{2bc}\\\\right)\\n\\\\beta=\\\\arccos\\\\left(\\\\frac{a^2+c^2-b^2}{2ac}\\\\right)\\n\\\\gamma=\\\\arccos\\\\left(\\\\frac{a^2+b^2-c^2}{2ab}\\\\right)\",\n \"Triangle\\n\\nThe law of tangents or tangent rule, can be used to find a side or an angle when you know two sides and an angle or two angles and a side. It states that: \\n\\\\frac{a-b}{a+b} = \\\\frac{\\\\tan[\\\\frac{1}{2}(\\\\alpha-\\\\beta)]}{\\\\tan[\\\\frac{1}{2}(\\\\alpha+\\\\beta)]}.\",\n \"Triangle\\n\\nSolution of triangles\",\n \"Triangle\\n\\n\\\"Solution of triangles\\\" is the main trigonometric problem: to find missing characteristics of a triangle (three angles, the lengths of the three sides etc.) when at least three of these characteristics are given. The triangle can be located on a plane or on a sphere. This problem often occurs in various trigonometric applications, such as geodesy, astronomy, construction, navigation etc.\",\n \"Triangle\\n\\nComputing the area of a triangle\",\n \"Triangle\\n\\nCalculating the area T of a triangle is an elementary problem encountered often in many different situations. The best known and simplest formula is:\\nT=\\\\frac{1}{2}bh\\nwhere b is the length of the base of the triangle, and h is the height or altitude of the triangle. The term \\\"base\\\" denotes any side, and \\\"height\\\" denotes the length of a perpendicular from the vertex opposite the side onto the line containing the side itself. In 499 CE Aryabhata, a great mathematician-astronomer from the classical age of Indian mathematics and Indian astronomy, used this method in the Aryabhatiya (section 2.6).\",\n \"Triangle\\n\\nAlthough simple, this formula is only useful if the height can be readily found, which is not always the case. For example, the surveyor of a triangular field might find it relatively easy to measure the length of each side, but relatively difficult to construct a 'height'. Various methods may be used in practice, depending on what is known about the triangle. The following is a selection of frequently used formulae for the area of a triangle.\",\n \"Triangle\\n\\nUsing trigonometry\",\n \"Triangle\\n\\nThe height of a triangle can be found through the application of trigonometry.\",\n \"Triangle\\n\\nKnowing SAS: Using the labels in the image on the right, the altitude is . Substituting this in the formula T=\\\\frac{1}{2}bh derived above, the area of the triangle can be expressed as:\\nT \\\\frac{1}{2}ab\\\\sin \\\\gamma \\n \\\\frac{1}{2}bc\\\\sin \\\\alpha = \\\\frac{1}{2}ca\\\\sin \\\\beta\",\n \"Triangle\\n\\n(where α is the interior angle at A, β is the interior angle at B, \\\\gamma is the interior angle at C and c is the line AB).\",\n \"Triangle\\n\\nFurthermore, since sin α sin (π − α) \\n sin (β + \\\\gamma), and similarly for the other two angles:\\nT \\\\frac{1}{2}ab\\\\sin (\\\\alpha+\\\\beta) \\n \\\\frac{1}{2}bc\\\\sin (\\\\beta+\\\\gamma) = \\\\frac{1}{2}ca\\\\sin (\\\\gamma+\\\\alpha).\",\n \"Triangle\\n\\nKnowing AAS:\\nT = \\\\frac {b^{2}(\\\\sin \\\\alpha)(\\\\sin (\\\\alpha + \\\\beta))}{2\\\\sin \\\\beta},\",\n \"Triangle\\n\\nand analogously if the known side is a or c.\",\n \"Triangle\\n\\nKnowing ASA: \\nT \\\\frac{a^{2}}{2(\\\\cot \\\\beta + \\\\cot \\\\gamma)} \\n \\\\frac{a^{2} (\\\\sin \\\\beta)(\\\\sin \\\\gamma)}{2\\\\sin(\\\\beta + \\\\gamma)},\",\n \"Triangle\\n\\nand analogously if the known side is b or c.\",\n \"Triangle\\n\\nUsing Heron's formula\",\n \"Triangle\\n\\nThe shape of the triangle is determined by the lengths of the sides. Therefore, the area can also be derived from the lengths of the sides. By Heron's formula:\\nT = \\\\sqrt{s(s-a)(s-b)(s-c)}\",\n \"Triangle\\n\\nwhere s= \\\\tfrac{a+b+c}{2} is the semiperimeter, or half of the triangle's perimeter.\",\n \"Triangle\\n\\nThree other equivalent ways of writing Heron's formula are\\nT = \\\\frac{1}{4} \\\\sqrt{(a^2+b^2+c^2)^2-2(a^4+b^4+c^4)}\\nT = \\\\frac{1}{4} \\\\sqrt{2(a^2b^2+a^2c^2+b^2c^2)-(a^4+b^4+c^4)}\\nT = \\\\frac{1}{4} \\\\sqrt{(a+b-c) (a-b+c) (-a+b+c) (a+b+c)}.\",\n \"Triangle\\n\\nUsing vectors\",\n \"Triangle\\n\\nThe area of a parallelogram embedded in a three-dimensional Euclidean space can be calculated using vectors. Let vectors AB and AC point respectively from A to B and from A to C. The area of parallelogram ABDC is then\\n|\\\\mathbf{AB}\\\\times\\\\mathbf{AC}|,\",\n \"Triangle\\n\\nwhich is the magnitude of the cross product of vectors AB and AC. The area of triangle ABC is half of this,\\n\\\\frac{1}{2}|\\\\mathbf{AB}\\\\times\\\\mathbf{AC}|.\",\n \"Triangle\\n\\nThe area of triangle ABC can also be expressed in terms of dot products as follows:\\n\\\\frac{1}{2} \\\\sqrt{(\\\\mathbf{AB} \\\\cdot \\\\mathbf{AB})(\\\\mathbf{AC} \\\\cdot \\\\mathbf{AC}) -(\\\\mathbf{AB} \\\\cdot \\\\mathbf{AC})^2} =\\\\frac{1}{2} \\\\sqrt{ |\\\\mathbf{AB}|^2 |\\\\mathbf{AC}|^2 -(\\\\mathbf{AB} \\\\cdot \\\\mathbf{AC})^2}.\\\\,\",\n \"Triangle\\n\\nIn two-dimensional Euclidean space, expressing vector AB as a free vector in Cartesian space equal to (x1,y1) and AC as (x2,y2), this can be rewritten as:\\n\\\\frac{1}{2}\\\\,|x_1 y_2 - x_2 y_1|.\\\\,\",\n \"Triangle\\n\\nUsing coordinates\",\n \"Triangle\\n\\nIf vertex A is located at the origin (0, 0) of a Cartesian coordinate system and the coordinates of the other two vertices are given by and , then the area can be computed as times the absolute value of the determinant\\nT \\\\frac{1}{2}\\\\left|\\\\det\\\\begin{pmatrix}x_B & x_C \\\\\\\\ y_B & y_C \\\\end{pmatrix}\\\\right| \\n \\\\frac{1}{2}|x_B y_C - x_C y_B|.\",\n \"Triangle\\n\\nFor three general vertices, the equation is:\\nT \\\\frac{1}{2} \\\\left| \\\\det\\\\begin{pmatrix}x_A & x_B & x_C \\\\\\\\ y_A & y_B & y_C \\\\\\\\ 1 & 1 & 1\\\\end{pmatrix} \\\\right| \\n \\\\frac{1}{2} \\\\big| x_A y_B - x_A y_C + x_B y_C - x_B y_A + x_C y_A - x_C y_B \\\\big|,\",\n \"Triangle\\n\\nwhich can be written as\\nT = \\\\frac{1}{2} \\\\big| (x_A - x_C) (y_B - y_A) - (x_A - x_B) (y_C - y_A) \\\\big|.\",\n \"Triangle\\n\\nIf the points are labeled sequentially in the counterclockwise direction, the above determinant expressions are positive and the absolute value signs can be omitted. The above formula is known as the shoelace formula or the surveyor's formula.\",\n \"Triangle\\n\\nIf we locate the vertices in the complex plane and denote them in counterclockwise sequence as , , and , and denote their complex conjugates as \\\\bar a, \\\\bar b, and \\\\bar c, then the formula\\nT=\\\\frac{i}{4}\\\\begin{vmatrix}a & \\\\bar a & 1 \\\\\\\\ b & \\\\bar b & 1 \\\\\\\\ c & \\\\bar c & 1 \\\\end{vmatrix}\",\n \"Triangle\\n\\nis equivalent to the shoelace formula.\",\n \"Triangle\\n\\nIn three dimensions, the area of a general triangle , and ) is the Pythagorean sum of the areas of the respective projections on the three principal planes (i.e. x 0, y \\n 0 and z = 0):\\nT = \\\\frac{1}{2} \\\\sqrt{\\\\begin{vmatrix} x_A & x_B & x_C \\\\\\\\ y_A & y_B & y_C \\\\\\\\ 1 & 1 & 1 \\\\end{vmatrix}^2 +\\n\\\\begin{vmatrix} y_A & y_B & y_C \\\\\\\\ z_A & z_B & z_C \\\\\\\\ 1 & 1 & 1 \\\\end{vmatrix}^2 +\\n\\\\begin{vmatrix} z_A & z_B & z_C \\\\\\\\ x_A & x_B & x_C \\\\\\\\ 1 & 1 & 1 \\\\end{vmatrix}^2 }.\",\n \"Triangle\\n\\nUsing line integrals\",\n \"Triangle\\n\\nThe area within any closed curve, such as a triangle, is given by the line integral around the curve of the algebraic or signed distance of a point on the curve from an arbitrary oriented straight line L. Points to the right of L as oriented are taken to be at negative distance from L, while the weight for the integral is taken to be the component of arc length parallel to L rather than arc length itself.\",\n \"Triangle\\n\\nThis method is well suited to computation of the area of an arbitrary polygon. Taking L to be the x-axis, the line integral between consecutive vertices (xi,yi) and (xi+1,yi+1) is given by the base times the mean height, namely . The sign of the area is an overall indicator of the direction of traversal, with negative area indicating counterclockwise traversal. The area of a triangle then falls out as the case of a polygon with three sides.\",\n \"Triangle\\n\\nWhile the line integral method has in common with other coordinate-based methods the arbitrary choice of a coordinate system, unlike the others it makes no arbitrary choice of vertex of the triangle as origin or of side as base. Furthermore, the choice of coordinate system defined by L commits to only two degrees of freedom rather than the usual three, since the weight is a local distance (e.g. in the above) whence the method does not require choosing an axis normal to L.\",\n \"Triangle\\n\\nWhen working in polar coordinates it is not necessary to convert to Cartesian coordinates to use line integration, since the line integral between consecutive vertices (ri,θi) and (ri+1,θi+1) of a polygon is given directly by . This is valid for all values of θ, with some decrease in numerical accuracy when |θ| is many orders of magnitude greater than π. With this formulation negative area indicates clockwise traversal, which should be kept in mind when mixing polar and cartesian coordinates. Just as the choice of y-axis () is immaterial for line integration in cartesian coordinates, so is the choice of zero heading () immaterial here.\",\n \"Triangle\\n\\nFormulas resembling Heron's formula\",\n \"Triangle\\n\\nThree formulas have the same structure as Heron's formula but are expressed in terms of different variables. First, denoting the medians from sides a, b, and c respectively as ma, mb, and mc and their semi-sum as σ, we have \\nT = \\\\frac{4}{3} \\\\sqrt{\\\\sigma (\\\\sigma - m_a)(\\\\sigma - m_b)(\\\\sigma - m_c)}.\",\n \"Triangle\\n\\nNext, denoting the altitudes from sides a, b, and c respectively as ha, hb, and hc, and denoting the semi-sum of the reciprocals of the altitudes as H = (h_a^{-1} + h_b^{-1} + h_c^{-1})/2 we have \\nT^{-1} = 4 \\\\sqrt{H(H-h_a^{-1})(H-h_b^{-1})(H-h_c^{-1})}.\",\n \"Triangle\\n\\nAnd denoting the semi-sum of the angles' sines as , we have \\nT = D^{2} \\\\sqrt{S(S-\\\\sin \\\\alpha)(S-\\\\sin \\\\beta)(S-\\\\sin \\\\gamma)}\",\n \"Triangle\\n\\nwhere D is the diameter of the circumcircle: D\\\\tfrac{a}{\\\\sin \\\\alpha} \\n \\\\tfrac{b}{\\\\sin \\\\beta} = \\\\tfrac{c}{\\\\sin \\\\gamma}.\",\n \"Triangle\\n\\nUsing Pick's theorem\",\n \"Triangle\\n\\nSee Pick's theorem for a technique for finding the area of any arbitrary lattice polygon (one drawn on a grid with vertically and horizontally adjacent lattice points at equal distances, and with vertices on lattice points).\",\n \"Triangle\\n\\nThe theorem states:\\nT = I + \\\\frac{1}{2}B - 1\",\n \"Triangle\\n\\nwhere I is the number of internal lattice points and B is the number of lattice points lying on the border of the polygon.\",\n \"Triangle\\n\\nOther area formulas\",\n \"Triangle\\n\\nNumerous other area formulas exist, such as\\nT = r \\\\cdot s,\",\n \"Triangle\\n\\nwhere r is the inradius, and s is the semiperimeter (in fact this formula holds for all tangential polygons), andSa ́ndor Nagydobai Kiss, \\\"A Distance Property of the Feuerbach Point and Its Extension\\\", Forum Geometricorum 16, 2016, 283–290. http://forumgeom.fau.edu/FG2016volume16/FG201634.pdf\",\n \"Triangle\\n\\nTr_a(s-a)\\nr_b(s-b)=r_c(s-c)\",\n \"Triangle\\n\\nwhere r_a, \\\\, r_b,\\\\, r_c are the radii of the excircles tangent to sides a, b, c respectively.\",\n \"Triangle\\n\\nWe also have\",\n \"Triangle\\n\\nT = \\\\frac{1}{2}D^{2}(\\\\sin \\\\alpha)(\\\\sin \\\\beta)(\\\\sin \\\\gamma)\",\n \"Triangle\\n\\nand \\nT \\\\frac{abc}{2D} \\n \\\\frac{abc}{4R}\",\n \"Triangle\\n\\nfor circumdiameter D; and \\nT = \\\\frac{\\\\tan \\\\alpha}{4}(b^{2}+c^{2}-a^{2})\",\n \"Triangle\\n\\nfor angle α ≠ 90°.\",\n \"Triangle\\n\\nThe area can also be expressed as \\nT = \\\\sqrt{rr_ar_br_c}.\",\n \"Triangle\\n\\nIn 1885, Baker gave a collection of over a hundred distinct area formulas for the triangle. These include:\\nT = \\\\frac{1}{2}[abch_ah_bh_c]^{1/3},\\nT = \\\\frac{1}{2} \\\\sqrt{abh_ah_b},\\nT = \\\\frac{a+b}{2(h_a^{-1} + h_b^{-1})},\\nT = \\\\frac{Rh_bh_c}{a}\",\n \"Triangle\\n\\nfor circumradius (radius of the circumcircle) R, and\\nT = \\\\frac{h_ah_b}{2 \\\\sin \\\\gamma}.\",\n \"Triangle\\n\\nUpper bound on the area\",\n \"Triangle\\n\\nThe area T of any triangle with perimeter p satisfies\",\n \"Triangle\\n\\nT\\\\le \\\\tfrac{p^2}{12\\\\sqrt{3}},\",\n \"Triangle\\n\\nwith equality holding if and only if the triangle is equilateral.\",\n \"Triangle\\n\\nOther upper bounds on the area T are given by\",\n \"Triangle\\n\\n4\\\\sqrt{3}T \\\\leq a^2+b^2+c^2\",\n \"Triangle\\n\\nand\",\n \"Triangle\\n\\n4\\\\sqrt{3}T \\\\leq \\\\frac{9abc}{a+b+c},\",\n \"Triangle\\n\\nboth again holding if and only if the triangle is equilateral.\",\n \"Triangle\\n\\nBisecting the area\",\n \"Triangle\\n\\nThere are infinitely many lines that bisect the area of a triangle.Dunn, J.A., and Pretty, J.E., \\\"Halving a triangle,\\\" Mathematical Gazette 56, May 1972, 105–108. Three of them are the medians, which are the only area bisectors that go through the centroid. Three other area bisectors are parallel to the triangle's sides.\",\n \"Triangle\\n\\nAny line through a triangle that splits both the triangle's area and its perimeter in half goes through the triangle's incenter. There can be one, two, or three of these for any given triangle.\",\n \"Triangle\\n\\nFurther formulas for general Euclidean triangles\",\n \"Triangle\\n\\nThe formulas in this section are true for all Euclidean triangles.\",\n \"Triangle\\n\\nMedians, angle bisectors, perpendicular side bisectors, and altitudes\",\n \"Triangle\\n\\nThe medians and the sides are related by\\n\\\\frac{3}{4}(a^{2}+b^{2}+c^{2})=m_a^{2}+m_b^{2}+m_c^{2}\",\n \"Triangle\\n\\nand\\nm_a\\\\frac{1}{2} \\\\sqrt{2b^{2}+2c^{2}-a^{2}}\\n \\\\sqrt{\\\\frac{1}{2}(a^{2}+b^{2}+c^{2})- \\\\frac{3}{4}a^{2}},\",\n \"Triangle\\n\\nand equivalently for mb and mc.\",\n \"Triangle\\n\\nFor angle A opposite side a, the length of the internal angle bisector is given by \\nw_A \\\\frac{2 \\\\sqrt{bcs(s-a)}}{b+c} \\n \\\\sqrt{bc\\\\left[1- \\\\frac{a^{2}}{(b+c)^{2}}\\\\right]} = \\\\frac{2bc}{b+c}\\\\cos \\\\frac{A}{2},\",\n \"Triangle\\n\\nfor semiperimeter s, where the bisector length is measured from the vertex to where it meets the opposite side.\",\n \"Triangle\\n\\nThe interior perpendicular bisectors are given by\",\n \"Triangle\\n\\np_a=\\\\frac{2aT}{a^2+b^2-c^2}, \\np_b=\\\\frac{2bT}{a^2+b^2-c^2}, \\np_c=\\\\frac{2cT}{a^2-b^2+c^2},\",\n \"Triangle\\n\\nwhere the sides are a \\\\ge b \\\\ge c and the area is T.\",\n \"Triangle\\n\\nThe altitude from, for example, the side of length a is\",\n \"Triangle\\n\\nh_a = \\\\frac{2T}{a}.\",\n \"Triangle\\n\\nCircumradius and inradius\",\n \"Triangle\\n\\nThe following formulas involve the circumradius R and the inradius r:\\nR = \\\\sqrt{\\\\frac{a^2b^2c^2}{(a+b+c)(-a+b+c)(a-b+c)(a+b-c)}};\\nr = \\\\sqrt{\\\\frac{(-a+b+c)(a-b+c)(a+b-c)}{4(a+b+c)}}; \\n\\\\frac{1}{r} = \\\\frac{1}{h_a} + \\\\frac{1}{h_b} + \\\\frac{1}{h_c}\",\n \"Triangle\\n\\nwhere ha etc. are the altitudes to the subscripted sides;\\n\\\\frac{r}{R} \\\\frac{4 T^{2}}{sabc} \\n \\\\cos \\\\alpha + \\\\cos \\\\beta + \\\\cos \\\\gamma -1;Longuet-Higgins, Michael S., \\\"On the ratio of the inradius to the circumradius of a triangle\\\", Mathematical Gazette 87, March 2003, 119–120.\",\n \"Triangle\\n\\nand\\n2Rr = \\\\frac{abc}{a+b+c}.\",\n \"Triangle\\n\\nThe product of two sides of a triangle equals the altitude to the third side times the diameter of the circumcircle:Altshiller-Court, Nathan, College Geometry, Dover, 2007.\",\n \"Triangle\\n\\nabh_cD, \\\\, \\\\, bc\\nh_aD, \\\\, \\\\, ca=h_bD.\",\n \"Triangle\\n\\nAdjacent triangles\",\n \"Triangle\\n\\nSuppose two adjacent but non-overlapping triangles share the same side of length f and share the same circumcircle, so that the side of length f is a chord of the circumcircle and the triangles have side lengths (a, b, f) and (c, d, f), with the two triangles together forming a cyclic quadrilateral with side lengths in sequence (a, b, c, d). ThenJohnson, Roger A., Advanced Euclidean Geometry, Dover Publ. Co., 2007\\nf^2 = \\\\frac{(ac+bd)(ad+bc)}{(ab+cd)}. \\\\,\",\n \"Triangle\\n\\nCentroid\",\n \"Triangle\\n\\nLet G be the centroid of a triangle with vertices A, B, and C, and let P be any interior point. Then the distances between the points are related by\\n(PA)^2 + (PB)^2 +(PC)^2 =(GA)^2 + (GB)^2 + (GC)^2 +3(PG)^2. \\\\,\",\n \"Triangle\\n\\nThe sum of the squares of the triangle's sides equals three times the sum of the squared distances of the centroid from the vertices:\",\n \"Triangle\\n\\nAB^2+BC^2+CA^2=3(GA^2+GB^2+GC^2).\",\n \"Triangle\\n\\nLet qa, qb, and qc be the distances from the centroid to the sides of lengths a, b, and c. Then\\n \\\\frac{q_a}{q_b} \\\\frac{b}{a}, \\\\ \\\\ \\\\ \\\\ \\\\frac{q_b}{q_c} \\n \\\\frac{c}{b}, \\\\ \\\\ \\\\ \\\\ \\\\frac{q_a}{q_c} = \\\\frac{c}{a} \\\\,\",\n \"Triangle\\n\\nand\\nq_a \\\\cdot a q_b \\\\cdot b \\n q_c \\\\cdot c = \\\\frac{2}{3} T. \\\\,\",\n \"Triangle\\n\\nCircumcenter, incenter, and orthocenter\",\n \"Triangle\\n\\nCarnot's Theorem states that the sum of the distances from the circumcenter to the three sides equals the sum of the circumradius and the inradius. Here a segment's length is considered to be negative if and only if the segment lies entirely outside the triangle. This method is especially useful for deducing the properties of more abstract forms of triangles, such as the ones induced by Lie algebras, that otherwise have the same properties as usual triangles.\",\n \"Triangle\\n\\nEuler's theorem states that the distance d between the circumcenter and the incenter is given by\\n\\\\displaystyle d^2=R(R-2r)\",\n \"Triangle\\n\\nor equivalently\\n\\\\frac{1}{R-d} + \\\\frac{1}{R+d} = \\\\frac{1}{r},\",\n \"Triangle\\n\\nwhere R is the circumradius and r is the inradius. Thus for all triangles R ≥ 2r, with equality holding for equilateral triangles.\",\n \"Triangle\\n\\nIf we denote that the orthocenter divides one altitude into segments of lengths u and v, another altitude into segment lengths w and x, and the third altitude into segment lengths y and z, then uv wx \\n yz.\",\n \"Triangle\\n\\nThe distance from a side to the circumcenter equals half the distance from the opposite vertex to the orthocenter.\",\n \"Triangle\\n\\nThe sum of the squares of the distances from the vertices to the orthocenter plus the sum of the squares of the sides equals twelve times the square of the circumradius.\",\n \"Triangle\\n\\nAngles\",\n \"Triangle\\n\\nFor any triangle,\",\n \"Triangle\\n\\nab\\\\cos C+c\\\\cos B, \\\\quad b\\nc\\\\cos A+a\\\\cos C, \\\\quad c=a\\\\cos B+b\\\\cos A.\",\n \"Triangle\\n\\nMorley's trisector theorem\",\n \"Triangle\\n\\nMorley's trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the Morley triangle.\",\n \"Triangle\\n\\nFigures inscribed in a triangle\",\n \"Triangle\\n\\nConics\",\n \"Triangle\\n\\nAs discussed above, every triangle has a unique inscribed circle (incircle) that is interior to the triangle and tangent to all three sides.\",\n \"Triangle\\n\\nEvery triangle has a unique Steiner inellipse which is interior to the triangle and tangent at the midpoints of the sides. Marden's theorem shows how to find the foci of this ellipse. This ellipse has the greatest area of any ellipse tangent to all three sides of the triangle.\",\n \"Triangle\\n\\nThe Mandart inellipse of a triangle is the ellipse inscribed within the triangle tangent to its sides at the contact points of its excircles.\",\n \"Triangle\\n\\nFor any ellipse inscribed in a triangle ABC, let the foci be P and Q. Then\",\n \"Triangle\\n\\n\\\\frac{\\\\overline{PA} \\\\cdot \\\\overline{QA}}{\\\\overline{CA} \\\\cdot \\\\overline{AB}} + \\\\frac{\\\\overline{PB} \\\\cdot \\\\overline{QB}}{\\\\overline{AB} \\\\cdot \\\\overline{BC}} + \\\\frac{\\\\overline{PC} \\\\cdot \\\\overline{QC}}{\\\\overline{BC} \\\\cdot \\\\overline{CA}} = 1.\",\n \"Triangle\\n\\nConvex polygon\",\n \"Triangle\\n\\nEvery convex polygon with area T can be inscribed in a triangle of area at most equal to 2T. Equality holds (exclusively) for a parallelogram.\",\n \"Triangle\\n\\nHexagon\",\n \"Triangle\\n\\nThe Lemoine hexagon is a cyclic hexagon with vertices given by the six intersections of the sides of a triangle with the three lines that are parallel to the sides and that pass through its symmedian point. In either its simple form or its self-intersecting form, the Lemoine hexagon is interior to the triangle with two vertices on each side of the triangle.\",\n \"Triangle\\n\\nSquares\",\n \"Triangle\\n\\nEvery acute triangle has three inscribed squares (squares in its interior such that all four of a square's vertices lie on a side of the triangle, so two of them lie on the same side and hence one side of the square coincides with part of a side of the triangle). In a right triangle two of the squares coincide and have a vertex at the triangle's right angle, so a right triangle has only two distinct inscribed squares. An obtuse triangle has only one inscribed square, with a side coinciding with part of the triangle's longest side. Within a given triangle, a longer common side is associated with a smaller inscribed square. If an inscribed square has side of length qa and the triangle has a side of length a, part of which side coincides with a side of the square, then qa, a, the altitude ha from the side a, and the triangle's area T are related according to \\nq_a\\\\frac{2Ta}{a^2+2T}\\n\\\\frac{ah_a}{a+h_a}.\",\n \"Triangle\\n\\nThe largest possible ratio of the area of the inscribed square to the area of the triangle is 1/2, which occurs when , , and the altitude of the triangle from the base of length a is equal to a. The smallest possible ratio of the side of one inscribed square to the side of another in the same non-obtuse triangle is 2\\\\sqrt{2}/3 0.94....Victor Oxman and Moshe Stupel, \\\"Why Are the Side Lengths of the Squares Inscribed in a Triangle so Close to Each Other?\\\", Forum Geometricorum 13 (2013) 113–115. http://forumgeom.fau.edu/FG2013volume13/FG201311index.html Both of these extreme cases occur for the isosceles right triangle.\",\n \"Triangle\\n\\nTriangles\",\n \"Triangle\\n\\nFrom an interior point in a reference triangle, the nearest points on the three sides serve as the vertices of the pedal triangle of that point. If the interior point is the circumcenter of the reference triangle, the vertices of the pedal triangle are the midpoints of the reference triangle's sides, and so the pedal triangle is called the midpoint triangle or medial triangle. The midpoint triangle subdivides the reference triangle into four congruent triangles which are similar to the reference triangle.\",\n \"Triangle\\n\\nThe Gergonne triangle or intouch triangle of a reference triangle has its vertices at the three points of tangency of the reference triangle's sides with its incircle. The extouch triangle of a reference triangle has its vertices at the points of tangency of the reference triangle's excircles with its sides (not extended).\",\n \"Triangle\\n\\nFigures circumscribed about a triangle\",\n \"Triangle\\n\\nThe tangential triangle of a reference triangle (other than a right triangle) is the triangle whose sides are on the tangent lines to the reference triangle's circumcircle at its vertices.\",\n \"Triangle\\n\\nAs mentioned above, every triangle has a unique circumcircle, a circle passing through all three vertices, whose center is the intersection of the perpendicular bisectors of the triangle's sides.\",\n \"Triangle\\n\\nFurther, every triangle has a unique Steiner circumellipse, which passes through the triangle's vertices and has its center at the triangle's centroid. Of all ellipses going through the triangle's vertices, it has the smallest area.\",\n \"Triangle\\n\\nThe Kiepert hyperbola is the unique conic which passes through the triangle's three vertices, its centroid, and its circumcenter.\",\n \"Triangle\\n\\nOf all triangles contained in a given convex polygon, there exists a triangle with maximal area whose vertices are all vertices of the given polygon.\",\n \"Triangle\\n\\nSpecifying the location of a point in a triangle\",\n \"Triangle\\n\\nOne way to identify locations of points in (or outside) a triangle is to place the triangle in an arbitrary location and orientation in the Cartesian plane, and to use Cartesian coordinates. While convenient for many purposes, this approach has the disadvantage of all points' coordinate values being dependent on the arbitrary placement in the plane.\",\n \"Triangle\\n\\nTwo systems avoid that feature, so that the coordinates of a point are not affected by moving the triangle, rotating it, or reflecting it as in a mirror, any of which give a congruent triangle, or even by rescaling it to give a similar triangle:\",\n \"Triangle\\n\\n* Trilinear coordinates specify the relative distances of a point from the sides, so that coordinates x : y : z indicate that the ratio of the distance of the point from the first side to its distance from the second side is x : y , etc.\\n* Barycentric coordinates of the form \\\\alpha :\\\\beta :\\\\gamma specify the point's location by the relative weights that would have to be put on the three vertices in order to balance the otherwise weightless triangle on the given point.\",\n \"Triangle\\n\\nNon-planar triangles\",\n \"Triangle\\n\\nA non-planar triangle is a triangle which is not contained in a (flat) plane. Some examples of non-planar triangles in non-Euclidean geometries are spherical triangles in spherical geometry and hyperbolic triangles in hyperbolic geometry.\",\n \"Triangle\\n\\nWhile the measures of the internal angles in planar triangles always sum to 180°, a hyperbolic triangle has measures of angles that sum to less than 180°, and a spherical triangle has measures of angles that sum to more than 180°. A hyperbolic triangle can be obtained by drawing on a negatively curved surface, such as a saddle surface, and a spherical triangle can be obtained by drawing on a positively curved surface such as a sphere. Thus, if one draws a giant triangle on the surface of the Earth, one will find that the sum of the measures of its angles is greater than 180°; in fact it will be between 180° and 540°. In particular it is possible to draw a triangle on a sphere such that the measure of each of its internal angles is equal to 90°, adding up to a total of 270°.\",\n \"Triangle\\n\\nSpecifically, on a sphere the sum of the angles of a triangle is\\n180° × (1 + 4f),\",\n \"Triangle\\n\\nwhere f is the fraction of the sphere's area which is enclosed by the triangle. For example, suppose that we draw a triangle on the Earth's surface with vertices at the North Pole, at a point on the equator at 0° longitude, and a point on the equator at 90° West longitude. The great circle line between the latter two points is the equator, and the great circle line between either of those points and the North Pole is a line of longitude; so there are right angles at the two points on the equator. Moreover, the angle at the North Pole is also 90° because the other two vertices differ by 90° of longitude. So the sum of the angles in this triangle is . The triangle encloses 1/4 of the northern hemisphere (90°/360° as viewed from the North Pole) and therefore 1/8 of the Earth's surface, so in the formula ; thus the formula correctly gives the sum of the triangle's angles as 270°.\",\n \"Triangle\\n\\nFrom the above angle sum formula we can also see that the Earth's surface is locally flat: If we draw an arbitrarily small triangle in the neighborhood of one point on the Earth's surface, the fraction f of the Earth's surface which is enclosed by the triangle will be arbitrarily close to zero. In this case the angle sum formula simplifies to 180°, which we know is what Euclidean geometry tells us for triangles on a flat surface.\",\n \"Triangle\\n\\nTriangles in construction\",\n \"Triangle\\n\\nRectangles have been the most popular and common geometric form for buildings since the shape is easy to stack and organize; as a standard, it is easy to design furniture and fixtures to fit inside rectangularly shaped buildings. But triangles, while more difficult to use conceptually, provide a great deal of strength. As computer technology helps architects design creative new buildings, triangular shapes are becoming increasingly prevalent as parts of buildings and as the primary shape for some types of skyscrapers as well as building materials. In Tokyo in 1989, architects had wondered whether it was possible to build a 500-story tower to provide affordable office space for this densely packed city, but with the danger to buildings from earthquakes, architects considered that a triangular shape would have been necessary if such a building was ever to have been built (it hasn't by 2011).\",\n \"Triangle\\n\\nIn New York City, as Broadway crisscrosses major avenues, the resulting blocks are cut like triangles, and buildings have been built on these shapes; one such building is the triangularly shaped Flatiron Building which real estate people admit has a \\\"warren of awkward spaces that do not easily accommodate modern office furniture\\\" but that has not prevented the structure from becoming a landmark icon. Designers have made houses in Norway using triangular themes. Triangle shapes have appeared in churches as well as public buildings including colleges as well as supports for innovative home designs.\",\n \"Triangle\\n\\nTriangles are sturdy; while a rectangle can collapse into a parallelogram from pressure to one of its points, triangles have a natural strength which supports structures against lateral pressures. A triangle will not change shape unless its sides are bent or extended or broken or if its joints break; in essence, each of the three sides supports the other two. A rectangle, in contrast, is more dependent on the strength of its joints in a structural sense. Some innovative designers have proposed making bricks not out of rectangles, but with triangular shapes which can be combined in three dimensions. It is likely that triangles will be used increasingly in new ways as architecture increases in complexity. It is important to remember that triangles are strong in terms of rigidity, but while packed in a tessellating arrangement triangles are not as strong as hexagons under compression (hence the prevalence of hexagonal forms in nature). Tessellated triangles still maintain superior strength for cantilevering however, and this is the basis for one of the strongest man made structures, the tetrahedral truss.\"\n]","isConversational":false}}},{"rowIdx":1789,"cells":{"id":{"kind":"string","value":"tc_2762"},"question":{"kind":"string","value":"Which Swedish scientist had a temperature scale named after him?"},"answer":{"kind":"string","value":"Anders Celsius"},"answer_aliases":{"kind":"list like","value":["celsius anders","anders celsius"],"string":"[\n \"celsius anders\",\n \"anders celsius\"\n]","isConversational":false},"documents":{"kind":"list like","value":["Carl Linnaeus\n\nCarl Linnaeus (; 23 May 1707 – 10 January 1778), also known after his ennoblement as Carl von Linné , was a Swedish botanist, physician, and zoologist, who formalised the modern system of naming organisms called binomial nomenclature. He is known by the epithet \"father of modern taxonomy\". Many of his writings were in Latin, and his name is rendered in Latin as (after 1761 Carolus a Linné).","Carl Linnaeus\n\nLinnaeus was born in the countryside of Småland, in southern Sweden. He received most of his higher education at Uppsala University, and began giving lectures in botany there in 1730. He lived abroad between 1735 and 1738, where he studied and also published a first edition of his ' in the Netherlands. He then returned to Sweden, where he became professor of medicine and botany at Uppsala. In the 1740s, he was sent on several journeys through Sweden to find and classify plants and animals. In the 1750s and 1760s, he continued to collect and classify animals, plants, and minerals, and published several volumes. At the time of his death, he was one of the most acclaimed scientists in Europe.","Carl Linnaeus\n\nThe Swiss philosopher Jean-Jacques Rousseau sent him the message: \"Tell him I know no greater man on earth.\" The German writer Johann Wolfgang von Goethe wrote: \"With the exception of Shakespeare and Spinoza, I know no one among the no longer living who has influenced me more strongly.\" Swedish author August Strindberg wrote: \"Linnaeus was in reality a poet who happened to become a naturalist\". Among other compliments, Linnaeus has been called ' (Prince of Botanists), \"The Pliny of the North,\" and \"The Second Adam\". He is also considered as one of the founders of modern ecology.","Carl Linnaeus\n\nIn botany, the author abbreviation used to indicate Linnaeus as the authority for species' names is L. In older publications, sometimes the abbreviation \"Linn.\" is found (for instance in: Cheeseman, T.F. (1906) – Manual of the New Zealand Flora). Linnaeus' remains comprise the type specimen for the species Homo sapiens, following the International Code of Zoological Nomenclature, since the sole specimen he is known to have examined when writing the species description was himself.[http://www.nhm.ac.uk/hosted-sites/iczn/code/ ICZN Chapter 16, Article 72.4.1.1] – \"For a nominal species or subspecies established before 2000, any evidence, published or unpublished, may be taken into account to determine what specimens constitute the type series.\" and Article 73.1.2 – \"If the nominal species-group taxon is based on a single specimen, either so stated or implied in the original publication, that specimen is the holotype fixed by monotypy (see Recommendation 73F). If the taxon was established before 2000 evidence derived from outside the work itself may be taken into account [Art. 72.4.1.1] to help identify the specimen.\"","Carl Linnaeus\n\nBiography","Carl Linnaeus\n\nChildhood","Carl Linnaeus\n\nLinnæus was born in the village of Råshult in Småland, Sweden, on 23 May 1707. He was the first child of Nicolaus (Nils) Ingemarsson (who later adopted the family name Linnæus) and Christina Brodersonia. His siblings were Anna Maria Linnæa, Sofia Juliana Linnæa, Samuel Linnæus, and Emerentia Linnæa.","Carl Linnaeus\n\nOne of a long line of peasants and priests, Nils was an amateur botanist, a Lutheran minister, and the curate of the small village of Stenbrohult in Småland. Christina was the daughter of the rector of Stenbrohult, Samuel Brodersonius.","Carl Linnaeus\n\nA year after Linnæus' birth, his grandfather Samuel Brodersonius died, and his father Nils became the rector of Stenbrohult. The family moved into the rectory from the curate's house. Carl had one brother, Samuel (who would eventually succeed their father as rector of Stenbrohult and write a manual on beekeeping). and three sisters.","Carl Linnaeus\n\nEven in his early years, Linnæus seemed to have a liking for plants, flowers in particular. Whenever he was upset, he was given a flower, which immediately calmed him. Nils spent much time in his garden and often showed flowers to Linnaeus and told him their names. Soon Linnæus was given his own patch of earth where he could grow plants.","Carl Linnaeus\n\nCarl's father was the first in his ancestry to adopt a permanent surname. Before that, ancestors had used the patronymic naming system of Scandinavian countries: his father was named Ingemarsson after his father Ingemar Bengtsson. When Nils was admitted to the University of Lund, he had to take on a family name. He adopted the Latinate name Linnæus after a giant linden tree (or lime tree), ' in Swedish, that grew on the family homestead. This name was spelled with the æ ligature. When Carl was born, he was named Carl Linnæus, with his father's family name. The son also always spelled it with the æ ligature, both in handwritten documents and in publications. Carl's patronymic would have been Nilsson, as in Carl Nilsson Linnæus.","Carl Linnaeus\n\nEarly education","Carl Linnaeus\n\nLinnaeus' father began teaching him basic Latin, religion, and geography at an early age. When Linnaeus was seven, Nils decided to hire a tutor for him. The parents picked Johan Telander, a son of a local yeoman. Linnaeus did not like him, writing in his autobiography that Telander \"was better calculated to extinguish a child's talents than develop them.\"","Carl Linnaeus\n\nTwo years after his tutoring had begun, he was sent to the Lower Grammar School at Växjö in 1717. Linnaeus rarely studied, often going to the countryside to look for plants. He reached the last year of the Lower School when he was fifteen, which was taught by the headmaster, Daniel Lannerus, who was interested in botany. Lannerus noticed Linnaeus' interest in botany and gave him the run of his garden.","Carl Linnaeus\n\nHe also introduced him to Johan Rothman, the state doctor of Småland and a teacher at Katedralskolan (a gymnasium) in Växjö. Also a botanist, Rothman broadened Linnaeus' interest in botany and helped him develop an interest in medicine. By the age of 17, Linnaeus had become well acquainted with the existing botanical literature. He remarks in his journal \"read day and night, knowing like the back of my hand, Arvidh Månsson's Rydaholm Book of Herbs, Tillandz's Flora Åboensis, Palmberg's Serta Florea Suecana, Bromelii Chloros Gothica and Rudbeckii Hortus Upsaliensis....\"","Carl Linnaeus\n\nLinnaeus entered the Växjö Katedralskola in 1724, where he studied mainly Greek, Hebrew, theology and mathematics, a curriculum designed for boys preparing for the priesthood. In the last year at the gymnasium, Linnaeus' father visited to ask the professors how his son's studies were progressing; to his dismay, most said that the boy would never become a scholar. Rothman believed otherwise, suggesting Linnaeus could have a future in medicine. The doctor offered to have Linnaeus live with his family in Växjö and to teach him physiology and botany. Nils accepted this offer.","Carl Linnaeus\n\nUniversity studies","Carl Linnaeus\n\nLund","Carl Linnaeus\n\nRothman showed Linnaeus that botany was a serious subject. He taught Linnaeus to classify plants according to Tournefort's system. Linnaeus was also taught about the sexual reproduction of plants, according to Sébastien Vaillant. In 1727, Linnaeus, age 21, enrolled in Lund University in Skåne. He was registered as ', the Latin form of his full name, which he also used later for his Latin publications.","Carl Linnaeus\n\nProfessor Kilian Stobæus, natural scientist, physician and historian, offered Linnaeus tutoring and lodging, as well as the use of his library, which included many books about botany. He also gave the student free admission to his lectures. In his spare time, Linnaeus explored the flora of Skåne, together with students sharing the same interests.","Carl Linnaeus\n\nUppsala","Carl Linnaeus\n\nIn August 1728, Linnaeus decided to attend Uppsala University on the advice of Rothman, who believed it would be a better choice if Linnaeus wanted to study both medicine and botany. Rothman based this recommendation on the two professors who taught at the medical faculty at Uppsala: Olof Rudbeck the Younger and Lars Roberg. Although Rudbeck and Roberg had undoubtedly been good professors, by then they were older and not so interested in teaching. Rudbeck no longer gave public lectures, and had others stand in for him. The botany, zoology, pharmacology and anatomy lectures were not in their best state. In Uppsala, Linnaeus met a new benefactor, Olof Celsius, who was a professor of theology and an amateur botanist. He received Linnaeus into his home and allowed him use of his library, which was one of the richest botanical libraries in Sweden.","Carl Linnaeus\n\nIn 1729, Linnaeus wrote a thesis, ' on plant sexual reproduction. This attracted the attention of Rudbeck; in May 1730, he selected Linnaeus to give lectures at the University although the young man was only a second-year student. His lectures were popular, and Linnaeus often addressed an audience of 300 people. In June, Linnaeus moved from Celsius' house to Rudbeck's to become the tutor of the three youngest of his 24 children. His friendship with Celsius did not wane and they continued their botanical expeditions. Over that winter, Linnaeus began to doubt Tournefort's system of classification and decided to create one of his own. His plan was to divide the plants by the number of stamens and pistils. He began writing several books, which would later result in, for example, ' and '. He also produced a book on the plants grown in the Uppsala Botanical Garden, '.","Carl Linnaeus\n\nRudbeck's former assistant, Nils Rosén, returned to the University in March 1731 with a degree in medicine. Rosén started giving anatomy lectures and tried to take over Linnaeus' botany lectures, but Rudbeck prevented that. Until December, Rosén gave Linnaeus private tutoring in medicine. In December, Linnaeus had a \"disagreement\" with Rudbeck's wife and had to move out of his mentor's house; his relationship with Rudbeck did not appear to suffer. That Christmas, Linnaeus returned home to Stenbrohult to visit his parents for the first time in about three years. His mother had disapproved of his failing to become a priest, but she was pleased to learn he was teaching at the University.","Carl Linnaeus\n\nExpedition to Lapland","Carl Linnaeus\n\nDuring a visit with his parents, Linnaeus told them about his plan to travel to Lapland; Rudbeck had made the journey in 1695, but the detailed results of his exploration were lost in a fire seven years afterwards. Linnaeus' hope was to find new plants, animals and possibly valuable minerals. He was also curious about the customs of the native Sami people, reindeer-herding nomads who wandered Scandinavia's vast tundras. In April 1732, Linnaeus was awarded a grant from the Royal Society of Sciences in Uppsala for his journey.","Carl Linnaeus\n\nLinnaeus began his expedition from Uppsala on May 12, 1732, just before he turned 25. He travelled on foot and horse, bringing with him his journal, botanical and ornithological manuscripts and sheets of paper for pressing plants. Near Gävle he found great quantities of Campanula serpyllifolia, later known as Linnaea borealis, the twinflower that would become his favourite. He sometimes dismounted on the way to examine a flower or rock and was particularly interested in mosses and lichens, the latter a main part of the diet of the reindeer, a common and economically important animal in Lapland.","Carl Linnaeus\n\nLinnaeus travelled clockwise around the coast of the Gulf of Bothnia, making major inland incursions from Umeå, Luleå and Tornio. He returned from his six-month-long, over 2000 km expedition in October, having gathered and observed many plants, birds and rocks. Although Lapland was a region with limited biodiversity, Linnaeus described about 100 previously unidentified plants. These became the basis of his book '. However, on the expedition to Lapland, Linnaeus used Latin names to describe organisms because he had not yet developed the binomial system.","Carl Linnaeus\n\nIn ' Linnaeus' ideas about nomenclature and classification were first used in a practical way, making this the first proto-modern Flora. The account covered 534 species, used the Linnaean classification system and included, for the described species, geographical distribution and taxonomic notes. It was Augustin Pyramus de Candolle who attributed Linnaeus with ' as the first example in the botanical genre of Flora writing. Botanical historian E. L. Greene described ' as \"the most classic and delightful\" of Linnaeus's works.","Carl Linnaeus\n\nIt was also during this expedition that Linnaeus had a flash of insight regarding the classification of mammals. Upon observing the lower jawbone of a horse at the side of a road he was traveling, Linnaeus remarked: \"If I only knew how many teeth and of what kind every animal had, how many teats and where they were placed, I should perhaps be able to work out a perfectly natural system for the arrangement of all quadrupeds.\"","Carl Linnaeus\n\nIn 1734, Linnaeus led a small group of students to Dalarna. Funded by the Governor of Dalarna, the expedition was to catalogue known natural resources and discover new ones, but also to gather intelligence on Norwegian mining activities at Røros.","Carl Linnaeus\n\nDoctorate","Carl Linnaeus\n\nBack in Uppsala, Linnaeus' relations with Nils Rosén worsened, and thus he gladly accepted an invitation from the student Claes Sohlberg to spend the Christmas holiday in Falun with Sohlberg's family. Sohlberg's father was a mining inspector, and let Linnaeus visit the mines near Falun. Sohlberg's father suggested to Linnaeus he should bring Sohlberg to the Dutch Republic and continue to tutor him there for an annual salary. At that time, the Dutch Republic was one of the most revered places to study natural history and a common place for Swedes to take their doctoral degree; Linnaeus, who was interested in both of these, accepted.","Carl Linnaeus\n\nIn April 1735, Linnaeus and Sohlberg set out for the Netherlands, with Linnaeus to take a doctoral degree in medicine at the University of Harderwijk. On the way, they stopped in Hamburg, where they met the mayor, who proudly showed them a wonder of nature which he possessed: the taxidermied remains of a seven-headed hydra. Linnaeus quickly discovered it was a fake: jaws and clawed feet from weasels and skins from snakes had been glued together. The provenance of the hydra suggested to Linnaeus it had been manufactured by monks to represent the Beast of Revelation. As much as this may have upset the mayor, Linnaeus made his observations public and the mayor's dreams of selling the hydra for an enormous sum were ruined. Fearing his wrath, Linnaeus and Sohlberg had to leave Hamburg quickly.","Carl Linnaeus\n\nWhen Linnaeus reached Harderwijk, he began working toward a degree immediately; at the time, Harderwijk was known for awarding \"instant\" degrees after as little as a week. First he handed in a thesis on the cause of malaria he had written in Sweden, which he then defended in a public debate. His dissertation, submitted on 23 June, was titled Dissertatio medica inauguralis in qua exhibetur hypothesis nova de febrium intermittentium causa (\"Inaugural thesis in medicine, in which a new hypothesis on the cause of intermittent fevers is presented\"). He concluded that malaria arose only in places with clay-rich soil. He is now known to have been wrong about the cause, not having a microscope good enough to see malarial parasites, which were spread by mosquitoes breeding in the water that collected in ruts and puddles. But he was right in predicting that traditional Chinese medicine, including the use of wormwood (Artemisia), is a potential source of antimalarial drug. (Artemisinins, derived from wormwood, are now the principal antimalarial drugs. )","Carl Linnaeus\n\nThe next step was to take an oral examination and to diagnose a patient. After less than two weeks, he took his degree and became a doctor, at the age of 28. During the summer, Linnaeus met a friend from Uppsala, Peter Artedi. Before their departure from Uppsala, Artedi and Linnaeus had decided should one of them die, the survivor would finish the other's work. Ten weeks later, Artedi drowned in one of the canals of Amsterdam, and his unfinished manuscript on the classification of fish was left to Linnaeus to complete.","Carl Linnaeus\n\nPublishing of '","Carl Linnaeus\n\nOne of the first scientists Linnaeus met in the Netherlands was Johan Frederik Gronovius to whom Linnaeus showed one of the several manuscripts he had brought with him from Sweden. The manuscript described a new system for classifying plants. When Gronovius saw it, he was very impressed, and offered to help pay for the printing. With an additional monetary contribution by the Scottish doctor Isaac Lawson, the manuscript was published as ' (1735).","Carl Linnaeus\n\nLinnaeus became acquainted with one of the most respected physicians and botanists in the Netherlands, Herman Boerhaave, who tried to convince Linnaeus to make a career there. Boerhaave offered him a journey to South Africa and America, but Linnaeus declined, stating he would not stand the heat. Instead, Boerhaave convinced Linnaeus that he should visit the botanist Johannes Burman. After his visit, Burman, impressed with his guest's knowledge, decided Linnaeus should stay with him during the winter. During his stay, Linnaeus helped Burman with his '. Burman also helped Linnaeus with the books on which he was working: ' and '.","Carl Linnaeus\n\nGeorge Clifford, Philip Miller, and Johann Jacob Dillenius","Carl Linnaeus\n\nIn August, during Linnaeus' stay with Burman, he met George Clifford III, a director of the Dutch East India Company and the owner of a rich botanical garden at the estate of Hartekamp in Heemstede. Clifford was very impressed with Linnaeus' ability to classify plants, and invited him to become his physician and superintendent of his garden. Linnaeus had already agreed to stay with Burman over the winter, and could thus not accept immediately. However, Clifford offered to compensate Burman by offering him a copy of Sir Hans Sloane's Natural History of Jamaica, a rare book, if he let Linnaeus stay with him, and Burman accepted. On 24 September 1735, Linnaeus moved to Hartekamp to become personal physician to Clifford, and curator of Clifford's herbarium. He was paid 1,000 florins a year, with free board and lodging. Though the agreement was only for a winter of that year, Linnaeus practically stayed there till 1738.","Carl Linnaeus\n\nIt was here that he wrote a book Hortus Cliffortianus, in the preface of which he described his experience as \"the happiest time of my life.\" (A portion of Hartekamp was declared as public garden in April 1956 by the Heemstede local authority, and was named \"Linnaeushof\". It eventually became, as it is claimed, the biggest playground in Europe. )","Carl Linnaeus\n\nIn July 1736, Linnaeus travelled to England, at Clifford's expense. He went to London to visit Sir Hans Sloane, a collector of natural history, and to see his cabinet, as well as to visit the Chelsea Physic Garden and its keeper, Philip Miller. He taught Miller about his new system of subdividing plants, as described in '. Miller was in fact reluctant to use the new binomial nomenclature, preferring the classifications of Joseph Pitton de Tournefort and John Ray at first. Linnaeus, nevertheless, applauded Miller's Gardeners Dictionary, The conservative Scot actually retained in his dictionary a number of pre-Linnaean binomial signifiers discarded by Linnaeus but which have been retained by modern botanists. He only fully changed to the Linnaean system in the edition of The Gardeners Dictionary of 1768. Miller ultimately was impressed, and from then on started to arrange the garden according to Linnaeus' system.","Carl Linnaeus\n\nLinnaeus also traveled to Oxford University to visit the botanist Johann Jacob Dillenius. He failed to make Dillenius publicly fully accept his new classification system, though the two men remained in correspondence for many years afterwards. Linnaeus dedicated his Critica botanica to him, as opus botanicum quo absolutius mundus non vidit. Linnaeus would later name a genus of tropical tree Dillenia in his honor. He then returned to Hartekamp, bringing with him many specimens of rare plants. The next year, he published ', in which he described 935 genera of plants, and shortly thereafter he supplemented it with ', with another sixty (sexaginta) genera.","Carl Linnaeus\n\nHis work at Hartekamp led to another book, ', a catalogue of the botanical holdings in the herbarium and botanical garden of Hartekamp. He wrote it in nine months (completed in July 1737), but it was not published until 1738. It contains the first use of the name Nepenthes, which Linnaeus used to describe a genus of pitcher plants. \"If this is not Helen's Nepenthes, it certainly will be for all botanists. What botanist would not be filled with admiration if, after a long journey, he should find this wonderful plant. In his astonishment past ills would be forgotten when beholding this admirable work of the Creator!\" (translated from Latin by Harry Veitch)","Carl Linnaeus\n\nLinnaeus stayed with Clifford at Hartekamp until 18 October 1737 (new style), when he left the house to return to Sweden. Illness and the kindness of Dutch friends obliged him to stay some months longer in Holland. In May 1738, he set out for Sweden again. On the way home, he stayed in Paris for about a month, visiting botanists such as Antoine de Jussieu. After his return, Linnaeus never left Sweden again.","Carl Linnaeus\n\nReturn to Sweden","Carl Linnaeus\n\nWhen Linnaeus returned to Sweden on 28 June 1738, he went to Falun, where he entered into an engagement to Sara Elisabeth Moræa. Three months later, he moved to Stockholm to find employment as a physician, and thus to make it possible to support a family. Once again, Linnaeus found a patron; he became acquainted with Count Carl Gustav Tessin, who helped him get work as a physician at the Admiralty. During this time in Stockholm, Linnaeus helped found the Royal Swedish Academy of Science; he became the first Praeses in the academy by drawing of lots.","Carl Linnaeus\n\nBecause his finances had improved and were now sufficient to support a family, he received permission to marry his fiancée, Sara Elisabeth Moræa. Their wedding was held 26 June 1739. Seven months later, Sara gave birth to their first son, Carl. Two years later, a daughter, Elisabeth Christina, was born, and the subsequent year Sara gave birth to Sara Magdalena, who died when 15 days old. Sara and Linnaeus would later have four other children: Lovisa, Sara Christina, Johannes and Sophia.","Carl Linnaeus\n\nIn May 1741, Linnaeus was appointed Professor of Medicine at Uppsala University, first with responsibility for medicine-related matters. Soon, he changed place with the other Professor of Medicine, Nils Rosén, and thus was responsible for the Botanical Garden (which he would thoroughly reconstruct and expand), botany and natural history, instead. In October that same year, his wife and nine-year-old son followed him to live in Uppsala.","Carl Linnaeus\n\nÖland and Gotland","Carl Linnaeus\n\nTen days after he was appointed Professor, he undertook an expedition to the island provinces of Öland and Gotland with six students from the university, to look for plants useful in medicine. First, they travelled to Öland and stayed there until 21 June, when they sailed to Visby in Gotland. Linnaeus and the students stayed on Gotland for about a month, and then returned to Uppsala. During this expedition, they found 100 previously unrecorded plants. The observations from the expedition were later published in ', written in Swedish. Like ', it contained both zoological and botanical observations, as well as observations concerning the culture in Öland and Gotland.","Carl Linnaeus\n\nDuring the summer of 1745, Linnaeus published two more books: ' and '. ' was a strictly botanical book, while ' was zoological. Anders Celsius had created the temperature scale named after him in 1742. Celsius' scale was inverted compared to today, the boiling point at 0 °C and freezing point at 100 °C. In 1745, Linnaeus inverted the scale to its present standard.","Carl Linnaeus\n\nVästergötland","Carl Linnaeus\n\nIn the summer of 1746, Linnaeus was once again commissioned by the Government to carry out an expedition, this time to the Swedish province of Västergötland. He set out from Uppsala on 12 June and returned on 11 August. On the expedition his primary companion was Erik Gustaf Lidbeck, a student who had accompanied him on his previous journey. Linnaeus described his findings from the expedition in the book ', published the next year. After returning from the journey the Government decided Linnaeus should take on another expedition to the southernmost province Scania. This journey was postponed, as Linnaeus felt too busy.","Carl Linnaeus\n\nIn 1747, Linnaeus was given the title archiater, or chief physician, by the Swedish king Adolf Frederick—a mark of great respect. The same year he was elected member of the Academy of Sciences in Berlin.","Carl Linnaeus\n\nScania","Carl Linnaeus\n\nIn the spring of 1749, Linnaeus could finally journey to Scania, again commissioned by the Government. With him he brought his student, Olof Söderberg. On the way to Scania, he made his last visit to his brothers and sisters in Stenbrohult since his father had died the previous year. The expedition was similar to the previous journeys in most aspects, but this time he was also ordered to find the best place to grow walnut and Swedish whitebeam trees; these trees were used by the military to make rifles. The journey was successful, and Linnaeus' observations were published the next year in '.","Carl Linnaeus\n\nRector of Uppsala University","Carl Linnaeus\n\nIn 1750, Linnaeus became rector of Uppsala University, starting a period where natural sciences were esteemed. Perhaps the most important contribution he made during his time at Uppsala was to teach; many of his students travelled to various places in the world to collect botanical samples. Linnaeus called the best of these students his \"apostles\". His lectures were normally very popular and were often held in the Botanical Garden. He tried to teach the students to think for themselves and not trust anybody, not even him. Even more popular than the lectures were the botanical excursions made every Saturday during summer, where Linnaeus and his students explored the flora and fauna in the vicinity of Uppsala.","Carl Linnaeus\n\nPhilosophia Botanica","Carl Linnaeus\n\nLinnaeus published Philosophia Botanica in 1751. The book contained a complete survey of the taxonomy system he had been using in his earlier works. It also contained information of how to keep a journal on travels and how to maintain a botanical garden.","Carl Linnaeus\n\nNutrix Noverca","Carl Linnaeus\n\nDuring Linnaeus' time it was normal for upper class women to have wet nurses for their babies. Linnaeus joined an ongoing campaign to end this practice in Sweden and promote breast-feeding by mothers. In 1752 Linnaeus published a thesis along with Frederick Lindberg, a physician student, based on their experiences. In the tradition of the period, this dissertation was essentially an idea of the presiding reviewer (prases) expounded upon by the student. Linnaeus' dissertation was translated into French by J.E. Gilibert in 1770 as La Nourrice marâtre, ou Dissertation sur les suites funestes du nourrisage mercénaire. Linnaeus suggested that children might absorb the personality of their wet nurse through the milk. He admired the child care practices of the Lapps and pointed out how healthy their babies were compared to those of Europeans who employed wet nurses. He compared the behaviour of wild animals and pointed out how none of them denied their newborns their breastmilk. It is thought that his activism played a role in his choice of the term Mammalia for the class of organisms.","Carl Linnaeus\n\nSpecies Plantarum","Carl Linnaeus\n\nLinnaeus published Species Plantarum, the work which is now internationally accepted as the starting point of modern botanical nomenclature, in 1753. The first volume was issued on 24 May, the second volume followed on 16 August of the same year. The book contained 1,200 pages and was published in two volumes; it described over 7,300 species. The same year the king dubbed him knight of the Order of the Polar Star, the first civilian in Sweden to become a knight in this order. He was then seldom seen not wearing the order.","Carl Linnaeus\n\nEnnoblement","Carl Linnaeus\n\nLinnaeus felt Uppsala was too noisy and unhealthy, so he bought two farms in 1758: Hammarby and Sävja. The next year, he bought a neighbouring farm, Edeby. He spent the summers with his family at Hammarby; initially it only had a small one-storey house, but in 1762 a new, larger main building was added. In Hammarby, Linnaeus made a garden where he could grow plants that could not be grown in the Botanical Garden in Uppsala. He began constructing a museum on a hill behind Hammarby in 1766, where he moved his library and collection of plants. A fire that destroyed about one third of Uppsala and had threatened his residence there necessitated the move.","Carl Linnaeus\n\nSince the initial release of ' in 1735, the book had been expanded and reprinted several times; the tenth edition was released in 1758. This edition established itself as the starting point for zoological nomenclature, the equivalent of '.","Carl Linnaeus\n\nThe Swedish king Adolf Frederick granted Linnaeus nobility in 1757, but he was not ennobled until 1761. With his ennoblement, he took the name Carl von Linné (Latinized as '), 'Linné' being a shortened and gallicised version of 'Linnæus', and the German nobiliary particle 'von' signifying his ennoblement. The noble family's coat of arms prominently features a twinflower, one of Linnaeus' favourite plants; it was given the scientific name Linnaea borealis in his honour by Gronovius. The shield in the coat of arms is divided into thirds: red, black and green for the three kingdoms of nature (animal, mineral and vegetable) in Linnaean classification; in the centre is an egg \"to denote Nature, which is continued and perpetuated in ovo.\" At the bottom is a phrase in Latin, borrowed from the Aeneid, which reads \"Famam extendere factis\": we extend our fame by our deeds. Linnaeus inscribed this personal motto in books that were gifted to him by friends.","Carl Linnaeus\n\nAfter his ennoblement, Linnaeus continued teaching and writing. His reputation had spread over the world, and he corresponded with many different people. For example, Catherine II of Russia sent him seeds from her country. He also corresponded with Giovanni Antonio Scopoli, \"the Linnaeus of the Austrian Empire\", who was a doctor and a botanist in Idrija, Duchy of Carniola (nowadays Slovenia). Scopoli communicated all of his research, findings, and descriptions (for example of the olm and the dormouse, two little animals hitherto unknown to Linnaeus). Linnaeus greatly respected him and showed great interest in his work. He named a solanaceous genus, Scopolia, the source of scopolamine, after him. Because of a great distance, they never met.","Carl Linnaeus\n\nFinal years","Carl Linnaeus\n\nLinnaeus was relieved of his duties in the Royal Swedish Academy of Science in 1763, but continued his work there as usual for more than ten years after. He stepped down as rector at Uppsala University in December 1772, mostly due to his declining health.","Carl Linnaeus\n\nLinnaeus' last years were troubled by illness. He had suffered from a disease called the Uppsala fever in 1764, but survived thanks to the care of Rosén. He developed sciatica in 1773, and the next year, he had a stroke which partially paralysed him. He suffered a second stroke in 1776, losing the use of his right side and leaving him bereft of his memory; while still able to admire his own writings, he could not recognise himself as their author.","Carl Linnaeus\n\nIn December 1777, he had another stroke which greatly weakened him, and eventually led to his death on 10 January 1778 in Hammarby. Despite his desire to be buried in Hammarby, he was buried in Uppsala Cathedral on 22 January.","Carl Linnaeus\n\nHis library and collections were left to his widow Sara and their children. Joseph Banks, an English botanist, wanted to buy the collection, but his son Carl refused and moved the collection to Uppsala. However, in 1783 Carl died and Sara inherited the collection, having outlived both her husband and son. She tried to sell it to Banks, but he was no longer interested; instead an acquaintance of his agreed to buy the collection. The acquaintance was a 24-year-old medical student, James Edward Smith, who bought the whole collection: 14,000 plants, 3,198 insects, 1,564 shells, about 3,000 letters and 1,600 books. Smith founded the Linnean Society of London five years later.","Carl Linnaeus\n\nThe von Linné name ended with his son Carl, who never married. His other son, Johannes, had died aged 3. There are over two hundred descendants of Linnaeus through two of his daughters.","Carl Linnaeus\n\nApostles","Carl Linnaeus\n\nDuring Linnaeus' time as Professor and Rector of Uppsala University, he taught many devoted students, 17 of whom he called \"apostles\". They were the most promising, most committed students, and all of them made botanical expeditions to various places in the world, often with his help. The amount of this help varied; sometimes he used his influence as Rector to grant his apostles a scholarship or a place on an expedition. To most of the apostles he gave instructions of what to look for on their journeys. Abroad, the apostles collected and organised new plants, animals and minerals according to Linnaeus' system. Most of them also gave some of their collection to Linnaeus when their journey was finished. Thanks to these students, the Linnaean system of taxonomy spread through the world without Linnaeus ever having to travel outside Sweden after his return from Holland. The British botanist William T. Stearn notes without Linnaeus' new system, it would not have been possible for the apostles to collect and organise so many new specimens. Many of the apostles died during their expeditions.","Carl Linnaeus\n\nEarly expeditions","Carl Linnaeus\n\nChristopher Tärnström, the first apostle and a 43-year-old pastor with a wife and children, made his journey in 1746. He boarded a Swedish East India Company ship headed for China. Tärnström never reached his destination, dying of a tropical fever on Côn Sơn Island the same year. Tärnström's widow blamed Linnaeus for making her children fatherless, causing Linnaeus to prefer sending out younger, unmarried students after Tärnström. Six other apostles later died on their expeditions, including Pehr Forsskål and Pehr Löfling.","Carl Linnaeus\n\nTwo years after Tärnström's expedition, Finnish-born Pehr Kalm set out as the second apostle to North America. There he spent two-and-a-half years studying the flora and fauna of Pennsylvania, New York, New Jersey and Canada. Linnaeus was overjoyed when Kalm returned, bringing back with him many pressed flowers and seeds. At least 90 of the 700 North American species described in Species Plantarum had been brought back by Kalm.","Carl Linnaeus\n\nCook expeditions and Japan","Carl Linnaeus\n\nDaniel Solander was living in Linnaeus' house during his time as a student in Uppsala. Linnaeus was very fond of him, promising Solander his oldest daughter's hand in marriage. On Linnaeus' recommendation, Solander travelled to England in 1760, where he met the English botanist Joseph Banks. With Banks, Solander joined James Cook on his expedition to Oceania on the Endeavour in 1768–71. Solander was not the only apostle to journey with James Cook; Anders Sparrman followed on the Resolution in 1772–75 bound for, among other places, Oceania and South America. Sparrman made many other expeditions, one of them to South Africa.","Carl Linnaeus\n\nPerhaps the most famous and successful apostle was Carl Peter Thunberg, who embarked on a nine-year expedition in 1770. He stayed in South Africa for three years, then travelled to Japan. All foreigners in Japan were forced to stay on the island of Dejima outside Nagasaki, so it was thus hard for Thunberg to study the flora. He did, however, manage to persuade some of the translators to bring him different plants, and he also found plants in the gardens of Dejima. He returned to Sweden in 1779, one year after Linnaeus' death.","Carl Linnaeus\n\nMajor publications","Carl Linnaeus\n\nSystema Naturae","Carl Linnaeus\n\nThe first edition of ' was printed in the Netherlands in 1735. It was a twelve-page work. By the time it reached its 10th edition in 1758, it classified 4,400 species of animals and 7,700 species of plants. In it, the unwieldy names mostly used at the time, such as \"'\", were supplemented with concise and now familiar \"binomials\", composed of the generic name, followed by a specific epithet – in the case given, Physalis angulata. These binomials could serve as a label to refer to the species. Higher taxa were constructed and arranged in a simple and orderly manner. Although the system, now known as binomial nomenclature, was partially developed by the Bauhin brothers (see Gaspard Bauhin and Johann Bauhin) almost 200 years earlier, Linnaeus was the first to use it consistently throughout the work, including in monospecific genera, and may be said to have popularised it within the scientific community.","Carl Linnaeus\n\nAfter the decline in Linnaeus' health in the early 1770s, publication of editions of Systema Naturae went in two different directions. Another Swedish scientist, Johan Andreas Murray issued the Regnum Vegetabile section separately in 1774 as the Systema Vegetabilium, rather confusingly labelled the 13th edition. Meanwhile a 13th edition of the entire Systema appeared in parts between 1788 and 1793. It was through the Systema Vegetabilium that Linnaeus' work became widely known in England, following its translation from the Latin by the Lichfield Botanical Society as A System of Vegetables (1783–1785).","Carl Linnaeus\n\n'","Carl Linnaeus\n\n' (or, more fully, ') was first published in 1753, as a two-volume work. Its prime importance is perhaps that it is the primary starting point of plant nomenclature as it exists today.","Carl Linnaeus\n\n'","Carl Linnaeus\n\n' was first published in 1737, delineating plant genera. Around 10 editions were published, not all of them by Linnaeus himself; the most important is the 1754 fifth edition. In it Linnaeus divided the plant Kingdom into 24 classes. One, Cryptogamia, included all the plants with concealed reproductive parts (algae, fungi, mosses and liverworts and ferns).","Carl Linnaeus\n\n'","Carl Linnaeus\n\n' (1751) was a summary of Linnaeus' thinking on plant classification and nomenclature, and an elaboration of the work he had previously published in ' (1736) and ' (1737). Other publications forming part of his plan to reform the foundations of botany include his ' and ': all were printed in Holland (as well as ' (1737) and ' (1735)), the Philosophia being simultaneously released in Stockholm.","Carl Linnaeus\n\nLinnaean collections","Carl Linnaeus\n\nAt the end of his lifetime the Linnean collection in Uppsala was considered one of the finest collections of natural history objects in Sweden. Next to his own collection he had also built up a museum for the university of Uppsala, which was supplied by material donated by Carl Gyllenborg (in 1744–1745), crown-prince Adolf Fredrik (in 1745), Erik Petreus (in 1746), Claes Grill (in 1746), Magnus Lagerström (in 1748 and 1750) and Jonas Alströmer (in 1749). The relation between the museum and the private collection was not formalized and the steady flow of material from Linnean pupils were incorporated to the private collection rather than to the museum. Linnaeus felt his work was reflecting the harmony of nature and he said in 1754 'the earth is then nothing else but a museum of the all-wise creator's masterpieces, divided into three chambers'. He had turned his own estate into a microcosm of that 'world museum'.","Carl Linnaeus\n\nIn April 1766 parts of the town were destroyed by a fire and the Linnean private collection was subsequently moved to a barn outside the town, and shortly afterwards to a single-room stone building close to his countryhouse at Hammarby near Uppsala. This resulted in a physical separation between the two collections, the museum collection remained in the botanical garden of the university. Some material which needed special care (alcohol specimens) or ample storage space was moved from the private collection to the museum.","Carl Linnaeus\n\nIn Hammarby the Linnean private collections suffered seriously from damp and the depredations by mice and insects. Carl von Linné's son (Carl Linnaeus) inherited the collections in 1778 and retained them until his own death in 1783. Shortly after Carl von Linné's death his son confirmed that mice had caused \"horrible damage\" to the plants and that also moths and mould had caused considerable damage. He tried to rescue them from the neglect they had suffered during his father's later years, and also added further specimens. This last activity however reduced rather than augmented the scientific value of the original material.","Carl Linnaeus\n\nIn 1784 the botanist James Edward Smith purchased nearly all of the Linnean private scientific effects from the widow and daughter of Carl Linnaeus and transferred them to London. Not all material in Linné's private collection was transported to England. Thirty-three fish specimens preserved in alcohol were not sent and were later lost.","Carl Linnaeus\n\nIn London Smith tended to neglect the zoological parts of the collection, he added some specimens and also gave some specimens away. Over the following centuries the Linnean collection in London suffered enormously at the hands of scientists who studied the collection, and in the process disturbed the original arrangement and labels, added specimens that did not belong to the original series and withdrew precious original type material.","Carl Linnaeus\n\nMuch material which had been intensively studied by Linné in his scientific career belonged to the collection of Queen Lovisa Ulrika (1720–1782) (in the Linnean publications referred to as \"Museum Ludovicae Ulricae\" or \"M. L. U.\"). This collection was donated by his grandson King Gustav IV Adolf (1778–1837) to the museum in Uppsala in 1804. Another important collection in this respect was that of her husband King Adolf Fredrik (1710–1771) (in the Linnean sources known as \"Museum Adolphi Friderici\" or \"Mus. Ad. Fr.\"), the wet parts (alcohol collection) of which were later donated to the Royal Swedish Academy of Sciences, and is today housed in the Swedish Museum of Natural History at Stockholm. The dry material was transferred to Uppsala.","Carl Linnaeus\n\nLinnaean taxonomy","Carl Linnaeus\n\nThe establishment of universally accepted conventions for the naming of organisms was Linnaeus' main contribution to taxonomy—his work marks the starting point of consistent use of binomial nomenclature. During the 18th century expansion of natural history knowledge, Linnaeus also developed what became known as the Linnaean taxonomy; the system of scientific classification now widely used in the biological sciences. A previous zoologist Rumphius (1627-1702) had more or less approximated the Linnaean system and his material contributed to the later development of the binomial scientific classification by Linnaeus.","Carl Linnaeus\n\nThe Linnaean system classified nature within a nested hierarchy, starting with three kingdoms. Kingdoms were divided into classes and they, in turn, into orders, and thence into genera (singular: genus), which were divided into Species (singular: species). Below the rank of species he sometimes recognized taxa of a lower (unnamed) rank; these have since acquired standardised names such as variety in botany and subspecies in zoology. Modern taxonomy includes a rank of family between order and genus and a rank of phylum between kingdom and class that were not present in Linnaeus' original system.","Carl Linnaeus\n\nLinnaeus' groupings were based upon shared physical characteristics, and not simply upon differences. Of his higher groupings, only those for animals are still in use, and the groupings themselves have been significantly changed since their conception, as have the principles behind them. Nevertheless, Linnaeus is credited with establishing the idea of a hierarchical structure of classification which is based upon observable characteristics and intended to reflect natural relationships. While the underlying details concerning what are considered to be scientifically valid \"observable characteristics\" have changed with expanding knowledge (for example, DNA sequencing, unavailable in Linnaeus' time, has proven to be a tool of considerable utility for classifying living organisms and establishing their evolutionary relationships), the fundamental principle remains sound.","Carl Linnaeus\n\nInfluences and economic beliefs","Carl Linnaeus\n\nLinnaeus' applied science was inspired not only by the instrumental utilitarianism general to the early Enlightenment, but also by his adherence to the older economic doctrine of Cameralism. Additionally, Linnaeus was a state interventionist. He supported tariffs, levies, export bounties, quotas, embargoes, navigation acts, subsidised investment capital, ceilings on wages, cash grants, state-licensed producer monopolies, and cartels.","Carl Linnaeus\n\nViews on mankind","Carl Linnaeus\n\nAccording to German biologist Ernst Haeckel, the question of man's origin began with Linnaeus. He helped future research in the natural history of man by describing humans just as he described any other plant or animal.","Carl Linnaeus\n\nAnthropomorpha","Carl Linnaeus\n\nLinnaeus classified humans among the primates (as they were later called) beginning with the first edition of '. During his time at Hartekamp, he had the opportunity to examine several monkeys and noted similarities between them and man. He pointed out both species basically have the same anatomy; except for speech, he found no other differences. Frängsmyr et al. (1983), p. 167, quotes Linnaeus explaining the real difference would necessarily be absent from his classification system, as it was not a morphological characteristic: \"I well know what a splendidly great difference there is [between] a man and a bestia [literally, \"beast\"; that is, a non-human animal] when I look at them from a point of view of morality. Man is the animal which the Creator has seen fit to honor with such a magnificent mind and has condescended to adopt as his favorite and for which he has prepared a nobler life\". See also [https://books.google.com/books?idwIkOAAAAQAAJ&pg\nPA179#vonepage&q&f\nfalse books.google.com] in which Linnaeus cites the significant capacity to reason as the distinguishing characteristic of humans.","Carl Linnaeus\n\nThus he placed man and monkeys under the same category, Anthropomorpha, meaning \"manlike.\" This classification received criticism from other biologists such as Johan Gottschalk Wallerius, Jacob Theodor Klein and Johann Georg Gmelin on the ground that it is illogical to describe a human as 'like a man'. In a letter to Gmelin from 1747, Linnaeus replied:","Carl Linnaeus\n\nIt does not please [you] that I've placed Man among the Anthropomorpha, perhaps because of the term 'with human form',\"antropomorphon\" but man learns to know himself. Let's not quibble over words. It will be the same to me whatever name we apply. But I seek from you and from the whole world a generic difference between man and simian that [follows] from the principles of Natural History.Others who followed were more inclined to give humans a special place in classification; Johann Friedrich Blumenbach in the first edition of his Manual of Natural History (1779), proposed that the primates be divided into the Quadrumana (four-handed, i.e. apes and monkeys) and Bimana (two-handed, i.e. humans). This distinction was taken up by other naturalists, most notably Georges Cuvier. Some elevated the distinction to the level of order. However, the many affinities between humans and other primates – and especially the great apes – made it clear that the distinction made no scientific sense. Charles Darwin wrote, in The Descent of Man in 1871:","Carl Linnaeus\n\nThe greater number of naturalists who have taken into consideration the whole structure of man, including his mental faculties, have followed Blumenbach and Cuvier, and have placed man in a separate Order, under the title of the Bimana, and therefore on an equality with the orders of the Quadrumana, Carnivora, etc. Recently many of our best naturalists have recurred to the view first propounded by Linnaeus, so remarkable for his sagacity, and have placed man in the same Order with the Quadrumana, under the title of the Primates. The justice of this conclusion will be admitted: for in the first place, we must bear in mind the comparative insignificance for classification of the great development of the brain in man, and that the strongly marked differences between the skulls of man and the Quadrumana (lately insisted upon by Bischoff, Aeby, and others) apparently follow from their differently developed brains.","Carl Linnaeus\n\nIn the second place, we must remember that nearly all the other and more important differences between man and the Quadrumana are manifestly adaptive in their nature, and relate chiefly to the erect position of man; such as the structure of his hand, foot, and pelvis, the curvature of his spine, and the position of his head. I absolutely know of none. If only someone might tell me a single one! If I would have called man a simian or vice versa, I would have brought together all the theologians against me. Perhaps I ought to have by virtue of the law of the discipline.","Carl Linnaeus\n\nThe theological concerns were twofold: first, putting man at the same level as monkeys or apes would lower the spiritually higher position that man was assumed to have in the great chain of being, and second, because the Bible says man was created in the image of God (theomorphism), if monkeys/apes and humans were not distinctly and separately designed, that would mean monkeys and apes were created in the image of God as well. This was something many could not accept. The conflict between world views that was caused by asserting man was a type of animal would simmer for a century until the much greater, and still ongoing, creation–evolution controversy began in earnest with the publication of On the Origin of Species by Charles Darwin in 1859.","Carl Linnaeus\n\nAfter such criticism, Linnaeus felt he needed to explain himself more clearly. The 10th edition of ' introduced new terms, including Mammalia and Primates, the latter of which would replace Anthropomorpha as well as giving humans the full binomial Homo sapiens. The new classification received less criticism, but many natural historians still believed he had demoted humans from their former place to rule over nature, not be a part of it. Linnaeus believed that man biologically belongs to the animal kingdom and had to be included in it. In his book ', he said, \"One should not vent one's wrath on animals, Theology decree that man has a soul and that the animals are mere 'aoutomata mechanica,' but I believe they would be better advised that animals have a soul and that the difference is of nobility.\"","Carl Linnaeus\n\nStrange people in distant lands","Carl Linnaeus\n\nLinnaeus added a second species to the genus Homo in ' based on a figure and description by Jacobus Bontius from a 1658 publication: Homo troglodytes (\"caveman\") and published a third in 1771: Homo lar. Swedish historian Gunnar Broberg states that the new human species Linnaeus described were actually simians or native people clad in skins to frighten colonial settlers, whose appearance had been exaggerated in accounts to Linnaeus.","Carl Linnaeus\n\nIn early editions of ', many well-known legendary creatures were included such as the phoenix, dragon and manticore as well as cryptids like the satyrus, which Linnaeus collected into the catch-all category Paradoxa. Broberg thought Linnaeus was trying to offer a natural explanation and demystify the world of superstition. Linnaeus tried to debunk some of these creatures, as he had with the hydra; regarding the purported remains of dragons, Linnaeus wrote that they were either derived from lizards or rays. For Homo troglodytes he asked the Swedish East India Company to search for one, but they did not find any signs of its existence. Homo lar has since been reclassified as Hylobates lar, the lar gibbon.","Carl Linnaeus\n\nFour races","Carl Linnaeus\n\nIn the first edition of ', Linnaeus subdivided the human species into four varieties based on continent and skin colour: \"Europæus albus\" (white European), \"Americanus rubescens\" (red American), \"Asiaticus fuscus\" (brown Asian) and \"Africanus Niger\" (black African). In the tenth edition of Systema Naturae he further detailed stereotypical characteristics for each variety, based on the concept of the four temperaments from classical antiquity, and changed the description of Asians' skin tone to \"luridus\" (yellow). Additionally, Linnaeus created a wastebasket taxon \"monstrosus\" for \"wild and monstrous humans, unknown groups, and more or less abnormal people\".","Carl Linnaeus\n\nCommemoration","Carl Linnaeus\n\nAnniversaries of Linnaeus' birth, especially in centennial years, have been marked by major celebrations. Linnaeus has appeared on numerous Swedish postage stamps and banknotes. There are numerous statues of Linnaeus in countries around the world. The Linnean Society of London has awarded the Linnean Medal for excellence in botany or zoology since 1888. Following approval by the Riksdag of Sweden, Växjö University and Kalmar College merged on 1 January 2010 to become Linnaeus University. Other things named after Linnaeus include the twinflower genus Linnaea, the crater Linné on the Earth's moon, a street in Cambridge, Massachusetts, and the cobalt sulfide mineral Linnaeite.","Carl Linnaeus\n\nCommentary on Linnaeus","Carl Linnaeus\n\nAndrew Dickson White wrote in A History of the Warfare of Science with Theology in Christendom (1896):","Carl Linnaeus\n\nLinnaeus ... was the most eminent naturalist of his time, a wide observer, a close thinker; but the atmosphere in which he lived and moved and had his being was saturated with biblical theology, and this permeated all his thinking. ... Toward the end of his life he timidly advanced the hypothesis that all the species of one genus constituted at the creation one species; and from the last edition of his Systema Naturæ he quietly left out the strongly orthodox statement of the fixity of each species, which he had insisted upon in his earlier works. ... warnings came speedily both from the Catholic and Protestant sides.","Carl Linnaeus\n\nThe mathematical PageRank algorithm, applied to 24 multilingual Wikipedia editions in 2014, published in PLOS ONE in 2015, placed Carl Linnaeus at the top historical figure, above Jesus, Aristotle, Napoleon, and Adolf Hitler (in that order).","Carl Linnaeus\n\nStandard author abbreviation"],"string":"[\n \"Carl Linnaeus\\n\\nCarl Linnaeus (; 23 May 1707 – 10 January 1778), also known after his ennoblement as Carl von Linné , was a Swedish botanist, physician, and zoologist, who formalised the modern system of naming organisms called binomial nomenclature. He is known by the epithet \\\"father of modern taxonomy\\\". Many of his writings were in Latin, and his name is rendered in Latin as (after 1761 Carolus a Linné).\",\n \"Carl Linnaeus\\n\\nLinnaeus was born in the countryside of Småland, in southern Sweden. He received most of his higher education at Uppsala University, and began giving lectures in botany there in 1730. He lived abroad between 1735 and 1738, where he studied and also published a first edition of his ' in the Netherlands. He then returned to Sweden, where he became professor of medicine and botany at Uppsala. In the 1740s, he was sent on several journeys through Sweden to find and classify plants and animals. In the 1750s and 1760s, he continued to collect and classify animals, plants, and minerals, and published several volumes. At the time of his death, he was one of the most acclaimed scientists in Europe.\",\n \"Carl Linnaeus\\n\\nThe Swiss philosopher Jean-Jacques Rousseau sent him the message: \\\"Tell him I know no greater man on earth.\\\" The German writer Johann Wolfgang von Goethe wrote: \\\"With the exception of Shakespeare and Spinoza, I know no one among the no longer living who has influenced me more strongly.\\\" Swedish author August Strindberg wrote: \\\"Linnaeus was in reality a poet who happened to become a naturalist\\\". Among other compliments, Linnaeus has been called ' (Prince of Botanists), \\\"The Pliny of the North,\\\" and \\\"The Second Adam\\\". He is also considered as one of the founders of modern ecology.\",\n \"Carl Linnaeus\\n\\nIn botany, the author abbreviation used to indicate Linnaeus as the authority for species' names is L. In older publications, sometimes the abbreviation \\\"Linn.\\\" is found (for instance in: Cheeseman, T.F. (1906) – Manual of the New Zealand Flora). Linnaeus' remains comprise the type specimen for the species Homo sapiens, following the International Code of Zoological Nomenclature, since the sole specimen he is known to have examined when writing the species description was himself.[http://www.nhm.ac.uk/hosted-sites/iczn/code/ ICZN Chapter 16, Article 72.4.1.1] – \\\"For a nominal species or subspecies established before 2000, any evidence, published or unpublished, may be taken into account to determine what specimens constitute the type series.\\\" and Article 73.1.2 – \\\"If the nominal species-group taxon is based on a single specimen, either so stated or implied in the original publication, that specimen is the holotype fixed by monotypy (see Recommendation 73F). If the taxon was established before 2000 evidence derived from outside the work itself may be taken into account [Art. 72.4.1.1] to help identify the specimen.\\\"\",\n \"Carl Linnaeus\\n\\nBiography\",\n \"Carl Linnaeus\\n\\nChildhood\",\n \"Carl Linnaeus\\n\\nLinnæus was born in the village of Råshult in Småland, Sweden, on 23 May 1707. He was the first child of Nicolaus (Nils) Ingemarsson (who later adopted the family name Linnæus) and Christina Brodersonia. His siblings were Anna Maria Linnæa, Sofia Juliana Linnæa, Samuel Linnæus, and Emerentia Linnæa.\",\n \"Carl Linnaeus\\n\\nOne of a long line of peasants and priests, Nils was an amateur botanist, a Lutheran minister, and the curate of the small village of Stenbrohult in Småland. Christina was the daughter of the rector of Stenbrohult, Samuel Brodersonius.\",\n \"Carl Linnaeus\\n\\nA year after Linnæus' birth, his grandfather Samuel Brodersonius died, and his father Nils became the rector of Stenbrohult. The family moved into the rectory from the curate's house. Carl had one brother, Samuel (who would eventually succeed their father as rector of Stenbrohult and write a manual on beekeeping). and three sisters.\",\n \"Carl Linnaeus\\n\\nEven in his early years, Linnæus seemed to have a liking for plants, flowers in particular. Whenever he was upset, he was given a flower, which immediately calmed him. Nils spent much time in his garden and often showed flowers to Linnaeus and told him their names. Soon Linnæus was given his own patch of earth where he could grow plants.\",\n \"Carl Linnaeus\\n\\nCarl's father was the first in his ancestry to adopt a permanent surname. Before that, ancestors had used the patronymic naming system of Scandinavian countries: his father was named Ingemarsson after his father Ingemar Bengtsson. When Nils was admitted to the University of Lund, he had to take on a family name. He adopted the Latinate name Linnæus after a giant linden tree (or lime tree), ' in Swedish, that grew on the family homestead. This name was spelled with the æ ligature. When Carl was born, he was named Carl Linnæus, with his father's family name. The son also always spelled it with the æ ligature, both in handwritten documents and in publications. Carl's patronymic would have been Nilsson, as in Carl Nilsson Linnæus.\",\n \"Carl Linnaeus\\n\\nEarly education\",\n \"Carl Linnaeus\\n\\nLinnaeus' father began teaching him basic Latin, religion, and geography at an early age. When Linnaeus was seven, Nils decided to hire a tutor for him. The parents picked Johan Telander, a son of a local yeoman. Linnaeus did not like him, writing in his autobiography that Telander \\\"was better calculated to extinguish a child's talents than develop them.\\\"\",\n \"Carl Linnaeus\\n\\nTwo years after his tutoring had begun, he was sent to the Lower Grammar School at Växjö in 1717. Linnaeus rarely studied, often going to the countryside to look for plants. He reached the last year of the Lower School when he was fifteen, which was taught by the headmaster, Daniel Lannerus, who was interested in botany. Lannerus noticed Linnaeus' interest in botany and gave him the run of his garden.\",\n \"Carl Linnaeus\\n\\nHe also introduced him to Johan Rothman, the state doctor of Småland and a teacher at Katedralskolan (a gymnasium) in Växjö. Also a botanist, Rothman broadened Linnaeus' interest in botany and helped him develop an interest in medicine. By the age of 17, Linnaeus had become well acquainted with the existing botanical literature. He remarks in his journal \\\"read day and night, knowing like the back of my hand, Arvidh Månsson's Rydaholm Book of Herbs, Tillandz's Flora Åboensis, Palmberg's Serta Florea Suecana, Bromelii Chloros Gothica and Rudbeckii Hortus Upsaliensis....\\\"\",\n \"Carl Linnaeus\\n\\nLinnaeus entered the Växjö Katedralskola in 1724, where he studied mainly Greek, Hebrew, theology and mathematics, a curriculum designed for boys preparing for the priesthood. In the last year at the gymnasium, Linnaeus' father visited to ask the professors how his son's studies were progressing; to his dismay, most said that the boy would never become a scholar. Rothman believed otherwise, suggesting Linnaeus could have a future in medicine. The doctor offered to have Linnaeus live with his family in Växjö and to teach him physiology and botany. Nils accepted this offer.\",\n \"Carl Linnaeus\\n\\nUniversity studies\",\n \"Carl Linnaeus\\n\\nLund\",\n \"Carl Linnaeus\\n\\nRothman showed Linnaeus that botany was a serious subject. He taught Linnaeus to classify plants according to Tournefort's system. Linnaeus was also taught about the sexual reproduction of plants, according to Sébastien Vaillant. In 1727, Linnaeus, age 21, enrolled in Lund University in Skåne. He was registered as ', the Latin form of his full name, which he also used later for his Latin publications.\",\n \"Carl Linnaeus\\n\\nProfessor Kilian Stobæus, natural scientist, physician and historian, offered Linnaeus tutoring and lodging, as well as the use of his library, which included many books about botany. He also gave the student free admission to his lectures. In his spare time, Linnaeus explored the flora of Skåne, together with students sharing the same interests.\",\n \"Carl Linnaeus\\n\\nUppsala\",\n \"Carl Linnaeus\\n\\nIn August 1728, Linnaeus decided to attend Uppsala University on the advice of Rothman, who believed it would be a better choice if Linnaeus wanted to study both medicine and botany. Rothman based this recommendation on the two professors who taught at the medical faculty at Uppsala: Olof Rudbeck the Younger and Lars Roberg. Although Rudbeck and Roberg had undoubtedly been good professors, by then they were older and not so interested in teaching. Rudbeck no longer gave public lectures, and had others stand in for him. The botany, zoology, pharmacology and anatomy lectures were not in their best state. In Uppsala, Linnaeus met a new benefactor, Olof Celsius, who was a professor of theology and an amateur botanist. He received Linnaeus into his home and allowed him use of his library, which was one of the richest botanical libraries in Sweden.\",\n \"Carl Linnaeus\\n\\nIn 1729, Linnaeus wrote a thesis, ' on plant sexual reproduction. This attracted the attention of Rudbeck; in May 1730, he selected Linnaeus to give lectures at the University although the young man was only a second-year student. His lectures were popular, and Linnaeus often addressed an audience of 300 people. In June, Linnaeus moved from Celsius' house to Rudbeck's to become the tutor of the three youngest of his 24 children. His friendship with Celsius did not wane and they continued their botanical expeditions. Over that winter, Linnaeus began to doubt Tournefort's system of classification and decided to create one of his own. His plan was to divide the plants by the number of stamens and pistils. He began writing several books, which would later result in, for example, ' and '. He also produced a book on the plants grown in the Uppsala Botanical Garden, '.\",\n \"Carl Linnaeus\\n\\nRudbeck's former assistant, Nils Rosén, returned to the University in March 1731 with a degree in medicine. Rosén started giving anatomy lectures and tried to take over Linnaeus' botany lectures, but Rudbeck prevented that. Until December, Rosén gave Linnaeus private tutoring in medicine. In December, Linnaeus had a \\\"disagreement\\\" with Rudbeck's wife and had to move out of his mentor's house; his relationship with Rudbeck did not appear to suffer. That Christmas, Linnaeus returned home to Stenbrohult to visit his parents for the first time in about three years. His mother had disapproved of his failing to become a priest, but she was pleased to learn he was teaching at the University.\",\n \"Carl Linnaeus\\n\\nExpedition to Lapland\",\n \"Carl Linnaeus\\n\\nDuring a visit with his parents, Linnaeus told them about his plan to travel to Lapland; Rudbeck had made the journey in 1695, but the detailed results of his exploration were lost in a fire seven years afterwards. Linnaeus' hope was to find new plants, animals and possibly valuable minerals. He was also curious about the customs of the native Sami people, reindeer-herding nomads who wandered Scandinavia's vast tundras. In April 1732, Linnaeus was awarded a grant from the Royal Society of Sciences in Uppsala for his journey.\",\n \"Carl Linnaeus\\n\\nLinnaeus began his expedition from Uppsala on May 12, 1732, just before he turned 25. He travelled on foot and horse, bringing with him his journal, botanical and ornithological manuscripts and sheets of paper for pressing plants. Near Gävle he found great quantities of Campanula serpyllifolia, later known as Linnaea borealis, the twinflower that would become his favourite. He sometimes dismounted on the way to examine a flower or rock and was particularly interested in mosses and lichens, the latter a main part of the diet of the reindeer, a common and economically important animal in Lapland.\",\n \"Carl Linnaeus\\n\\nLinnaeus travelled clockwise around the coast of the Gulf of Bothnia, making major inland incursions from Umeå, Luleå and Tornio. He returned from his six-month-long, over 2000 km expedition in October, having gathered and observed many plants, birds and rocks. Although Lapland was a region with limited biodiversity, Linnaeus described about 100 previously unidentified plants. These became the basis of his book '. However, on the expedition to Lapland, Linnaeus used Latin names to describe organisms because he had not yet developed the binomial system.\",\n \"Carl Linnaeus\\n\\nIn ' Linnaeus' ideas about nomenclature and classification were first used in a practical way, making this the first proto-modern Flora. The account covered 534 species, used the Linnaean classification system and included, for the described species, geographical distribution and taxonomic notes. It was Augustin Pyramus de Candolle who attributed Linnaeus with ' as the first example in the botanical genre of Flora writing. Botanical historian E. L. Greene described ' as \\\"the most classic and delightful\\\" of Linnaeus's works.\",\n \"Carl Linnaeus\\n\\nIt was also during this expedition that Linnaeus had a flash of insight regarding the classification of mammals. Upon observing the lower jawbone of a horse at the side of a road he was traveling, Linnaeus remarked: \\\"If I only knew how many teeth and of what kind every animal had, how many teats and where they were placed, I should perhaps be able to work out a perfectly natural system for the arrangement of all quadrupeds.\\\"\",\n \"Carl Linnaeus\\n\\nIn 1734, Linnaeus led a small group of students to Dalarna. Funded by the Governor of Dalarna, the expedition was to catalogue known natural resources and discover new ones, but also to gather intelligence on Norwegian mining activities at Røros.\",\n \"Carl Linnaeus\\n\\nDoctorate\",\n \"Carl Linnaeus\\n\\nBack in Uppsala, Linnaeus' relations with Nils Rosén worsened, and thus he gladly accepted an invitation from the student Claes Sohlberg to spend the Christmas holiday in Falun with Sohlberg's family. Sohlberg's father was a mining inspector, and let Linnaeus visit the mines near Falun. Sohlberg's father suggested to Linnaeus he should bring Sohlberg to the Dutch Republic and continue to tutor him there for an annual salary. At that time, the Dutch Republic was one of the most revered places to study natural history and a common place for Swedes to take their doctoral degree; Linnaeus, who was interested in both of these, accepted.\",\n \"Carl Linnaeus\\n\\nIn April 1735, Linnaeus and Sohlberg set out for the Netherlands, with Linnaeus to take a doctoral degree in medicine at the University of Harderwijk. On the way, they stopped in Hamburg, where they met the mayor, who proudly showed them a wonder of nature which he possessed: the taxidermied remains of a seven-headed hydra. Linnaeus quickly discovered it was a fake: jaws and clawed feet from weasels and skins from snakes had been glued together. The provenance of the hydra suggested to Linnaeus it had been manufactured by monks to represent the Beast of Revelation. As much as this may have upset the mayor, Linnaeus made his observations public and the mayor's dreams of selling the hydra for an enormous sum were ruined. Fearing his wrath, Linnaeus and Sohlberg had to leave Hamburg quickly.\",\n \"Carl Linnaeus\\n\\nWhen Linnaeus reached Harderwijk, he began working toward a degree immediately; at the time, Harderwijk was known for awarding \\\"instant\\\" degrees after as little as a week. First he handed in a thesis on the cause of malaria he had written in Sweden, which he then defended in a public debate. His dissertation, submitted on 23 June, was titled Dissertatio medica inauguralis in qua exhibetur hypothesis nova de febrium intermittentium causa (\\\"Inaugural thesis in medicine, in which a new hypothesis on the cause of intermittent fevers is presented\\\"). He concluded that malaria arose only in places with clay-rich soil. He is now known to have been wrong about the cause, not having a microscope good enough to see malarial parasites, which were spread by mosquitoes breeding in the water that collected in ruts and puddles. But he was right in predicting that traditional Chinese medicine, including the use of wormwood (Artemisia), is a potential source of antimalarial drug. (Artemisinins, derived from wormwood, are now the principal antimalarial drugs. )\",\n \"Carl Linnaeus\\n\\nThe next step was to take an oral examination and to diagnose a patient. After less than two weeks, he took his degree and became a doctor, at the age of 28. During the summer, Linnaeus met a friend from Uppsala, Peter Artedi. Before their departure from Uppsala, Artedi and Linnaeus had decided should one of them die, the survivor would finish the other's work. Ten weeks later, Artedi drowned in one of the canals of Amsterdam, and his unfinished manuscript on the classification of fish was left to Linnaeus to complete.\",\n \"Carl Linnaeus\\n\\nPublishing of '\",\n \"Carl Linnaeus\\n\\nOne of the first scientists Linnaeus met in the Netherlands was Johan Frederik Gronovius to whom Linnaeus showed one of the several manuscripts he had brought with him from Sweden. The manuscript described a new system for classifying plants. When Gronovius saw it, he was very impressed, and offered to help pay for the printing. With an additional monetary contribution by the Scottish doctor Isaac Lawson, the manuscript was published as ' (1735).\",\n \"Carl Linnaeus\\n\\nLinnaeus became acquainted with one of the most respected physicians and botanists in the Netherlands, Herman Boerhaave, who tried to convince Linnaeus to make a career there. Boerhaave offered him a journey to South Africa and America, but Linnaeus declined, stating he would not stand the heat. Instead, Boerhaave convinced Linnaeus that he should visit the botanist Johannes Burman. After his visit, Burman, impressed with his guest's knowledge, decided Linnaeus should stay with him during the winter. During his stay, Linnaeus helped Burman with his '. Burman also helped Linnaeus with the books on which he was working: ' and '.\",\n \"Carl Linnaeus\\n\\nGeorge Clifford, Philip Miller, and Johann Jacob Dillenius\",\n \"Carl Linnaeus\\n\\nIn August, during Linnaeus' stay with Burman, he met George Clifford III, a director of the Dutch East India Company and the owner of a rich botanical garden at the estate of Hartekamp in Heemstede. Clifford was very impressed with Linnaeus' ability to classify plants, and invited him to become his physician and superintendent of his garden. Linnaeus had already agreed to stay with Burman over the winter, and could thus not accept immediately. However, Clifford offered to compensate Burman by offering him a copy of Sir Hans Sloane's Natural History of Jamaica, a rare book, if he let Linnaeus stay with him, and Burman accepted. On 24 September 1735, Linnaeus moved to Hartekamp to become personal physician to Clifford, and curator of Clifford's herbarium. He was paid 1,000 florins a year, with free board and lodging. Though the agreement was only for a winter of that year, Linnaeus practically stayed there till 1738.\",\n \"Carl Linnaeus\\n\\nIt was here that he wrote a book Hortus Cliffortianus, in the preface of which he described his experience as \\\"the happiest time of my life.\\\" (A portion of Hartekamp was declared as public garden in April 1956 by the Heemstede local authority, and was named \\\"Linnaeushof\\\". It eventually became, as it is claimed, the biggest playground in Europe. )\",\n \"Carl Linnaeus\\n\\nIn July 1736, Linnaeus travelled to England, at Clifford's expense. He went to London to visit Sir Hans Sloane, a collector of natural history, and to see his cabinet, as well as to visit the Chelsea Physic Garden and its keeper, Philip Miller. He taught Miller about his new system of subdividing plants, as described in '. Miller was in fact reluctant to use the new binomial nomenclature, preferring the classifications of Joseph Pitton de Tournefort and John Ray at first. Linnaeus, nevertheless, applauded Miller's Gardeners Dictionary, The conservative Scot actually retained in his dictionary a number of pre-Linnaean binomial signifiers discarded by Linnaeus but which have been retained by modern botanists. He only fully changed to the Linnaean system in the edition of The Gardeners Dictionary of 1768. Miller ultimately was impressed, and from then on started to arrange the garden according to Linnaeus' system.\",\n \"Carl Linnaeus\\n\\nLinnaeus also traveled to Oxford University to visit the botanist Johann Jacob Dillenius. He failed to make Dillenius publicly fully accept his new classification system, though the two men remained in correspondence for many years afterwards. Linnaeus dedicated his Critica botanica to him, as opus botanicum quo absolutius mundus non vidit. Linnaeus would later name a genus of tropical tree Dillenia in his honor. He then returned to Hartekamp, bringing with him many specimens of rare plants. The next year, he published ', in which he described 935 genera of plants, and shortly thereafter he supplemented it with ', with another sixty (sexaginta) genera.\",\n \"Carl Linnaeus\\n\\nHis work at Hartekamp led to another book, ', a catalogue of the botanical holdings in the herbarium and botanical garden of Hartekamp. He wrote it in nine months (completed in July 1737), but it was not published until 1738. It contains the first use of the name Nepenthes, which Linnaeus used to describe a genus of pitcher plants. \\\"If this is not Helen's Nepenthes, it certainly will be for all botanists. What botanist would not be filled with admiration if, after a long journey, he should find this wonderful plant. In his astonishment past ills would be forgotten when beholding this admirable work of the Creator!\\\" (translated from Latin by Harry Veitch)\",\n \"Carl Linnaeus\\n\\nLinnaeus stayed with Clifford at Hartekamp until 18 October 1737 (new style), when he left the house to return to Sweden. Illness and the kindness of Dutch friends obliged him to stay some months longer in Holland. In May 1738, he set out for Sweden again. On the way home, he stayed in Paris for about a month, visiting botanists such as Antoine de Jussieu. After his return, Linnaeus never left Sweden again.\",\n \"Carl Linnaeus\\n\\nReturn to Sweden\",\n \"Carl Linnaeus\\n\\nWhen Linnaeus returned to Sweden on 28 June 1738, he went to Falun, where he entered into an engagement to Sara Elisabeth Moræa. Three months later, he moved to Stockholm to find employment as a physician, and thus to make it possible to support a family. Once again, Linnaeus found a patron; he became acquainted with Count Carl Gustav Tessin, who helped him get work as a physician at the Admiralty. During this time in Stockholm, Linnaeus helped found the Royal Swedish Academy of Science; he became the first Praeses in the academy by drawing of lots.\",\n \"Carl Linnaeus\\n\\nBecause his finances had improved and were now sufficient to support a family, he received permission to marry his fiancée, Sara Elisabeth Moræa. Their wedding was held 26 June 1739. Seven months later, Sara gave birth to their first son, Carl. Two years later, a daughter, Elisabeth Christina, was born, and the subsequent year Sara gave birth to Sara Magdalena, who died when 15 days old. Sara and Linnaeus would later have four other children: Lovisa, Sara Christina, Johannes and Sophia.\",\n \"Carl Linnaeus\\n\\nIn May 1741, Linnaeus was appointed Professor of Medicine at Uppsala University, first with responsibility for medicine-related matters. Soon, he changed place with the other Professor of Medicine, Nils Rosén, and thus was responsible for the Botanical Garden (which he would thoroughly reconstruct and expand), botany and natural history, instead. In October that same year, his wife and nine-year-old son followed him to live in Uppsala.\",\n \"Carl Linnaeus\\n\\nÖland and Gotland\",\n \"Carl Linnaeus\\n\\nTen days after he was appointed Professor, he undertook an expedition to the island provinces of Öland and Gotland with six students from the university, to look for plants useful in medicine. First, they travelled to Öland and stayed there until 21 June, when they sailed to Visby in Gotland. Linnaeus and the students stayed on Gotland for about a month, and then returned to Uppsala. During this expedition, they found 100 previously unrecorded plants. The observations from the expedition were later published in ', written in Swedish. Like ', it contained both zoological and botanical observations, as well as observations concerning the culture in Öland and Gotland.\",\n \"Carl Linnaeus\\n\\nDuring the summer of 1745, Linnaeus published two more books: ' and '. ' was a strictly botanical book, while ' was zoological. Anders Celsius had created the temperature scale named after him in 1742. Celsius' scale was inverted compared to today, the boiling point at 0 °C and freezing point at 100 °C. In 1745, Linnaeus inverted the scale to its present standard.\",\n \"Carl Linnaeus\\n\\nVästergötland\",\n \"Carl Linnaeus\\n\\nIn the summer of 1746, Linnaeus was once again commissioned by the Government to carry out an expedition, this time to the Swedish province of Västergötland. He set out from Uppsala on 12 June and returned on 11 August. On the expedition his primary companion was Erik Gustaf Lidbeck, a student who had accompanied him on his previous journey. Linnaeus described his findings from the expedition in the book ', published the next year. After returning from the journey the Government decided Linnaeus should take on another expedition to the southernmost province Scania. This journey was postponed, as Linnaeus felt too busy.\",\n \"Carl Linnaeus\\n\\nIn 1747, Linnaeus was given the title archiater, or chief physician, by the Swedish king Adolf Frederick—a mark of great respect. The same year he was elected member of the Academy of Sciences in Berlin.\",\n \"Carl Linnaeus\\n\\nScania\",\n \"Carl Linnaeus\\n\\nIn the spring of 1749, Linnaeus could finally journey to Scania, again commissioned by the Government. With him he brought his student, Olof Söderberg. On the way to Scania, he made his last visit to his brothers and sisters in Stenbrohult since his father had died the previous year. The expedition was similar to the previous journeys in most aspects, but this time he was also ordered to find the best place to grow walnut and Swedish whitebeam trees; these trees were used by the military to make rifles. The journey was successful, and Linnaeus' observations were published the next year in '.\",\n \"Carl Linnaeus\\n\\nRector of Uppsala University\",\n \"Carl Linnaeus\\n\\nIn 1750, Linnaeus became rector of Uppsala University, starting a period where natural sciences were esteemed. Perhaps the most important contribution he made during his time at Uppsala was to teach; many of his students travelled to various places in the world to collect botanical samples. Linnaeus called the best of these students his \\\"apostles\\\". His lectures were normally very popular and were often held in the Botanical Garden. He tried to teach the students to think for themselves and not trust anybody, not even him. Even more popular than the lectures were the botanical excursions made every Saturday during summer, where Linnaeus and his students explored the flora and fauna in the vicinity of Uppsala.\",\n \"Carl Linnaeus\\n\\nPhilosophia Botanica\",\n \"Carl Linnaeus\\n\\nLinnaeus published Philosophia Botanica in 1751. The book contained a complete survey of the taxonomy system he had been using in his earlier works. It also contained information of how to keep a journal on travels and how to maintain a botanical garden.\",\n \"Carl Linnaeus\\n\\nNutrix Noverca\",\n \"Carl Linnaeus\\n\\nDuring Linnaeus' time it was normal for upper class women to have wet nurses for their babies. Linnaeus joined an ongoing campaign to end this practice in Sweden and promote breast-feeding by mothers. In 1752 Linnaeus published a thesis along with Frederick Lindberg, a physician student, based on their experiences. In the tradition of the period, this dissertation was essentially an idea of the presiding reviewer (prases) expounded upon by the student. Linnaeus' dissertation was translated into French by J.E. Gilibert in 1770 as La Nourrice marâtre, ou Dissertation sur les suites funestes du nourrisage mercénaire. Linnaeus suggested that children might absorb the personality of their wet nurse through the milk. He admired the child care practices of the Lapps and pointed out how healthy their babies were compared to those of Europeans who employed wet nurses. He compared the behaviour of wild animals and pointed out how none of them denied their newborns their breastmilk. It is thought that his activism played a role in his choice of the term Mammalia for the class of organisms.\",\n \"Carl Linnaeus\\n\\nSpecies Plantarum\",\n \"Carl Linnaeus\\n\\nLinnaeus published Species Plantarum, the work which is now internationally accepted as the starting point of modern botanical nomenclature, in 1753. The first volume was issued on 24 May, the second volume followed on 16 August of the same year. The book contained 1,200 pages and was published in two volumes; it described over 7,300 species. The same year the king dubbed him knight of the Order of the Polar Star, the first civilian in Sweden to become a knight in this order. He was then seldom seen not wearing the order.\",\n \"Carl Linnaeus\\n\\nEnnoblement\",\n \"Carl Linnaeus\\n\\nLinnaeus felt Uppsala was too noisy and unhealthy, so he bought two farms in 1758: Hammarby and Sävja. The next year, he bought a neighbouring farm, Edeby. He spent the summers with his family at Hammarby; initially it only had a small one-storey house, but in 1762 a new, larger main building was added. In Hammarby, Linnaeus made a garden where he could grow plants that could not be grown in the Botanical Garden in Uppsala. He began constructing a museum on a hill behind Hammarby in 1766, where he moved his library and collection of plants. A fire that destroyed about one third of Uppsala and had threatened his residence there necessitated the move.\",\n \"Carl Linnaeus\\n\\nSince the initial release of ' in 1735, the book had been expanded and reprinted several times; the tenth edition was released in 1758. This edition established itself as the starting point for zoological nomenclature, the equivalent of '.\",\n \"Carl Linnaeus\\n\\nThe Swedish king Adolf Frederick granted Linnaeus nobility in 1757, but he was not ennobled until 1761. With his ennoblement, he took the name Carl von Linné (Latinized as '), 'Linné' being a shortened and gallicised version of 'Linnæus', and the German nobiliary particle 'von' signifying his ennoblement. The noble family's coat of arms prominently features a twinflower, one of Linnaeus' favourite plants; it was given the scientific name Linnaea borealis in his honour by Gronovius. The shield in the coat of arms is divided into thirds: red, black and green for the three kingdoms of nature (animal, mineral and vegetable) in Linnaean classification; in the centre is an egg \\\"to denote Nature, which is continued and perpetuated in ovo.\\\" At the bottom is a phrase in Latin, borrowed from the Aeneid, which reads \\\"Famam extendere factis\\\": we extend our fame by our deeds. Linnaeus inscribed this personal motto in books that were gifted to him by friends.\",\n \"Carl Linnaeus\\n\\nAfter his ennoblement, Linnaeus continued teaching and writing. His reputation had spread over the world, and he corresponded with many different people. For example, Catherine II of Russia sent him seeds from her country. He also corresponded with Giovanni Antonio Scopoli, \\\"the Linnaeus of the Austrian Empire\\\", who was a doctor and a botanist in Idrija, Duchy of Carniola (nowadays Slovenia). Scopoli communicated all of his research, findings, and descriptions (for example of the olm and the dormouse, two little animals hitherto unknown to Linnaeus). Linnaeus greatly respected him and showed great interest in his work. He named a solanaceous genus, Scopolia, the source of scopolamine, after him. Because of a great distance, they never met.\",\n \"Carl Linnaeus\\n\\nFinal years\",\n \"Carl Linnaeus\\n\\nLinnaeus was relieved of his duties in the Royal Swedish Academy of Science in 1763, but continued his work there as usual for more than ten years after. He stepped down as rector at Uppsala University in December 1772, mostly due to his declining health.\",\n \"Carl Linnaeus\\n\\nLinnaeus' last years were troubled by illness. He had suffered from a disease called the Uppsala fever in 1764, but survived thanks to the care of Rosén. He developed sciatica in 1773, and the next year, he had a stroke which partially paralysed him. He suffered a second stroke in 1776, losing the use of his right side and leaving him bereft of his memory; while still able to admire his own writings, he could not recognise himself as their author.\",\n \"Carl Linnaeus\\n\\nIn December 1777, he had another stroke which greatly weakened him, and eventually led to his death on 10 January 1778 in Hammarby. Despite his desire to be buried in Hammarby, he was buried in Uppsala Cathedral on 22 January.\",\n \"Carl Linnaeus\\n\\nHis library and collections were left to his widow Sara and their children. Joseph Banks, an English botanist, wanted to buy the collection, but his son Carl refused and moved the collection to Uppsala. However, in 1783 Carl died and Sara inherited the collection, having outlived both her husband and son. She tried to sell it to Banks, but he was no longer interested; instead an acquaintance of his agreed to buy the collection. The acquaintance was a 24-year-old medical student, James Edward Smith, who bought the whole collection: 14,000 plants, 3,198 insects, 1,564 shells, about 3,000 letters and 1,600 books. Smith founded the Linnean Society of London five years later.\",\n \"Carl Linnaeus\\n\\nThe von Linné name ended with his son Carl, who never married. His other son, Johannes, had died aged 3. There are over two hundred descendants of Linnaeus through two of his daughters.\",\n \"Carl Linnaeus\\n\\nApostles\",\n \"Carl Linnaeus\\n\\nDuring Linnaeus' time as Professor and Rector of Uppsala University, he taught many devoted students, 17 of whom he called \\\"apostles\\\". They were the most promising, most committed students, and all of them made botanical expeditions to various places in the world, often with his help. The amount of this help varied; sometimes he used his influence as Rector to grant his apostles a scholarship or a place on an expedition. To most of the apostles he gave instructions of what to look for on their journeys. Abroad, the apostles collected and organised new plants, animals and minerals according to Linnaeus' system. Most of them also gave some of their collection to Linnaeus when their journey was finished. Thanks to these students, the Linnaean system of taxonomy spread through the world without Linnaeus ever having to travel outside Sweden after his return from Holland. The British botanist William T. Stearn notes without Linnaeus' new system, it would not have been possible for the apostles to collect and organise so many new specimens. Many of the apostles died during their expeditions.\",\n \"Carl Linnaeus\\n\\nEarly expeditions\",\n \"Carl Linnaeus\\n\\nChristopher Tärnström, the first apostle and a 43-year-old pastor with a wife and children, made his journey in 1746. He boarded a Swedish East India Company ship headed for China. Tärnström never reached his destination, dying of a tropical fever on Côn Sơn Island the same year. Tärnström's widow blamed Linnaeus for making her children fatherless, causing Linnaeus to prefer sending out younger, unmarried students after Tärnström. Six other apostles later died on their expeditions, including Pehr Forsskål and Pehr Löfling.\",\n \"Carl Linnaeus\\n\\nTwo years after Tärnström's expedition, Finnish-born Pehr Kalm set out as the second apostle to North America. There he spent two-and-a-half years studying the flora and fauna of Pennsylvania, New York, New Jersey and Canada. Linnaeus was overjoyed when Kalm returned, bringing back with him many pressed flowers and seeds. At least 90 of the 700 North American species described in Species Plantarum had been brought back by Kalm.\",\n \"Carl Linnaeus\\n\\nCook expeditions and Japan\",\n \"Carl Linnaeus\\n\\nDaniel Solander was living in Linnaeus' house during his time as a student in Uppsala. Linnaeus was very fond of him, promising Solander his oldest daughter's hand in marriage. On Linnaeus' recommendation, Solander travelled to England in 1760, where he met the English botanist Joseph Banks. With Banks, Solander joined James Cook on his expedition to Oceania on the Endeavour in 1768–71. Solander was not the only apostle to journey with James Cook; Anders Sparrman followed on the Resolution in 1772–75 bound for, among other places, Oceania and South America. Sparrman made many other expeditions, one of them to South Africa.\",\n \"Carl Linnaeus\\n\\nPerhaps the most famous and successful apostle was Carl Peter Thunberg, who embarked on a nine-year expedition in 1770. He stayed in South Africa for three years, then travelled to Japan. All foreigners in Japan were forced to stay on the island of Dejima outside Nagasaki, so it was thus hard for Thunberg to study the flora. He did, however, manage to persuade some of the translators to bring him different plants, and he also found plants in the gardens of Dejima. He returned to Sweden in 1779, one year after Linnaeus' death.\",\n \"Carl Linnaeus\\n\\nMajor publications\",\n \"Carl Linnaeus\\n\\nSystema Naturae\",\n \"Carl Linnaeus\\n\\nThe first edition of ' was printed in the Netherlands in 1735. It was a twelve-page work. By the time it reached its 10th edition in 1758, it classified 4,400 species of animals and 7,700 species of plants. In it, the unwieldy names mostly used at the time, such as \\\"'\\\", were supplemented with concise and now familiar \\\"binomials\\\", composed of the generic name, followed by a specific epithet – in the case given, Physalis angulata. These binomials could serve as a label to refer to the species. Higher taxa were constructed and arranged in a simple and orderly manner. Although the system, now known as binomial nomenclature, was partially developed by the Bauhin brothers (see Gaspard Bauhin and Johann Bauhin) almost 200 years earlier, Linnaeus was the first to use it consistently throughout the work, including in monospecific genera, and may be said to have popularised it within the scientific community.\",\n \"Carl Linnaeus\\n\\nAfter the decline in Linnaeus' health in the early 1770s, publication of editions of Systema Naturae went in two different directions. Another Swedish scientist, Johan Andreas Murray issued the Regnum Vegetabile section separately in 1774 as the Systema Vegetabilium, rather confusingly labelled the 13th edition. Meanwhile a 13th edition of the entire Systema appeared in parts between 1788 and 1793. It was through the Systema Vegetabilium that Linnaeus' work became widely known in England, following its translation from the Latin by the Lichfield Botanical Society as A System of Vegetables (1783–1785).\",\n \"Carl Linnaeus\\n\\n'\",\n \"Carl Linnaeus\\n\\n' (or, more fully, ') was first published in 1753, as a two-volume work. Its prime importance is perhaps that it is the primary starting point of plant nomenclature as it exists today.\",\n \"Carl Linnaeus\\n\\n'\",\n \"Carl Linnaeus\\n\\n' was first published in 1737, delineating plant genera. Around 10 editions were published, not all of them by Linnaeus himself; the most important is the 1754 fifth edition. In it Linnaeus divided the plant Kingdom into 24 classes. One, Cryptogamia, included all the plants with concealed reproductive parts (algae, fungi, mosses and liverworts and ferns).\",\n \"Carl Linnaeus\\n\\n'\",\n \"Carl Linnaeus\\n\\n' (1751) was a summary of Linnaeus' thinking on plant classification and nomenclature, and an elaboration of the work he had previously published in ' (1736) and ' (1737). Other publications forming part of his plan to reform the foundations of botany include his ' and ': all were printed in Holland (as well as ' (1737) and ' (1735)), the Philosophia being simultaneously released in Stockholm.\",\n \"Carl Linnaeus\\n\\nLinnaean collections\",\n \"Carl Linnaeus\\n\\nAt the end of his lifetime the Linnean collection in Uppsala was considered one of the finest collections of natural history objects in Sweden. Next to his own collection he had also built up a museum for the university of Uppsala, which was supplied by material donated by Carl Gyllenborg (in 1744–1745), crown-prince Adolf Fredrik (in 1745), Erik Petreus (in 1746), Claes Grill (in 1746), Magnus Lagerström (in 1748 and 1750) and Jonas Alströmer (in 1749). The relation between the museum and the private collection was not formalized and the steady flow of material from Linnean pupils were incorporated to the private collection rather than to the museum. Linnaeus felt his work was reflecting the harmony of nature and he said in 1754 'the earth is then nothing else but a museum of the all-wise creator's masterpieces, divided into three chambers'. He had turned his own estate into a microcosm of that 'world museum'.\",\n \"Carl Linnaeus\\n\\nIn April 1766 parts of the town were destroyed by a fire and the Linnean private collection was subsequently moved to a barn outside the town, and shortly afterwards to a single-room stone building close to his countryhouse at Hammarby near Uppsala. This resulted in a physical separation between the two collections, the museum collection remained in the botanical garden of the university. Some material which needed special care (alcohol specimens) or ample storage space was moved from the private collection to the museum.\",\n \"Carl Linnaeus\\n\\nIn Hammarby the Linnean private collections suffered seriously from damp and the depredations by mice and insects. Carl von Linné's son (Carl Linnaeus) inherited the collections in 1778 and retained them until his own death in 1783. Shortly after Carl von Linné's death his son confirmed that mice had caused \\\"horrible damage\\\" to the plants and that also moths and mould had caused considerable damage. He tried to rescue them from the neglect they had suffered during his father's later years, and also added further specimens. This last activity however reduced rather than augmented the scientific value of the original material.\",\n \"Carl Linnaeus\\n\\nIn 1784 the botanist James Edward Smith purchased nearly all of the Linnean private scientific effects from the widow and daughter of Carl Linnaeus and transferred them to London. Not all material in Linné's private collection was transported to England. Thirty-three fish specimens preserved in alcohol were not sent and were later lost.\",\n \"Carl Linnaeus\\n\\nIn London Smith tended to neglect the zoological parts of the collection, he added some specimens and also gave some specimens away. Over the following centuries the Linnean collection in London suffered enormously at the hands of scientists who studied the collection, and in the process disturbed the original arrangement and labels, added specimens that did not belong to the original series and withdrew precious original type material.\",\n \"Carl Linnaeus\\n\\nMuch material which had been intensively studied by Linné in his scientific career belonged to the collection of Queen Lovisa Ulrika (1720–1782) (in the Linnean publications referred to as \\\"Museum Ludovicae Ulricae\\\" or \\\"M. L. U.\\\"). This collection was donated by his grandson King Gustav IV Adolf (1778–1837) to the museum in Uppsala in 1804. Another important collection in this respect was that of her husband King Adolf Fredrik (1710–1771) (in the Linnean sources known as \\\"Museum Adolphi Friderici\\\" or \\\"Mus. Ad. Fr.\\\"), the wet parts (alcohol collection) of which were later donated to the Royal Swedish Academy of Sciences, and is today housed in the Swedish Museum of Natural History at Stockholm. The dry material was transferred to Uppsala.\",\n \"Carl Linnaeus\\n\\nLinnaean taxonomy\",\n \"Carl Linnaeus\\n\\nThe establishment of universally accepted conventions for the naming of organisms was Linnaeus' main contribution to taxonomy—his work marks the starting point of consistent use of binomial nomenclature. During the 18th century expansion of natural history knowledge, Linnaeus also developed what became known as the Linnaean taxonomy; the system of scientific classification now widely used in the biological sciences. A previous zoologist Rumphius (1627-1702) had more or less approximated the Linnaean system and his material contributed to the later development of the binomial scientific classification by Linnaeus.\",\n \"Carl Linnaeus\\n\\nThe Linnaean system classified nature within a nested hierarchy, starting with three kingdoms. Kingdoms were divided into classes and they, in turn, into orders, and thence into genera (singular: genus), which were divided into Species (singular: species). Below the rank of species he sometimes recognized taxa of a lower (unnamed) rank; these have since acquired standardised names such as variety in botany and subspecies in zoology. Modern taxonomy includes a rank of family between order and genus and a rank of phylum between kingdom and class that were not present in Linnaeus' original system.\",\n \"Carl Linnaeus\\n\\nLinnaeus' groupings were based upon shared physical characteristics, and not simply upon differences. Of his higher groupings, only those for animals are still in use, and the groupings themselves have been significantly changed since their conception, as have the principles behind them. Nevertheless, Linnaeus is credited with establishing the idea of a hierarchical structure of classification which is based upon observable characteristics and intended to reflect natural relationships. While the underlying details concerning what are considered to be scientifically valid \\\"observable characteristics\\\" have changed with expanding knowledge (for example, DNA sequencing, unavailable in Linnaeus' time, has proven to be a tool of considerable utility for classifying living organisms and establishing their evolutionary relationships), the fundamental principle remains sound.\",\n \"Carl Linnaeus\\n\\nInfluences and economic beliefs\",\n \"Carl Linnaeus\\n\\nLinnaeus' applied science was inspired not only by the instrumental utilitarianism general to the early Enlightenment, but also by his adherence to the older economic doctrine of Cameralism. Additionally, Linnaeus was a state interventionist. He supported tariffs, levies, export bounties, quotas, embargoes, navigation acts, subsidised investment capital, ceilings on wages, cash grants, state-licensed producer monopolies, and cartels.\",\n \"Carl Linnaeus\\n\\nViews on mankind\",\n \"Carl Linnaeus\\n\\nAccording to German biologist Ernst Haeckel, the question of man's origin began with Linnaeus. He helped future research in the natural history of man by describing humans just as he described any other plant or animal.\",\n \"Carl Linnaeus\\n\\nAnthropomorpha\",\n \"Carl Linnaeus\\n\\nLinnaeus classified humans among the primates (as they were later called) beginning with the first edition of '. During his time at Hartekamp, he had the opportunity to examine several monkeys and noted similarities between them and man. He pointed out both species basically have the same anatomy; except for speech, he found no other differences. Frängsmyr et al. (1983), p. 167, quotes Linnaeus explaining the real difference would necessarily be absent from his classification system, as it was not a morphological characteristic: \\\"I well know what a splendidly great difference there is [between] a man and a bestia [literally, \\\"beast\\\"; that is, a non-human animal] when I look at them from a point of view of morality. Man is the animal which the Creator has seen fit to honor with such a magnificent mind and has condescended to adopt as his favorite and for which he has prepared a nobler life\\\". See also [https://books.google.com/books?idwIkOAAAAQAAJ&pg\\nPA179#vonepage&q&f\\nfalse books.google.com] in which Linnaeus cites the significant capacity to reason as the distinguishing characteristic of humans.\",\n \"Carl Linnaeus\\n\\nThus he placed man and monkeys under the same category, Anthropomorpha, meaning \\\"manlike.\\\" This classification received criticism from other biologists such as Johan Gottschalk Wallerius, Jacob Theodor Klein and Johann Georg Gmelin on the ground that it is illogical to describe a human as 'like a man'. In a letter to Gmelin from 1747, Linnaeus replied:\",\n \"Carl Linnaeus\\n\\nIt does not please [you] that I've placed Man among the Anthropomorpha, perhaps because of the term 'with human form',\\\"antropomorphon\\\" but man learns to know himself. Let's not quibble over words. It will be the same to me whatever name we apply. But I seek from you and from the whole world a generic difference between man and simian that [follows] from the principles of Natural History.Others who followed were more inclined to give humans a special place in classification; Johann Friedrich Blumenbach in the first edition of his Manual of Natural History (1779), proposed that the primates be divided into the Quadrumana (four-handed, i.e. apes and monkeys) and Bimana (two-handed, i.e. humans). This distinction was taken up by other naturalists, most notably Georges Cuvier. Some elevated the distinction to the level of order. However, the many affinities between humans and other primates – and especially the great apes – made it clear that the distinction made no scientific sense. Charles Darwin wrote, in The Descent of Man in 1871:\",\n \"Carl Linnaeus\\n\\nThe greater number of naturalists who have taken into consideration the whole structure of man, including his mental faculties, have followed Blumenbach and Cuvier, and have placed man in a separate Order, under the title of the Bimana, and therefore on an equality with the orders of the Quadrumana, Carnivora, etc. Recently many of our best naturalists have recurred to the view first propounded by Linnaeus, so remarkable for his sagacity, and have placed man in the same Order with the Quadrumana, under the title of the Primates. The justice of this conclusion will be admitted: for in the first place, we must bear in mind the comparative insignificance for classification of the great development of the brain in man, and that the strongly marked differences between the skulls of man and the Quadrumana (lately insisted upon by Bischoff, Aeby, and others) apparently follow from their differently developed brains.\",\n \"Carl Linnaeus\\n\\nIn the second place, we must remember that nearly all the other and more important differences between man and the Quadrumana are manifestly adaptive in their nature, and relate chiefly to the erect position of man; such as the structure of his hand, foot, and pelvis, the curvature of his spine, and the position of his head. I absolutely know of none. If only someone might tell me a single one! If I would have called man a simian or vice versa, I would have brought together all the theologians against me. Perhaps I ought to have by virtue of the law of the discipline.\",\n \"Carl Linnaeus\\n\\nThe theological concerns were twofold: first, putting man at the same level as monkeys or apes would lower the spiritually higher position that man was assumed to have in the great chain of being, and second, because the Bible says man was created in the image of God (theomorphism), if monkeys/apes and humans were not distinctly and separately designed, that would mean monkeys and apes were created in the image of God as well. This was something many could not accept. The conflict between world views that was caused by asserting man was a type of animal would simmer for a century until the much greater, and still ongoing, creation–evolution controversy began in earnest with the publication of On the Origin of Species by Charles Darwin in 1859.\",\n \"Carl Linnaeus\\n\\nAfter such criticism, Linnaeus felt he needed to explain himself more clearly. The 10th edition of ' introduced new terms, including Mammalia and Primates, the latter of which would replace Anthropomorpha as well as giving humans the full binomial Homo sapiens. The new classification received less criticism, but many natural historians still believed he had demoted humans from their former place to rule over nature, not be a part of it. Linnaeus believed that man biologically belongs to the animal kingdom and had to be included in it. In his book ', he said, \\\"One should not vent one's wrath on animals, Theology decree that man has a soul and that the animals are mere 'aoutomata mechanica,' but I believe they would be better advised that animals have a soul and that the difference is of nobility.\\\"\",\n \"Carl Linnaeus\\n\\nStrange people in distant lands\",\n \"Carl Linnaeus\\n\\nLinnaeus added a second species to the genus Homo in ' based on a figure and description by Jacobus Bontius from a 1658 publication: Homo troglodytes (\\\"caveman\\\") and published a third in 1771: Homo lar. Swedish historian Gunnar Broberg states that the new human species Linnaeus described were actually simians or native people clad in skins to frighten colonial settlers, whose appearance had been exaggerated in accounts to Linnaeus.\",\n \"Carl Linnaeus\\n\\nIn early editions of ', many well-known legendary creatures were included such as the phoenix, dragon and manticore as well as cryptids like the satyrus, which Linnaeus collected into the catch-all category Paradoxa. Broberg thought Linnaeus was trying to offer a natural explanation and demystify the world of superstition. Linnaeus tried to debunk some of these creatures, as he had with the hydra; regarding the purported remains of dragons, Linnaeus wrote that they were either derived from lizards or rays. For Homo troglodytes he asked the Swedish East India Company to search for one, but they did not find any signs of its existence. Homo lar has since been reclassified as Hylobates lar, the lar gibbon.\",\n \"Carl Linnaeus\\n\\nFour races\",\n \"Carl Linnaeus\\n\\nIn the first edition of ', Linnaeus subdivided the human species into four varieties based on continent and skin colour: \\\"Europæus albus\\\" (white European), \\\"Americanus rubescens\\\" (red American), \\\"Asiaticus fuscus\\\" (brown Asian) and \\\"Africanus Niger\\\" (black African). In the tenth edition of Systema Naturae he further detailed stereotypical characteristics for each variety, based on the concept of the four temperaments from classical antiquity, and changed the description of Asians' skin tone to \\\"luridus\\\" (yellow). Additionally, Linnaeus created a wastebasket taxon \\\"monstrosus\\\" for \\\"wild and monstrous humans, unknown groups, and more or less abnormal people\\\".\",\n \"Carl Linnaeus\\n\\nCommemoration\",\n \"Carl Linnaeus\\n\\nAnniversaries of Linnaeus' birth, especially in centennial years, have been marked by major celebrations. Linnaeus has appeared on numerous Swedish postage stamps and banknotes. There are numerous statues of Linnaeus in countries around the world. The Linnean Society of London has awarded the Linnean Medal for excellence in botany or zoology since 1888. Following approval by the Riksdag of Sweden, Växjö University and Kalmar College merged on 1 January 2010 to become Linnaeus University. Other things named after Linnaeus include the twinflower genus Linnaea, the crater Linné on the Earth's moon, a street in Cambridge, Massachusetts, and the cobalt sulfide mineral Linnaeite.\",\n \"Carl Linnaeus\\n\\nCommentary on Linnaeus\",\n \"Carl Linnaeus\\n\\nAndrew Dickson White wrote in A History of the Warfare of Science with Theology in Christendom (1896):\",\n \"Carl Linnaeus\\n\\nLinnaeus ... was the most eminent naturalist of his time, a wide observer, a close thinker; but the atmosphere in which he lived and moved and had his being was saturated with biblical theology, and this permeated all his thinking. ... Toward the end of his life he timidly advanced the hypothesis that all the species of one genus constituted at the creation one species; and from the last edition of his Systema Naturæ he quietly left out the strongly orthodox statement of the fixity of each species, which he had insisted upon in his earlier works. ... warnings came speedily both from the Catholic and Protestant sides.\",\n \"Carl Linnaeus\\n\\nThe mathematical PageRank algorithm, applied to 24 multilingual Wikipedia editions in 2014, published in PLOS ONE in 2015, placed Carl Linnaeus at the top historical figure, above Jesus, Aristotle, Napoleon, and Adolf Hitler (in that order).\",\n \"Carl Linnaeus\\n\\nStandard author abbreviation\"\n]","isConversational":false}}},{"rowIdx":1790,"cells":{"id":{"kind":"string","value":"tc_2763"},"question":{"kind":"string","value":"How many colors are there in the spectrum when white light is separated?"},"answer":{"kind":"string","value":"Seven"},"answer_aliases":{"kind":"list like","value":["seven","7"],"string":"[\n \"seven\",\n \"7\"\n]","isConversational":false},"documents":{"kind":"list like","value":["Color\n\nColor (American English) or colour (Commonwealth English) is the visual perceptual property corresponding in humans to the categories called red, blue, yellow, etc. Color derives from the spectrum of light (distribution of light power versus wavelength) interacting in the eye with the spectral sensitivities of the light receptors. Color categories and physical specifications of color are also associated with objects or materials based on their physical properties such as light absorption, reflection, or emission spectra. By defining a color space colors can be identified numerically by their coordinates.","Color\n\nBecause perception of color stems from the varying spectral sensitivity of different types of cone cells in the retina to different parts of the spectrum, colors may be defined and quantified by the degree to which they stimulate these cells. These physical or physiological quantifications of color, however, do not fully explain the psychophysical perception of color appearance.","Color\n\nThe science of color is sometimes called chromatics, colorimetry, or simply color science. It includes the perception of color by the human eye and brain, the origin of color in materials, color theory in art, and the physics of electromagnetic radiation in the visible range (that is, what we commonly refer to simply as light).","Color\n\nPhysics of color","Color\n\nElectromagnetic radiation is characterized by its wavelength (or frequency) and its intensity. When the wavelength is within the visible spectrum (the range of wavelengths humans can perceive, approximately from 390 nm to 700 nm), it is known as \"visible light\".","Color\n\nMost light sources emit light at many different wavelengths; a source's spectrum is a distribution giving its intensity at each wavelength. Although the spectrum of light arriving at the eye from a given direction determines the color sensation in that direction, there are many more possible spectral combinations than color sensations. In fact, one may formally define a color as a class of spectra that give rise to the same color sensation, although such classes would vary widely among different species, and to a lesser extent among individuals within the same species. In each such class the members are called metamers of the color in question.","Color\n\nSpectral colors","Color\n\nThe familiar colors of the rainbow in the spectrum – named using the Latin word for appearance or apparition by Isaac Newton in 1671 – include all those colors that can be produced by visible light of a single wavelength only, the pure spectral or monochromatic colors. The table at right shows approximate frequencies (in terahertz) and wavelengths (in nanometers) for various pure spectral colors. The wavelengths listed are as measured in air or vacuum (see refractive index).","Color\n\nThe color table should not be interpreted as a definitive list – the pure spectral colors form a continuous spectrum, and how it is divided into distinct colors linguistically is a matter of culture and historical contingency (although people everywhere have been shown to perceive colors in the same way ). A common list identifies six main bands: red, orange, yellow, green, blue, and violet. Newton's conception included a seventh color, indigo, between blue and violet. It is possible that what Newton referred to as blue is nearer to what today we call cyan, and that indigo was simply the dark blue of the indigo dye that was being imported at the time.","Color\n\nThe intensity of a spectral color, relative to the context in which it is viewed, may alter its perception considerably; for example, a low-intensity orange-yellow is brown, and a low-intensity yellow-green is olive-green.","Color\n\nColor of objects","Color\n\nThe color of an object depends on both the physics of the object in its environment and the characteristics of the perceiving eye and brain. Physically, objects can be said to have the color of the light leaving their surfaces, which normally depends on the spectrum of the incident illumination and the reflectance properties of the surface, as well as potentially on the angles of illumination and viewing. Some objects not only reflect light, but also transmit light or emit light themselves, which also contribute to the color. A viewer's perception of the object's color depends not only on the spectrum of the light leaving its surface, but also on a host of contextual cues, so that color differences between objects can be discerned mostly independent of the lighting spectrum, viewing angle, etc. This effect is known as color constancy.","Color\n\nSome generalizations of the physics can be drawn, neglecting perceptual effects for now:","Color\n\n* Light arriving at an opaque surface is either reflected \"specularly\" (that is, in the manner of a mirror), scattered (that is, reflected with diffuse scattering), or absorbed – or some combination of these. * Opaque objects that do not reflect specularly (which tend to have rough surfaces) have their color determined by which wavelengths of light they scatter strongly (with the light that is not scattered being absorbed). If objects scatter all wavelengths with roughly equal strength, they appear white. If they absorb all wavelengths, they appear black. * Opaque objects that specularly reflect light of different wavelengths with different efficiencies look like mirrors tinted with colors determined by those differences. An object that reflects some fraction of impinging light and absorbs the rest may look black but also be faintly reflective; examples are black objects coated with layers of enamel or lacquer. * Objects that transmit light are either translucent (scattering the transmitted light) or transparent (not scattering the transmitted light). If they also absorb (or reflect) light of various wavelengths differentially, they appear tinted with a color determined by the nature of that absorption (or that reflectance).","Color\n\n* Objects may emit light that they generate from having excited electrons, rather than merely reflecting or transmitting light. The electrons may be excited due to elevated temperature (incandescence), as a result of chemical reactions (chemoluminescence), after absorbing light of other frequencies (\"fluorescence\" or \"phosphorescence\") or from electrical contacts as in light emitting diodes, or other light sources.","Color\n\nTo summarize, the color of an object is a complex result of its surface properties, its transmission properties, and its emission properties, all of which contribute to the mix of wavelengths in the light leaving the surface of the object. The perceived color is then further conditioned by the nature of the ambient illumination, and by the color properties of other objects nearby, and via other characteristics of the perceiving eye and brain.","Color\n\nPerception","Color\n\nDevelopment of theories of color vision","Color\n\nAlthough Aristotle and other ancient scientists had already written on the nature of light and color vision, it was not until Newton that light was identified as the source of the color sensation. In 1810, Goethe published his comprehensive Theory of Colors in which he ascribed physiological effects to color that are now understood as psychological.","Color\n\nIn 1801 Thomas Young proposed his trichromatic theory, based on the observation that any color could be matched with a combination of three lights. This theory was later refined by James Clerk Maxwell and Hermann von Helmholtz. As Helmholtz puts it, \"the principles of Newton's law of mixture were experimentally confirmed by Maxwell in 1856. Young's theory of color sensations, like so much else that this marvelous investigator achieved in advance of his time, remained unnoticed until Maxwell directed attention to it.\"","Color\n\nAt the same time as Helmholtz, Ewald Hering developed the opponent process theory of color, noting that color blindness and afterimages typically come in opponent pairs (red-green, blue-orange, yellow-violet, and black-white). Ultimately these two theories were synthesized in 1957 by Hurvich and Jameson, who showed that retinal processing corresponds to the trichromatic theory, while processing at the level of the lateral geniculate nucleus corresponds to the opponent theory.","Color\n\nIn 1931, an international group of experts known as the Commission internationale de l'éclairage (CIE) developed a mathematical color model, which mapped out the space of observable colors and assigned a set of three numbers to each.","Color\n\nColor in the eye","Color\n\nThe ability of the human eye to distinguish colors is based upon the varying sensitivity of different cells in the retina to light of different wavelengths. Humans being trichromatic, the retina contains three types of color receptor cells, or cones. One type, relatively distinct from the other two, is most responsive to light that we perceive as blue or blue-violet, with wavelengths around 450 nm; cones of this type are sometimes called short-wavelength cones, S cones, or blue cones. The other two types are closely related genetically and chemically: middle-wavelength cones, M cones, or green cones are most sensitive to light perceived as green, with wavelengths around 540 nm, while the long-wavelength cones, L cones, or red cones, are most sensitive to light we perceive as greenish yellow, with wavelengths around 570 nm.","Color\n\nLight, no matter how complex its composition of wavelengths, is reduced to three color components by the eye. For each location in the visual field, the three types of cones yield three signals based on the extent to which each is stimulated. These amounts of stimulation are sometimes called tristimulus values.","Color\n\nThe response curve as a function of wavelength varies for each type of cone. Because the curves overlap, some tristimulus values do not occur for any incoming light combination. For example, it is not possible to stimulate only the mid-wavelength (so-called \"green\") cones; the other cones will inevitably be stimulated to some degree at the same time. The set of all possible tristimulus values determines the human color space. It has been estimated that humans can distinguish roughly 10 million different colors.","Color\n\nThe other type of light-sensitive cell in the eye, the rod, has a different response curve. In normal situations, when light is bright enough to strongly stimulate the cones, rods play virtually no role in vision at all. On the other hand, in dim light, the cones are understimulated leaving only the signal from the rods, resulting in a colorless response. (Furthermore, the rods are barely sensitive to light in the \"red\" range.) In certain conditions of intermediate illumination, the rod response and a weak cone response can together result in color discriminations not accounted for by cone responses alone. These effects, combined, are summarized also in the Kruithof curve, that describes the change of color perception and pleasingness of light as function of temperature and intensity.","Color\n\nColor in the brain","Color\n\nWhile the mechanisms of color vision at the level of the retina are well-described in terms of tristimulus values, color processing after that point is organized differently. A dominant theory of color vision proposes that color information is transmitted out of the eye by three opponent processes, or opponent channels, each constructed from the raw output of the cones: a red–green channel, a blue–yellow channel, and a black–white \"luminance\" channel. This theory has been supported by neurobiology, and accounts for the structure of our subjective color experience. Specifically, it explains why we cannot perceive a \"reddish green\" or \"yellowish blue\", and it predicts the color wheel: it is the collection of colors for which at least one of the two color channels measures a value at one of its extremes.","Color\n\nThe exact nature of color perception beyond the processing already described, and indeed the status of color as a feature of the perceived world or rather as a feature of our perception of the world – a type of qualia – is a matter of complex and continuing philosophical dispute.","Color\n\nNonstandard color perception","Color\n\nColor deficiency","Color\n\nIf one or more types of a person's color-sensing cones are missing or less responsive than normal to incoming light, that person can distinguish fewer colors and is said to be color deficient or color blind (though this latter term can be misleading; almost all color deficient individuals can distinguish at least some colors). Some kinds of color deficiency are caused by anomalies in the number or nature of cones in the retina. Others (like central or cortical achromatopsia) are caused by neural anomalies in those parts of the brain where visual processing takes place.","Color\n\nTetrachromacy","Color\n\nWhile most humans are trichromatic (having three types of color receptors), many animals, known as tetrachromats, have four types. These include some species of spiders, most marsupials, birds, reptiles, and many species of fish. Other species are sensitive to only two axes of color or do not perceive color at all; these are called dichromats and monochromats respectively. A distinction is made between retinal tetrachromacy (having four pigments in cone cells in the retina, compared to three in trichromats) and functional tetrachromacy (having the ability to make enhanced color discriminations based on that retinal difference). As many as half of all women are retinal tetrachromats. The phenomenon arises when an individual receives two slightly different copies of the gene for either the medium- or long-wavelength cones, which are carried on the x-chromosome. To have two different genes, a person must have two x-chromosomes, which is why the phenomenon only occurs in women. For some of these retinal tetrachromats, color discriminations are enhanced, making them functional tetrachromats.","Color\n\nSynesthesia","Color\n\nIn certain forms of synesthesia/ideasthesia, perceiving letters and numbers (grapheme–color synesthesia) or hearing musical sounds (music–color synesthesia) will lead to the unusual additional experiences of seeing colors. Behavioral and functional neuroimaging experiments have demonstrated that these color experiences lead to changes in behavioral tasks and lead to increased activation of brain regions involved in color perception, thus demonstrating their reality, and similarity to real color percepts, albeit evoked through a non-standard route.","Color\n\nAfterimages","Color\n\nAfter exposure to strong light in their sensitivity range, photoreceptors of a given type become desensitized. For a few seconds after the light ceases, they will continue to signal less strongly than they otherwise would. Colors observed during that period will appear to lack the color component detected by the desensitized photoreceptors. This effect is responsible for the phenomenon of afterimages, in which the eye may continue to see a bright figure after looking away from it, but in a complementary color.","Color\n\nAfterimage effects have also been utilized by artists, including Vincent van Gogh.","Color\n\nColor constancy","Color\n\nWhen an artist uses a limited color palette, the eye tends to compensate by seeing any gray or neutral color as the color which is missing from the color wheel. For example, in a limited palette consisting of red, yellow, black, and white, a mixture of yellow and black will appear as a variety of green, a mixture of red and black will appear as a variety of purple, and pure gray will appear bluish.","Color\n\nThe trichromatic theory is strictly true when the visual system is in a fixed state of adaptation. In reality, the visual system is constantly adapting to changes in the environment and compares the various colors in a scene to reduce the effects of the illumination. If a scene is illuminated with one light, and then with another, as long as the difference between the light sources stays within a reasonable range, the colors in the scene appear relatively constant to us. This was studied by Edwin Land in the 1970s and led to his retinex theory of color constancy.","Color\n\nIt should be noted, that both phenomena are readily explained and mathematically modeled with modern theories of chromatic adaptation and color appearance (e.g. CIECAM02, iCAM). There is no need to dismiss the trichromatic theory of vision, but rather it can be enhanced with an understanding of how the visual system adapts to changes in the viewing environment.","Color\n\nColor naming","Color\n\nColors vary in several different ways, including hue (shades of red, orange, yellow, green, blue, and violet), saturation, brightness, and gloss. Some color words are derived from the name of an object of that color, such as \"orange\" or \"salmon\", while others are abstract, like \"red\".","Color\n\nIn the 1969 study Basic Color Terms: Their Universality and Evolution, Brent Berlin and Paul Kay describe a pattern in naming \"basic\" colors (like \"red\" but not \"red-orange\" or \"dark red\" or \"blood red\", which are \"shades\" of red). All languages that have two \"basic\" color names distinguish dark/cool colors from bright/warm colors. The next colors to be distinguished are usually red and then yellow or green. All languages with six \"basic\" colors include black, white, red, green, blue, and yellow. The pattern holds up to a set of twelve: black, gray, white, pink, red, orange, yellow, green, blue, purple, brown, and azure (distinct from blue in Russian and Italian, but not English).","Color\n\nAssociations","Color\n\nIndividual colors have a variety of cultural associations such as national colors (in general described in individual color articles and color symbolism). The field of color psychology attempts to identify the effects of color on human emotion and activity. Chromotherapy is a form of alternative medicine attributed to various Eastern traditions. Colors have different associations in different countries and cultures.","Color\n\nDifferent colors have been demonstrated to have effects on cognition. For example, researchers at the University of Linz in Austria demonstrated that the color red significantly decreases cognitive functioning in men.","Color\n\nSpectral colors and color reproduction","Color\n\nMost light sources are mixtures of various wavelengths of light. Many such sources can still effectively produce a spectral color, as the eye cannot distinguish them from single-wavelength sources. For example, most computer displays reproduce the spectral color orange as a combination of red and green light; it appears orange because the red and green are mixed in the right proportions to allow the eye's cones to respond the way they do to the spectral color orange.","Color\n\nA useful concept in understanding the perceived color of a non-monochromatic light source is the dominant wavelength, which identifies the single wavelength of light that produces a sensation most similar to the light source. Dominant wavelength is roughly akin to hue.","Color\n\nThere are many color perceptions that by definition cannot be pure spectral colors due to desaturation or because they are purples (mixtures of red and violet light, from opposite ends of the spectrum). Some examples of necessarily non-spectral colors are the achromatic colors (black, gray, and white) and colors such as pink, tan, and magenta.","Color\n\nTwo different light spectra that have the same effect on the three color receptors in the human eye will be perceived as the same color. They are metamers of that color. This is exemplified by the white light emitted by fluorescent lamps, which typically has a spectrum of a few narrow bands, while daylight has a continuous spectrum. The human eye cannot tell the difference between such light spectra just by looking into the light source, although reflected colors from objects can look different. (This is often exploited; for example, to make fruit or tomatoes look more intensely red.)","Color\n\nSimilarly, most human color perceptions can be generated by a mixture of three colors called primaries. This is used to reproduce color scenes in photography, printing, television, and other media. There are a number of methods or color spaces for specifying a color in terms of three particular primary colors. Each method has its advantages and disadvantages depending on the particular application.","Color\n\nNo mixture of colors, however, can produce a response truly identical to that of a spectral color, although one can get close, especially for the longer wavelengths, where the CIE 1931 color space chromaticity diagram has a nearly straight edge. For example, mixing green light (530 nm) and blue light (460 nm) produces cyan light that is slightly desaturated, because response of the red color receptor would be greater to the green and blue light in the mixture than it would be to a pure cyan light at 485 nm that has the same intensity as the mixture of blue and green.","Color\n\nBecause of this, and because the primaries in color printing systems generally are not pure themselves, the colors reproduced are never perfectly saturated spectral colors, and so spectral colors cannot be matched exactly. However, natural scenes rarely contain fully saturated colors, thus such scenes can usually be approximated well by these systems. The range of colors that can be reproduced with a given color reproduction system is called the gamut. The CIE chromaticity diagram can be used to describe the gamut.","Color\n\nAnother problem with color reproduction systems is connected with the acquisition devices, like cameras or scanners. The characteristics of the color sensors in the devices are often very far from the characteristics of the receptors in the human eye. In effect, acquisition of colors can be relatively poor if they have special, often very \"jagged\", spectra caused for example by unusual lighting of the photographed scene.\nA color reproduction system \"tuned\" to a human with normal color vision may give very inaccurate results for other observers.","Color\n\nThe different color response of different devices can be problematic if not properly managed. For color information stored and transferred in digital form, color management techniques, such as those based on ICC profiles, can help to avoid distortions of the reproduced colors. Color management does not circumvent the gamut limitations of particular output devices, but can assist in finding good mapping of input colors into the gamut that can be reproduced.","Color\n\nAdditive coloring","Color\n\nAdditive color is light created by mixing together light of two or more different colors. Red, green, and blue are the additive primary colors normally used in additive color systems such as projectors and computer terminals.","Color\n\nSubtractive coloring","Color\n\nSubtractive coloring uses dyes, inks, pigments, or filters to absorb some wavelengths of light and not others. The color that a surface displays comes from the parts of the visible spectrum that are not absorbed and therefore remain visible. Without pigments or dye, fabric fibers, paint base and paper are usually made of particles that scatter white light (all colors) well in all directions. When a pigment or ink is added, wavelengths are absorbed or \"subtracted\" from white light, so light of another color reaches the eye.","Color\n\nIf the light is not a pure white source (the case of nearly all forms of artificial lighting), the resulting spectrum will appear a slightly different color. Red paint, viewed under blue light, may appear black. Red paint is red because it scatters only the red components of the spectrum. If red paint is illuminated by blue light, it will be absorbed by the red paint, creating the appearance of a black object.","Color\n\nStructural color","Color\n\nStructural colors are colors caused by interference effects rather than by pigments. Color effects are produced when a material is scored with fine parallel lines, formed of one or more parallel thin layers, or otherwise composed of microstructures on the scale of the color's wavelength. If the microstructures are spaced randomly, light of shorter wavelengths will be scattered preferentially to produce Tyndall effect colors: the blue of the sky (Rayleigh scattering, caused by structures much smaller than the wavelength of light, in this case air molecules), the luster of opals, and the blue of human irises. If the microstructures are aligned in arrays, for example the array of pits in a CD, they behave as a diffraction grating: the grating reflects different wavelengths in different directions due to interference phenomena, separating mixed \"white\" light into light of different wavelengths. If the structure is one or more thin layers then it will reflect some wavelengths and transmit others, depending on the layers' thickness.","Color\n\nStructural color is studied in the field of thin-film optics. A layman's term that describes particularly the most ordered or the most changeable structural colors is iridescence. Structural color is responsible for the blues and greens of the feathers of many birds (the blue jay, for example), as well as certain butterfly wings and beetle shells. Variations in the pattern's spacing often give rise to an iridescent effect, as seen in peacock feathers, soap bubbles, films of oil, and mother of pearl, because the reflected color depends upon the viewing angle. Numerous scientists have carried out research in butterfly wings and beetle shells, including Isaac Newton and Robert Hooke. Since 1942, electron micrography has been used, advancing the development of products that exploit structural color, such as \"photonic\" cosmetics.","Color\n\nMentions of color in social media","Color\n\nAccording to Pantone, the top three colors in social media for 2012 were red (186 million mentions; accredited to Taylor Swift's Red album, NASA's landing on Mars, and red carpet coverage), blue (125 million mentions; accredited to the United States presidential election, 2012, Mars rover Curiosity finding blue rocks, and blue sports teams), and Green (102 million mentions; accredited to \"environmental friendliness\", Green Bay Packers, and green eyed girls).","Color\n\nAdditional terms","Color\n\n* Color wheel: an illustrative organization of color hues in a circle that shows relationships.\n* Colorfulness, chroma, purity, or saturation: how \"intense\" or \"concentrated\" a color is. Technical definitions distinguish between colorfulness, chroma, and saturation as distinct perceptual attributes and include purity as a physical quantity. These terms, and others related to light and color are internationally agreed upon and published in the CIE Lighting Vocabulary. More readily available texts on colorimetry also define and explain these terms. \n* Dichromatism: a phenomenon where the hue is dependent on concentration and/or thickness of the absorbing substance.\n* Hue: the color's direction from white, for example in a color wheel or chromaticity diagram.\n* Shade: a color made darker by adding black.\n* Tint: a color made lighter by adding white.\n* Value, brightness, lightness, or luminosity: how light or dark a color is.","Electromagnetic spectrum\n\nThe electromagnetic spectrum is the collective term for all known frequencies and their linked wave lengths of the known photons ( electromagnetic radiation ). The \"electromagnetic spectrum\" of an object has a different meaning, and is instead the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object.","Electromagnetic spectrum\n\nThe electromagnetic spectrum extends from below the low frequencies used for modern radio communication to gamma radiation at the short-wavelength (high-frequency) end, thereby covering wavelengths from thousands of kilometers down to a fraction of the size of an atom. Visible light lies toward the shorter end, with wavelengths from 400 to 700 nanometres. The limit for long wavelengths is the size of the universe itself, while it is thought that the short wavelength limit is in the vicinity of the Planck length. Until the middle of the 20th century it was believed by most physicists that this spectrum was infinite and continuous.","Electromagnetic spectrum\n\nNearly all types of electromagnetic radiation can be used for spectroscopy, to study and characterize matter. Other technological uses are described under electromagnetic radiation.","Electromagnetic spectrum\n\nHistory of electromagnetic spectrum discovery","Electromagnetic spectrum\n\nFor most of history, visible light was the only known part of the electromagnetic spectrum. The ancient Greeks recognized that light traveled in straight lines and studied some of its properties, including reflection and refraction. The study of light continued, and during the 16th and 17th centuries conflicting theories regarded light as either a wave or a particle.","Electromagnetic spectrum\n\nThe first discovery of electromagnetic radiation other than visible light came in 1800, when William Herschel discovered infrared radiation. He was studying the temperature of different colors by moving a thermometer through light split by a prism. He noticed that the highest temperature was beyond red. He theorized that this temperature change was due to \"calorific rays\" that were a type of light ray that could not be seen.","Electromagnetic spectrum\n\nThe next year, Johann Ritter, working at the other end of the spectrum, noticed what he called \"chemical rays\" (invisible light rays that induced certain chemical reactions). These behaved similarly to visible violet light rays, but were beyond them in the spectrum. They were later renamed ultraviolet radiation.","Electromagnetic spectrum\n\nElectromagnetic radiation had been first linked to electromagnetism in 1845, when Michael Faraday noticed that the polarization of light traveling through a transparent material responded to a magnetic field (see Faraday effect). During the 1860s James Maxwell developed four partial differential equations for the electromagnetic field. Two of these equations predicted the possibility of, and behavior of, waves in the field. Analyzing the speed of these theoretical waves, Maxwell realized that they must travel at a speed that was about the known speed of light. This startling coincidence in value led Maxwell to make the inference that light itself is a type of electromagnetic wave.","Electromagnetic spectrum\n\nMaxwell's equations predicted an infinite number of frequencies of electromagnetic waves, all traveling at the speed of light. This was the first indication of the existence of the entire electromagnetic spectrum.","Electromagnetic spectrum\n\nMaxwell's predicted waves included waves at very low frequencies compared to infrared, which in theory might be created by oscillating charges in an ordinary electrical circuit of a certain type. Attempting to prove Maxwell's equations and detect such low frequency electromagnetic radiation, in 1886 the physicist Heinrich Hertz built an apparatus to generate and detect what are now called radio waves. Hertz found the waves and was able to infer (by measuring their wavelength and multiplying it by their frequency) that they traveled at the speed of light. Hertz also demonstrated that the new radiation could be both reflected and refracted by various dielectric media, in the same manner as light. For example, Hertz was able to focus the waves using a lens made of tree resin. In a later experiment, Hertz similarly produced and measured the properties of microwaves. These new types of waves paved the way for inventions such as the wireless telegraph and the radio.","Electromagnetic spectrum\n\nIn 1895 Wilhelm Röntgen noticed a new type of radiation emitted during an experiment with an evacuated tube subjected to a high voltage. He called these radiations x-rays and found that they were able to travel through parts of the human body but were reflected or stopped by denser matter such as bones. Before long, many uses were found for them in the field of medicine.","Electromagnetic spectrum\n\nThe last portion of the electromagnetic spectrum was filled in with the discovery of gamma rays. In 1900 Paul Villard was studying the radioactive emissions of radium when he identified a new type of radiation that he first thought consisted of particles similar to known alpha and beta particles, but with the power of being far more penetrating than either. However, in 1910, British physicist William Henry Bragg demonstrated that gamma rays are electromagnetic radiation, not particles, and in 1914, Ernest Rutherford (who had named them gamma rays in 1903 when he realized that they were fundamentally different from charged alpha and beta particles) and Edward Andrade measured their wavelengths, and found that gamma rays were similar to X-rays, but with shorter wavelengths and higher frequencies.","Electromagnetic spectrum\n\nRange of the spectrum","Electromagnetic spectrum\n\nElectromagnetic waves are typically described by any of the following three physical properties: the frequency f, wavelength λ, or photon energy E. Frequencies observed in astronomy range from (1 GeV gamma rays) down to the local plasma frequency of the ionized interstellar medium (~1 kHz). Wavelength is inversely proportional to the wave frequency, so gamma rays have very short wavelengths that are fractions of the size of atoms, where as wavelengths on the opposite end of the spectrum can be as long as the universe. Photon energy is directly proportional to the wave frequency, so gamma ray photons have the highest energy (around a billion electron volts), while radio wave photons have very low energy (around a femtoelectronvolt). These relations are illustrated by the following equations:\nf \\frac{c}{\\lambda}, \\quad\\text{or}\\quad f \n \\frac{E}{h}, \\quad\\text{or}\\quad E=\\frac{hc}{\\lambda},\nwhere:\n*c = is the speed of light in a vacuum\n*h \n is Planck's constant.","Electromagnetic spectrum\n\nWhenever electromagnetic waves exist in a medium with matter, their wavelength is decreased. Wavelengths of electromagnetic radiation, no matter what medium they are traveling through, are usually quoted in terms of the vacuum wavelength, although this is not always explicitly stated.","Electromagnetic spectrum\n\nGenerally, electromagnetic radiation is classified by wavelength into radio wave, microwave, terahertz (or sub-millimeter) radiation, infrared, the visible region that is perceived as light, ultraviolet, X-rays and gamma rays. The behavior of EM radiation depends on its wavelength. When EM radiation interacts with single atoms and molecules, its behavior also depends on the amount of energy per quantum (photon) it carries.","Electromagnetic spectrum\n\nSpectroscopy can detect a much wider region of the EM spectrum than the visible range of 400 nm to 700 nm. A common laboratory spectroscope can detect wavelengths from 2 nm to 2500 nm. Detailed information about the physical properties of objects, gases, or even stars can be obtained from this type of device. Spectroscopes are widely used in astrophysics. For example, many hydrogen atoms emit a radio wave photon that has a wavelength of 21.12 cm. Also, frequencies of 30 Hz and below can be produced by and are important in the study of certain stellar nebulae and frequencies as high as have been detected from astrophysical sources.","Electromagnetic spectrum\n\nRationale for spectrum regional names","Electromagnetic spectrum\n\nElectromagnetic radiation interacts with matter in different ways across the spectrum. These types of interaction are so different that historically different names have been applied to different parts of the spectrum, as though these were different types of radiation. Thus, although these \"different kinds\" of electromagnetic radiation form a quantitatively continuous spectrum of frequencies and wavelengths, the spectrum remains divided for practical reasons related to these qualitative interaction differences.","Electromagnetic spectrum\n\nTypes of radiation","Electromagnetic spectrum\n\nBoundaries","Electromagnetic spectrum\n\nA discussion of the regions (or bands or types) of the electromagnetic spectrum is given below. Note that there are no precisely defined boundaries between the bands of the electromagnetic spectrum; rather they fade into each other like the bands in a rainbow (which is the sub-spectrum of visible light). Radiation of each frequency and wavelength (or in each band) has a mix of properties of the two regions of the spectrum that bound it. For example, red light resembles infrared radiation in that it can excite and add energy to some chemical bonds and indeed must do so to power the chemical mechanisms responsible for photosynthesis and the working of the visual system.","Electromagnetic spectrum\n\nRegions of the spectrum","Electromagnetic spectrum\n\nThe types of electromagnetic radiation are broadly classified into the following classes:\n# Gamma radiation\n# X-ray radiation\n# Ultraviolet radiation\n# Visible radiation\n# Infrared radiation\n# Terahertz radiation\n# Microwave radiation\n# Radio waves\nThis classification goes in the increasing order of wavelength, which is characteristic of the type of radiation.\nWhile, in general, the classification scheme is accurate, in reality there is often some overlap between neighboring types of electromagnetic energy. For example, SLF radio waves at 60 Hz may be received and studied by astronomers, or may be ducted along wires as electric power, although the latter is, in the strict sense, not electromagnetic radiation at all (see near and far field).","Electromagnetic spectrum\n\nThe distinction between X-rays and gamma rays is partly based on sources: the photons generated from nuclear decay or other nuclear and subnuclear/particle process, are always termed gamma rays, whereas X-rays are generated by electronic transitions involving highly energetic inner atomic electrons. In general, nuclear transitions are much more energetic than electronic transitions, so gamma-rays are more energetic than X-rays, but exceptions exist. By analogy to electronic transitions, muonic atom transitions are also said to produce X-rays, even though their energy may exceed 6 MeV, whereas there are many (77 known to be less than 10 keV) low-energy nuclear transitions (e.g., the nuclear transition of thorium-229), and, despite being one million-fold less energetic than some muonic X-rays, the emitted photons are still called gamma rays due to their nuclear origin.","Electromagnetic spectrum\n\nThe convention that EM radiation that is known to come from the nucleus, is always called \"gamma ray\" radiation is the only convention that is universally respected, however. Many astronomical gamma ray sources (such as gamma ray bursts) are known to be too energetic (in both intensity and wavelength) to be of nuclear origin. Quite often, in high energy physics and in medical radiotherapy, very high energy EMR (in the >10 MeV region)—which is of higher energy than any nuclear gamma ray—is not called X-ray or gamma-ray, but instead by the generic term of \"high energy photons.\"","Electromagnetic spectrum\n\nThe region of the spectrum where a particular observed electromagnetic radiation falls, is reference frame-dependent (due to the Doppler shift for light), so EM radiation that one observer would say is in one region of the spectrum could appear to an observer moving at a substantial fraction of the speed of light with respect to the first to be in another part of the spectrum. For example, consider the cosmic microwave background. It was produced, when matter and radiation decoupled, by the de-excitation of hydrogen atoms to the ground state. These photons were from Lyman series transitions, putting them in the ultraviolet (UV) part of the electromagnetic spectrum. Now this radiation has undergone enough cosmological red shift to put it into the microwave region of the spectrum for observers moving slowly (compared to the speed of light) with respect to the cosmos.","Electromagnetic spectrum\n\nRadio frequency","Electromagnetic spectrum\n\nRadio waves generally are utilized by antennas of appropriate size (according to the principle of resonance), with wavelengths ranging from hundreds of meters to about one millimeter. They are used for transmission of data, via modulation. Television, mobile phones, wireless networking, and amateur radio all use radio waves. The use of the radio spectrum is regulated by many governments through frequency allocation.","Electromagnetic spectrum\n\nRadio waves can be made to carry information by varying a combination of the amplitude, frequency, and phase of the wave within a frequency band. When EM radiation impinges upon a conductor, it couples to the conductor, travels along it, and induces an electric current on the surface of that conductor by exciting the electrons of the conducting material. This effect (the skin effect) is used in antennas.","Electromagnetic spectrum\n\nMicrowaves","Electromagnetic spectrum\n\nThe super-high frequency (SHF) and extremely high frequency (EHF) of microwaves are on the short side of radio waves. Microwaves are waves that are typically short enough (measured in millimeters) to employ tubular metal waveguides of reasonable diameter. Microwave energy is produced with klystron and magnetron tubes, and with solid state diodes such as Gunn and IMPATT devices. Microwaves are absorbed by molecules that have a dipole moment in liquids. In a microwave oven, this effect is used to heat food. Low-intensity microwave radiation is used in Wi-Fi, although this is at intensity levels unable to cause thermal heating.","Electromagnetic spectrum\n\nVolumetric heating, as used by microwave ovens, transfers energy through the material electromagnetically, not as a thermal heat flux. The benefit of this is a more uniform heating and reduced heating time; microwaves can heat material in less than 1% of the time of conventional heating methods.","Electromagnetic spectrum\n\nWhen active, the average microwave oven is powerful enough to cause interference at close range with poorly shielded electromagnetic fields such as those found in mobile medical devices and poorly made consumer electronics.","Electromagnetic spectrum\n\nTerahertz radiation","Electromagnetic spectrum\n\nTerahertz radiation is a region of the spectrum between far infrared and microwaves. Until recently, the range was rarely studied and few sources existed for microwave energy at the high end of the band (sub-millimeter waves or so-called terahertz waves), but applications such as imaging and communications are now appearing. Scientists are also looking to apply terahertz technology in the armed forces, where high-frequency waves might be directed at enemy troops to incapacitate their electronic equipment.","Electromagnetic spectrum\n\nInfrared radiation","Electromagnetic spectrum\n\nThe infrared part of the electromagnetic spectrum covers the range from roughly 300 GHz to 400 THz (1 mm - 750 nm). It can be divided into three parts:\n*Far-infrared, from 300 GHz to 30 THz (1 mm - 10 μm). The lower part of this range may also be called microwaves or terahertz waves. This radiation is typically absorbed by so-called rotational modes in gas-phase molecules, by molecular motions in liquids, and by phonons in solids. The water in Earth's atmosphere absorbs so strongly in this range that it renders the atmosphere in effect opaque. However, there are certain wavelength ranges (\"windows\") within the opaque range that allow partial transmission, and can be used for astronomy. The wavelength range from approximately 200 μm up to a few mm is often referred to as \"sub-millimeter\" in astronomy, reserving far infrared for wavelengths below 200 μm. *Mid-infrared, from 30 to 120 THz (10 - 2.5 μm). Hot objects (black-body radiators) can radiate strongly in this range, and human skin at normal body temperature radiates strongly at the lower end of this region. This radiation is absorbed by molecular vibrations, where the different atoms in a molecule vibrate around their equilibrium positions.","Electromagnetic spectrum\n\nThis range is sometimes called the fingerprint region, since the mid-infrared absorption spectrum of a compound is very specific for that compound. *Near-infrared, from 120 to 400 THz (2,500 - 750 nm). Physical processes that are relevant for this range are similar to those for visible light. The highest frequences in this region can be detected directly by some types of photographic film, and by many types of solid state image sensors for infrared photography and videography.","Electromagnetic spectrum\n\nVisible radiation (light)","Electromagnetic spectrum\n\nAbove infrared in frequency comes visible light. The Sun emits its peak power in the visible region, although integrating the entire emission power spectrum through all wavelengths shows that the Sun emits slightly more infrared than visible light. By definition, visible light is the part of the EM spectrum the human eye is the most sensitive to. Visible light (and near-infrared light) is typically absorbed and emitted by electrons in molecules and atoms that move from one energy level to another. This action allows the chemical mechanisms that underlie human vision and plant photosynthesis. The light that excites the human visual system is a very small portion of the electromagnetic spectrum. A rainbow shows the optical (visible) part of the electromagnetic spectrum; infrared (if it could be seen) would be located just beyond the red side of the rainbow with ultraviolet appearing just beyond the violet end.","Electromagnetic spectrum\n\nElectromagnetic radiation with a wavelength between 380 nm and 760 nm (400–790 terahertz) is detected by the human eye and perceived as visible light. Other wavelengths, especially near infrared (longer than 760 nm) and ultraviolet (shorter than 380 nm) are also sometimes referred to as light, especially when the visibility to humans is not relevant. White light is a combination of lights of different wavelengths in the visible spectrum. Passing white light through a prism splits it up into the several colors of light observed in the visible spectrum between 400 nm and 780 nm.","Electromagnetic spectrum\n\nIf radiation having a frequency in the visible region of the EM spectrum reflects off an object, say, a bowl of fruit, and then strikes the eyes, this results in visual perception of the scene. The brain's visual system processes the multitude of reflected frequencies into different shades and hues, and through this insufficiently-understood psychophysical phenomenon, most people perceive a bowl of fruit.","Electromagnetic spectrum\n\nAt most wavelengths, however, the information carried by electromagnetic radiation is not directly detected by human senses. Natural sources produce EM radiation across the spectrum, and technology can also manipulate a broad range of wavelengths. Optical fiber transmits light that, although not necessarily in the visible part of the spectrum (it is usually infrared), can carry information. The modulation is similar to that used with radio waves.","Electromagnetic spectrum\n\nUltraviolet radiation","Electromagnetic spectrum\n\nNext in frequency comes ultraviolet (UV). The wavelength of UV rays is shorter than the violet end of the visible spectrum but longer than the X-ray.","Electromagnetic spectrum\n\nUV in the very shortest wavelength range (next to X-rays) is capable of ionizing atoms (see photoelectric effect), greatly changing their physical behavior.","Electromagnetic spectrum\n\nAt the middle range of UV, UV rays cannot ionize but can break chemical bonds, making molecules unusually reactive. Sunburn, for example, is caused by the disruptive effects of middle range UV radiation on skin cells, which is the main cause of skin cancer. UV rays in the middle range can irreparably damage the complex DNA molecules in the cells producing thymine dimers making it a very potent mutagen.","Electromagnetic spectrum\n\nThe Sun emits significant UV radiation (about 10% of its total power), including extremely short wavelength UV that could potentially destroy most life on land (ocean water would provide some protection for life there). However, most of the Sun's damaging UV wavelengths are absorbed by the atmosphere and ozone layer before they reach the surface. The higher energy (shortest wavelength) ranges of UV (called \"vacuum UV\") are absorbed by nitrogen and, at longer wavelengths, by simple diatomic oxygen in the air. Most of the UV in the mid-range of energy is blocked by the ozone layer, which absorbs strongly in the important 200–315 nm range, the lower energy part of which is too long for ordinary dioxygen in air to absorb. The very lowest energy range of UV between 315 nm and visible light (called UV-A) is not blocked well by the atmosphere, but does not cause sunburn and does less biological damage. However, it is not harmless and does create oxygen radicals, mutations and skin damage. See ultraviolet for more information.","Electromagnetic spectrum\n\nX-rays","Electromagnetic spectrum\n\nAfter UV come X-rays, which, like the upper ranges of UV are also ionizing. However, due to their higher energies, X-rays can also interact with matter by means of the Compton effect. Hard X-rays have shorter wavelengths than soft X-rays and as they can pass through many substances with little absorption, they can be used to 'see through' objects with 'thicknesses' less than that equivalent to a few meters of water. One notable use is diagnostic X-ray imaging in medicine (a process known as radiography). X-rays are useful as probes in high-energy physics. In astronomy, the accretion disks around neutron stars and black holes emit X-rays, enabling studies of these phenomena. X-rays are also emitted by the coronas of stars and are strongly emitted by some types of nebulae. However, X-ray telescopes must be placed outside the Earth's atmosphere to see astronomical X-rays, since the great depth of the atmosphere of Earth is opaque to X-rays (with areal density of 1000 grams per cm2), equivalent to 10 meters thickness of water. This is an amount sufficient to block almost all astronomical X-rays (and also astronomical gamma rays—see below).","Electromagnetic spectrum\n\nGamma rays","Electromagnetic spectrum\n\nAfter hard X-rays come gamma rays, which were discovered by Paul Villard in 1900. These are the most energetic photons, having no defined lower limit to their wavelength. In astronomy they are valuable for studying high-energy objects or regions, however as with X-rays this can only be done with telescopes outside the Earth's atmosphere. Gamma rays are used experimentally by physicists for their penetrating ability and are produced by a number of radioisotopes. They are used for irradiation of foods and seeds for sterilization, and in medicine they are occasionally used in radiation cancer therapy.[http://www.revisionworld.com/gcse-revision/physics/waves/uses-electromagnetic-waves Uses of Electromagnetic Waves | gcse-revision, physics, waves, uses-electromagnetic-waves | Revision World] More commonly, gamma rays are used for diagnostic imaging in nuclear medicine, an example being PET scans. The wavelength of gamma rays can be measured with high accuracy through the effects of Compton scattering.","White\n\nWhite is an achromatic color, a color without hue. An incoming light to the human eye that stimulates all its three types of color sensitive cone cells in nearly equal amounts results in white. White is one of the most common colors in nature, the color of sunlight, snow, milk, chalk, limestone and other common minerals. In many cultures white represents or signifies purity, innocence, and light, and is the symbolic opposite of black, or darkness. According to surveys in Europe and the United States, white is the color most often associated with perfection, the good, honesty, cleanliness, the beginning, the new, neutrality, and exactitude.","White\n\nIn ancient Egypt and ancient Rome, priestesses wore white as a symbol of purity, and Romans wore a white toga as a symbol of citizenship. In the Middle Ages and Renaissance a white unicorn symbolized chastity, and a white lamb sacrifice and purity; the widows of kings dressed in white rather than black as the color of mourning. It sometimes symbolizes royalty; it was the color of the French kings (black being the color of the queens) and of the monarchist movement after the French Revolution as well as of the movement called the White Russians (not to be confounded with Belarus, literally \"White Russia\") who fought the Bolsheviks during the Russian Civil War (1917–1922). Greek and Roman temples were faced with white marble, and beginning in the 18th century, with the advent of neoclassical architecture, white became the most common color of new churches, capitols and other government buildings, especially in the United States. It was also widely used in 20th century modern architecture as a symbol of modernity, simplicity and strength.","White\n\nWhite is an important color for almost all world religions. The Pope, the head of the Roman Catholic Church, has worn white since 1566, as a symbol of purity and sacrifice. In Islam, and in the Shinto religion of Japan, it is worn by pilgrims; and by the Brahmins in India. In Western cultures and in Japan, white is the most common color for wedding dresses, symbolizing purity and virginity. In many Asian cultures, white is also the color of mourning.","White\n\nThe white color on television screens and computer monitors is created with the RGB color model by mixing red, green and blue light at equal intensities.","White\n\nWhite in nature and culture","White\n\nFile:Alps.jpg|Ice and snow. The Weisshorn (\"white mountain\"), in the high Alps.\nFile:Milk glass.jpg|A glass of milk\nFile:Cloud.jpg|Cumulus clouds\nFile:Taj Mahal (Edited).jpeg|White marble - the Taj Mahal.\nFile: Ivory cover of the Lorsch Gospels, c. 810, Carolingian, Victoria and Albert Museum.jpg| Ivory cover of the Lorsch Gospels, circa 810 AD, (Victoria and Albert Museum, London.)\nFile:Three Maries.jpg|Alabaster statue of the three Maries, (circa 1450), Warsaw Museum.\nFile:Andalusian.jpg|A white Andalusian horse. White is commonly associated with innocence, perfection and purity.\nFile:Polar bear with young - ANWR.jpg|Polar bear with young, Arctic National Wildlife Refuge, Alaska. \nFile:Douvres (6).JPG|The White Cliffs of Dover are composed of chalk, or calcium carbonate.","White\n\nIn nature, snow and clouds appear white because they are composed of water droplets or ice crystals mixed with air; when white sunlight enters snow, very little of the spectrum is absorbed; almost all of the light is reflected or scattered by the air and water molecules, so the snow appears to be the color of sunlight, white. Beaches with sand containing high amounts of quartz or eroded limestone also appear white, since quartz and limestone reflect or scatter sunlight, rather than absorbing it. Tropical white sand beaches may also have a high quantity of white calcium carbonate from tiny bits of seashells ground to fine sand by the action of the waves. An individual that has an aversion or hatred for the color white is called a leukophobe.","White\n\nEtymology","White\n\nThe word white continues Old English ', ultimately from a Common Germanic ' also reflected in OHG ', ON ', Goth. '. The root is ultimately from Proto-Indo-European language ', surviving also in Sanskrit ' \"to be white or bright\" and Slavonic ' \"light\". \nThe Icelandic word for white, ', is directly derived from the Old Norse form of the word '.\nCommon Germanic also had the word *blankaz (\"white, bright, blinding\"), borrowed into Late Latin as *blancus, which provided the source for Romance words for \"white\" (Catalan, Occitan and French blanc, Spanish blanco, Italian bianco, Galician-Portuguese branco, etc.). The antonym of white is black.","White\n\nSome non-European languages have a wide variety of terms for white. The Inuit language has seven different words for seven different nuances of white. Sanskrit has specific words for bright white, the white of teeth, the white of sandalwood, the white of the autumn moon, the white of silver, the white of cow's milk, the white of pearls, the white of a ray of sunlight, and the white of stars. Japanese has six different words, depending upon brilliance or dullness, or if the color is inert or dynamic.","White\n\nWhite in history and art","White\n\nThe Ancient World","White\n\nWhite was one of the first colors used by Paleolithic artists; they used calcite or chalk, sometimes as a background, sometimes as a highlight, along with charcoal and red and yellow ochre in their vivid cave paintings.","White\n\nIn ancient Egypt, white was connected with the goddess Isis. The priests and priestesses of Isis dressed only in white linen, and it was used to wrap mummies.","White\n\nIn Greece and other ancient civilizations, white was often associated with mother's milk. In Greek mythology, the chief god Zeus was nourished at the breast of the nymph Amalthea. In the Talmud, milk was one of four sacred substances, along with wine, honey, and the rose.","White\n\nThe ancient Greeks saw the world in terms of darkness and light, so white was a fundamental color. According to Pliny the Elder in his Natural History, Apelles (4th century BC) and the other famous painters of ancient Greece used only four colors in their paintings; white, red, yellow and black; For painting, the Greeks used lead white, made by a long and laborious process.","White\n\nA plain white toga, known as a toga virilis, was worn for ceremonial occasions by all Roman citizens over the age of 14–18. Magistrates and certain priests wore a toga praetexta, with a broad purple stripe.\nIn the time of the Emperor Augustus, no Roman man was allowed to appear in the Roman forum without a toga.","White\n\nThe ancient Romans had two words for white; albus, a plain white, (the source of the word albino); and candidus, a brighter white. A man who wanted public office in Rome wore a white toga brightened with chalk, called a toga candida, the origin of the word candidate. The Latin word candere meant to shine, to be bright. It was the origin of the words candle and candid.","White\n\nIn ancient Rome, the priestesses of the goddess Vesta dressed in white linen robes, a white palla or shawl, and a white veil. They protected the sacred fire and the penates of Rome. White symbolized their purity, loyalty, and chastity.","White\n\nFile:Paintings from the Chauvet cave (museum replica).jpg|Prehistoric paintings in Chauvet Cave, France (30,000 to 32,000 BC)\nFile:Ägyptischer Maler um 1360 v. Chr. 001.jpg|Painting of the goddess Isis (1380–1385 BC). The priests of her cult wore white linen.\nFile:Maler der Grabkammer des Thot 001.jpg|Paintings of women in white from a tomb (1448–1422 BC).\nFile:Chief Vestal.jpg|Statue of the chief Vestal Virgin, wearing a white palla and a white veil.","White\n\nThe Middle Ages and the Renaissance","White\n\nThe early Christian church adopted the Roman symbolism of white as the color of purity, sacrifice and virtue. It became the color worn by priests during Mass, the color worn by monks of the Cistercian Order, and, under Pope Pius V, a former monk of the Dominican Order, it became the official color worn by the pope himself. Monks of the Order of Saint Benedict dressed in the white or gray of natural undyed wool, but later changed to black, the color of humility and penitence.","White\n\nIn Medieval art, the white lamb became the symbol of the sacrifice of Christ on behalf of mankind. John the Baptist described Christ as the lamb of God, who took the sins of the world upon himself. The white lamb was the center of one of the most famous paintings of the Medieval period, the Ghent Altarpiece by Jan van Eyck.","White\n\nWhite was also the symbolic color of the transfiguration. The Gospel of Saint Mark describes Jesus' clothing in this event as \"shining, exceeding white as snow.\" Artists such as Fra Angelico used their greatest skill to capture the whiteness of his garments. In his painting of the transfiguration at the Convent of Saint Mark in Florence, Fra Angelico emphasized the white garment by using a light gold background, placed in an almond-shaped halo.","White\n\nThe white unicorn was a common subject of Medieval and Renaissance manuscripts, paintings and tapestries. It was a symbol of purity, chastity and grace, which could only be captured by a virgin. It was often portrayed in the lap of the Virgin Mary.","White\n\nDuring the Middle Ages, painters rarely ever mixed colors; but in the Renaissance, the influential humanist and scholar Leon Battista Alberti encouraged artists to add white to their colors to make them lighter, brighter, and to add hilaritas, or gaiety. Many painters followed his advice, and the palette of the Renaissance was considerably brighter.","White\n\nIn the Middle Ages and Renaissance, white was commonly worn by widows as a color of mourning. The widows of the kings of France wore white until Anne of Brittany in the 16th century. A white tunic was also worn by many knights, along with a red cloak, which showed the knights were willing to give their blood for the king or Church.","White\n\nFile:Sodoma - Life of St Benedict, Scene 31 - Benedict Feeds the Monk - WGA21581.jpg|The monks of the order of Saint Benedict (circa 480-542) first dressed in undyed white or gray wool robes, here shown in painting by Sodoma on the life of Saint Benedict (1504). They later changed to black robes, the color of humility and penitence. File:Unicorn hunt - British Library Royal 12 F xiii f10v (detail).jpg|The white unicorn frequently appeared in Medieval art, often as a symbol of virginity and purity. This the unicorn hunt from the Rochester Bestiary, from about 1230, in the British Library. File:Bartolomeo Passarotti Pope Pius V.jpg|Under Pope Pius V (1504–1572), a former monk of the Dominican Order, white became the official color worn by the Pope. File:Ghent Altarpiece D - Adoration of the Lamb 2.jpg|The white lamb in the Ghent Altarpiece by Jan van Eyck. (1432)\nFile:Transfiguration by fra Angelico (San Marco Cell 6).jpg|The Transfiguration by Fra Angelico (1440–1442)\nFile:Leonardo da Vinci - Portrait of Cecilia Gallerani (Lady with an Ermine) - WGA12698.jpg|Lady with an ermine, by Leonardo da Vinci (1490). The ermine symbolized nobility and purity.","White\n\nIt was believed that an ermine would rather die than allow its white fur to become dirty. File:Mary Queen of Scots in mourning.jpg|Mary Stuart wore white in mourning for her husband, King Francis II of France, who died in 1560.","White\n\n18th and 19th centuries","White\n\nWhite was the dominant color of architectural interiors in the Baroque period and especially the Rococo style that followed it in the 18th century. Church interiors were designed to show the power, glory and wealth of the church. They seemed to be alive, filled with curves, asymmetry, mirrors, gilding, statuary and reliefs, unified by white.","White\n\nWhite was also a fashionable color for both men and women in the 18th century. Men in the aristocracy and upper classes wore powdered white wigs and white stockings, and women wore elaborate embroidered white and pastel gowns.","White\n\nAfter the French Revolution, a more austere white (blanc cassé) became the most fashionable color in women's costumes which were modeled after the outfits of Ancient Greece and Republican Rome. Because of the rather revealing design of these dresses, the ladies wearing them were called les merveilleuses (the marvellous) by French men of that era. The Empire style under Emperor Napoléon I was modeled after the more conservative outfits of Ancient Imperial Rome. The dresses were high in fashion but low in warmth considering the more severe weather conditions of northern France; in 1814 the former wife of Napoleon, Joséphine de Beauharnais, caught pneumonia and died after taking a walk in the cold night air with Tsar Alexander I of Russia.","White\n\nWhite was the universal color of both men and women's underwear and of sheets in the 18th and 19th centuries. It was unthinkable to have sheets or underwear of any other color. The reason was simple; the manner of washing linen in boiling water caused colors to fade. When linen was worn out, it was collected and turned into high-quality paper.","White\n\nThe 19th-century American painter James McNeill Whistler (1834–1903), working at the same time as the French impressionists, created a series of paintings with musical titles where he used color to create moods, the way composers used music. His painting \"Symphony in White No. 1 - The White Girl\", which used his mistress Joanna Hiffernan as a model, used delicate colors to portray innocence and fragility, and a moment of uncertainty.","White\n\nFile:BasilikaOttobeurenHauptschiff02.JPG|A highly theatrical white Rococo interior from the 18th century, at the Basilica at Ottobeuren, in Bavaria.\nFile:Marie-Antoinette par Elisabeth Vigée-Lebrun - 1783.jpg|White gown of Marie Antoinette, painted by Elisabeth Vigée-Lebrun in 1783. \nFile:Gilbert Stuart, George Washington (Lansdowne portrait, 1796).jpg|President George Washington in a white powdered wig. The first five Presidents of the United States wore dark suits with powdered wigs for formal occasions.\nFile:Emprjose.jpg|Portrait of Joséphine de Beauharnais in a classic Empire gown, modeled after the clothing of ancient Rome. (1801), by François Gérard. (The State Hermitage Museum).\nFile:Whistler James Symphony in White no 1 (The White Girl) 1862.jpg|Symphony in White No. 1 - The White Girl, by James McNeill Whistler (1862).","White\n\n20th and 21st centuries","White\n\nThe White movement was the opposition that formed against the Bolsheviks during the Russian Civil War, which followed the Russian Revolution in 1917. It was finally defeated by the Bolsheviks in 1921-22, and many of its members emigrated to Europe.","White\n\nAt the end of the 19th century, lead white was still the most popular pigment; but between 1916 and 1918, chemical companies in Norway and the United States began to produce titanium white, made from titanium oxide. It had first been identified in the 18th century by the German chemist Martin Klaproth, who also discovered uranium. It had twice the covering power of lead white, and was the brightest white pigment known. By 1945, 80 percent of the white pigments sold were titanium white.","White\n\nThe absoluteness of white appealed to modernist painters. It was used in its simplest form by the Russian suprematist painter Kazimir Malevich in his 1917 painting 'the white square,' the companion to his earlier 'black square.' It was also used by the Dutch modernist painter Piet Mondrian. His most famous paintings consisted of a pure white canvas with grid of vertical and horizontal black lines and rectangles of primary colors.","White\n\nBlack and white also appealed to modernist architects, such as Le Corbusier (1887–1965). He said a house was \"a machine for living in\" and called for a \"calm and powerful architecture\" built of reinforced concrete and steel, without any ornament or frills. Almost all the buildings of contemporary architect Richard Meier, such as his museum in Rome to house the ancient Roman Ara Pacis, or Altar of Peace, are stark white, in the tradition of Le Corbusier.","White\n\nFile:За единую Россію.jpg|Poster for the White Army during the Russian Civil War (1917–22). The poster says: \"for a United Russia.\" \nFile:Kazimir_Malevich_-_%27Suprematist_Composition-_White_on_White%27,_oil_on_canvas,_1918,_Museum_of_Modern_Art.jpg|White on White (1917) by Kazimir Malevich, Museum of Modern Art, New York\nFile:VillaSavoye.jpg|The Villa Savoye (1928–31) by Le Corbusier. Le Corbusier called for a \"calm and powerful\" architecture built of steel and reinforced concrete.","White\n\nScience","White\n\nOptics and white light","White\n\nWhite is the color the human visual system senses when the incoming light to the eye stimulates all three types of color sensitive cone cells in the eye in nearly equal amounts. Materials that do not emit light themselves appear white if their surfaces reflect back most of the light that strikes them in a diffuse way.","White\n\nIn 1666, Isaac Newton demonstrated that white light could be broken up into its composite colors by passing it through a prism, then using a second prism to reassemble them. Before Newton, most scientists believed that white was the fundamental color of light.","White\n\nWhite light can be generated by the sun, by stars, or by earthbound sources such as fluorescent lamps, white LEDs and incandescent bulbs. On the screen of a color television or computer, white is produced by mixing the primary colors of light: red, green and blue (RGB) at full intensity, a process called additive mixing (see image below). White light can be fabricated using light with only two wavelengths, for instance by mixing light from a red and cyan laser or yellow and blue lasers. This light will however have very few practical applications since color rendering of objects will be greatly distorted.","White\n\nThe fact that light sources with vastly different spectral power distributions can result in a similar sensory experience is due to the way the light is processed by the visual system. One color that arise from two different spectral power distributions is called a metamerism.","White\n\nThe International Commission on Illumination defines white (adapted) as \"a color stimulus that an observer who is adapted to the viewing environment would judge to be perfectly achromatic and to have a luminance factor of unity. The color stimulus that is considered to be the adapted white may be different at different locations within a scene.","White\n\nThe adaptation mentioned in the CIE definition above is the chromatic adaptation by which the same colored object in a scene experienced under very different illuminations will be perceived as having nearly the same color. The same principle is used in photography and cinematography where the choice of white point determines a transformation of all other color stimuli. Changes in or manipulation of the white point can be used to explain some optical illusions such as The dress.","White\n\nFile:Synthese+.svg|In the RGB color model, used to create colors on TV and computer screens, white is made by mixing red, blue and green light at full intensity.\nFile:Dispersion prism.jpg|White light refracted in a prism revealing the color components.","White\n\nMany of the light sources that emit white light emit light at almost all visible wavelengths (sun light, incandescent lamps of various Color temperatures). This has led to the notion that white light can be defined as a mixture of \"all colors\" or \"all visible wavelengths\". This misconception is widespread and might originally stem from the fact that Newton discovered that sunlight is composed of light with wavelengths across the visible spectrum. Concluding that since \"all colors\" produce white light then white must be made up of \"all colors\" is a common logical error called affirming the consequent, which might be the cause of the misunderstanding.","White\n\nWhy snow, clouds and beaches are white","White\n\nSnow is a mixture of air and tiny ice crystals. When white sunlight enters snow, very little of the spectrum is absorbed; almost all of the light is reflected or scattered by the air and water molecules, so the snow appears to be the color of sunlight, white. Sometimes the light bounces around inside the ice crystals before being scattered, making the snow seem to sparkle.","White\n\nIn the case of glaciers, the ice is more tightly pressed together and contains little air. As sunlight enters the ice, more light of the red spectrum is absorbed, so the light scattered will be bluish.","White\n\nClouds are white for the same reason as ice. They are composed of water droplets or ice crystals mixed with air, very little light that strikes them is absorbed, and most of the light is scattered, appearing to the eye as white. Shadows of other clouds above can make clouds look gray, and some clouds have their own shadow on the bottom of the cloud.","White\n\nMany mountains with winter or year-round snow cover are named accordingly: Mauna Kea means white mountain in Hawaiian, Mont Blanc means white mountain in French. Changbai Mountains literally meaning perpetually white mountains, marks the border between China and Korea.","White\n\nBeaches with sand containing high amounts of quartz or eroded limestone also appear white, since quartz and limestone reflect or scatter sunlight, rather than absorbing it. Tropical white sand beaches may also have a high quantity of white calcium carbonate from tiny bits of seashells ground to fine sand by the action of the waves.","White\n\nFile:Snow-covered fir trees.jpg|Snow is composed of ice and air; it scatters or reflects sunlight without absorbing other colors of the spectrum.","White\n\nFile:MontBlanc2c.jpg|Mont Blanc in the Alps. It takes its name from the white snow on its summit.\nFile:Cumulus clouds in fair weather.jpeg|Cumulus clouds look white because the water droplets reflect and scatter the sunlight without absorbing other colors.\nFile:Pensacola Beach 1957 White Sand.jpg|Pensacola Beach, Florida. White sand beaches look white because the quartz or eroded limestone in the sand reflects or scatters sunlight without absorbing other colors.","White\n\nChemistry- white pigments and dyes","White\n\nChalk is a kind of limestone, made of the mineral calcite, or calcium carbonate. It was originally deposited under the sea as the scales or plates of tiny micro-organisms called Coccolithophore. It was the first white pigment used by prehistoric artists in cave paintings. The chalk used on blackboards today is usually made of gypsum or calcium sulphate, a powder pressed into sticks.","White\n\nBianco di San Giovanni is a pigment used in the Renaissance, which was described by the painter Cennino Cennini in the 15th century. It is similar to chalk, made of calcium carbonate with calcium hydroxide. It was made of dried lime which was made into a powder, then soaked in water for eight days, with the water changed each day. It was then made into cakes and dried in the sun.","White\n\nLead white was being produced during the 4th century BC; the process is described is Pliny the Elder, Vitruvius and the ancient Greek author Theophrastus. Pieces of lead were put into clay pots which had a separate compartment filled with vinegar. The pots in turn were piled on shelves close to cow dung. The combined fumes of the vinegar and the cow dung caused the lead to corrode into lead carbonate. It was a slow process which could take a month or more. It made an excellent white and was used by artists for centuries, but it was also toxic. It was replaced in the 19th century by zinc white and titanium white.","White\n\nTitanium white is the most popular white for artists today; it is the brightest available white pigment, and has twice the coverage of lead white. It first became commercially available in 1921. It is made out of titanium dioxide, from the minerals brookite, anatase, rutile, or ilmenite, currently the major source. Because of its brilliant whiteness, it is used as a colorant for most toothpaste and sunscreen.","White\n\nZinc white is made from zinc oxide. It is similar to but not as opaque as titanium white. It is added to some breakfast cereals, since zinc is an important nutrient.","White\n\nSome materials can be made to look \"whiter than white\", this is achieved using optical brightener agents (OBA). These are chemical compounds that absorb light in the ultraviolet and violet region (usually 340-370 nm) of the electromagnetic spectrum, and re-emit light in the blue region (typically 420-470 nm). OBAs are often used in paper and clothing to create an impression of very bright white. This is due to the fact that the materials actually send out more visible light than they receive.","White\n\nChinese white is a variety of zinc white made for artists.","White\n\nFile:Titanium(IV) oxide.jpg|Titanium white, made with titanium dioxide, is the brightest white paint available. It also colors most toothpaste and sunscreen. \nFile:Zinc oxide.jpg|Zinc white, made from zinc oxide.","White\n\nBleach and bleaching","White\n\nBleaching is a process for whitening fabrics which has been practiced for thousands of years. Sometimes it was simply a matter of leaving the fabric in the sun, to be faded by the bright light. In the 18th century several scientists developed varieties of chlorine bleach, including sodium hypochlorite and calcium hypochlorite (bleaching powder). Bleaching agents that do not contain chlorine most often are based on peroxides, such as hydrogen peroxide, sodium percarbonate and sodium perborate. While most bleaches are oxidizing agents, a fewer number are reducing agents such as sodium dithionite.","White\n\nBleaches attack the chromophores, the part of a molecule which absorbs light and causes fabrics to have different colors. An oxidizing bleach works by breaking the chemical bonds that make up the chromophore. This changes the molecule into a different substance that either does not contain a chromophore, or contains a chromophore that does not absorb visible light. A reducing bleach works by converting double bonds in the chromophore into single bonds. This eliminates the ability of the chromophore to absorb visible light.","White\n\nSunlight acts as a bleach through a similar process. High energy photons of light, often in the violet or ultraviolet range, can disrupt the bonds in the chromophore, rendering the resulting substance colorless.","White\n\nSome detergents go one step further; they contain fluorescent chemicals which glow, making the fabric look literally whiter than white.","White\n\nAstronomy","White\n\nA white dwarf is a stellar remnant composed mostly of electron-degenerate matter. They are very dense; a white dwarf's mass is comparable to that of the Sun and its volume is comparable to that of the Earth. Its faint luminosity comes from the emission of stored thermal energy.","White\n\nA white dwarf is very hot when it is formed, but since it has no source of energy, it will gradually radiate away its energy and cool down. This means that its radiation, which initially has a high color temperature, will lessen and redden with time. Over a very long time, a white dwarf will cool to temperatures at which it will no longer emit significant heat or light, and it will become a cold black dwarf. However, since no white dwarf can be older than the age of the Universe (approximately 13.8 billion years), even the oldest white dwarfs still radiate at temperatures of a few thousand kelvins, and no black dwarfs are thought to exist yet.","White\n\nFile:Sirius A and B Hubble photo.jpg|Image of Sirius A and Sirius B taken by the Hubble Space Telescope. Sirius B, a white dwarf, is the faint pinprick of light to the lower left of the much brighter Sirius A.","White\n\nBiology","White\n\nMost white animals have their color as a form of camouflage in winter.","White\n\nFile:Dove 001.JPG|The dove is an international symbol of peace.\nFile:Ivory Gull Portrait.jpg|The ivory gull.\nFile:Cygnus olor 2 (Marek Szczepanek).jpg|Mute swans. Swans of the Northern Hemisphere are white, while those of the Southern Hemisphere are black and white. \nFile:Polarfuchs 1 2004-11-17.jpg|The Arctic fox\nFile:Mustela erminea winter cropped.jpg|The ermine, or stoat. Once considered the most noble of animals because it would rather die than dirty its fur, it is now considered an invasive species.\nFile:Uncia uncia.jpg|A snow leopard.\nFile:Delphinapterus leucas 2.jpg|A beluga whale. Its color helps it hide from its chief enemies, the polar bear and killer whales.\nFile:White pearl necklace.jpg|White pearls are hard objects produced within the soft tissue of a living shelled mollusk, like an oyster or clam. They are made of calcium carbonate in minute crystalline form. \nFile:Betula pendula 001.jpg|The silver birch's bark is silvery-white.\nFile:Proteus anguinus Postojnska Jama Slovenija.jpg|Olms in Postojna Cave, Slovenia. Their skin color is pale or whitish.\nFile:Large white spread wings.jpg|A cabbage butterfly (Pieris brassicae).","White\n\nAssociations and symbolism","White\n\nInnocence and sacrifice","White\n\nIn Western culture, white is the color most often associated with innocence. In Biblical times, lambs and other white animals were sacrificed to expiate sins. In Christianity Christ is considered the \"lamb of God,\" who died for the sins of mankind. The white lily is considered the flower of purity and innocence, and is often associated with the Virgin Mary.","White\n\nThe beginning and the new","White\n\nWhite is the color in Western culture most often associated with beginnings and the new. In Christianity, children are baptized wearing white, and, wear white for their first communion. Christ after his Resurrection is traditionally portrayed dressed in white. Eggs, another symbol of the new, are used to celebrate Easter.","White\n\nThe Queen of the United Kingdom traditionally wears white when she opens the session of Parliament. In high society, debutantes traditionally wear white for their first ball.","White\n\nWeddings","White\n\nWhite has long been the traditional color worn by brides at royal weddings, but the white wedding gown for ordinary people appeared in the 19th century. Before that time, most brides wore their best Sunday clothing, of whatever color. The white lace wedding gown of Queen Victoria in 1840 had a large impact on the color and fashion of wedding dresses in both Europe and America down to the present day.","White\n\nFile:Wedding of Queen Victoria and Prince Albert.jpg|The wedding dress of Queen Victoria (1840) set the fashion for wedding dresses of the Victorian era and for the 20th century.\nFile:Wedding of Nicholas II and Alexandra Feodorovna by Laurits Tuxen (1895, Hermitage).jpg|The wedding of Czar Nicholas II of Russia and Alexandra Feodorovna (Alix of Hesse), the granddaughter of Queen Victoria, in 1894.\nFile:Wedding kimono.jpg|Brides in China and other parts of Asia traditionally wear red, the color of happiness and good fortune, but in the Shinto religion of Japan brides traditionally wear a white wedding kimono.\nFile:MyBarong created this Custom tailored Barong Tagalog for my wedding.jpg|The Barong Tagalog is a traditional Folk costume of the Philippines; this attire is worn on formal gatherings and weddings.","White\n\nCleanliness","White\n\nWhite is the color most associated with cleanliness. Objects which are expected to be clean, such as refrigerators and dishes, toilets and sinks, bed linen and towels, are traditionally white. White was the traditional color of the coats of doctors, nurses, scientists and laboratory technicians, though nowadays a pale blue or green is often used. White is also the color most often worn by chefs, bakers, and butchers, and the color of the aprons of waiters in French restaurants.","White\n\nGhosts, phantoms and two of the Four Horsemen of the Apocalypse","White\n\nWhite is the color associated with ghosts and phantoms. In the past the dead were traditionally buried in a white shroud. Ghosts are said to be the spirits of the dead who, for various reasons, are unable to rest or enter heaven, and so walk the earth in their white shrouds. White is also connected with the paleness of death. A common expression in English is \"pale as a ghost.\"","White\n\nThe woman in white, Weiße Frau, or dame blanche is a familiar figure in English, German and French ghost stories. She is a spectral apparition of a female clad in white, in most cases the ghost of an ancestor, sometimes giving warning about death and disaster. The most notable Weiße Frau is the legendary ghost of the German Hohenzollern dynasty.","White\n\nSeeing a white horse in a dream is said to be presentiment of death. \nIn the Book of Revelation, the last book in the New Testament of the Bible, the Four Horsemen of the Apocalypse are supposed to announce the Apocalypse before the Last Judgement. The man on a white horse with a bow and arrow. according to different interpretations, represents either War and Conquest, the Antichrist, or Christ himself, cleansing the world of sin. Death rides a horse whose color is described in ancient Greek as khlōros (χλωρός) in the original Koine Greek, which can mean either green/greenish-yellow or pale/pallid. \nFile:Apparition DB.JPG|The woman in white or dame blanche is a familiar figure in English, French and German ghost stories.\nFile:Apocalypse vasnetsov.jpg|The biblical Four Horsemen of the Apocalypse. Conquest, with a bow, rides a white horse. Death rides a pale or light green horse. (Painting by Viktor Vasnetsov, 1887).","White\n\nBlack and white","White\n\nBlack and white often represent the contrast between light and darkness, day and night, good and evil.","White\n\nIn taoism, the two opposite natures of the universe, yin and yang, are often symbolized in black and white, Ancient games of strategy, such as go and chess, use black and white to represent the two sides.","White\n\nIn the French monarchy, white symbolized the King and his power par la grâce de Dieu (\"by the grace of God\") and in contrast black was the color of the queen who according to the Salic Law which excluded women from the throne (and thus from power) could never become the ruling monarch.","White\n\nBlack and white also often represent formality and seriousness, as in the costumes of judges and priests, business suits, of formal evening dress. Monks of the Dominican Order wear a black cloak over a white habit. Until 1972 agents of the Federal Bureau of Investigation were required to wear white shirts with their suits, to project the correct image of the FBI.","White\n\nFile:Yin and Yang.svg|In Taoism, white represents the yang, one of the two opposite natures of the universe.","White\n\nNames taken from white","White\n\nWhite is the source of more names for women in western countries than any other color. Names taken from white include Alba, Albine (Latin). Blanche and Blanchette (French); Bianca (Italian); Jennifer (Celt); Genevieve, Candice (from Latin Candida); Fenela, Fiona and Finola (Irish); Gwendoline, Gwenael, Nol(g)wen (white woman) (Celt), Nives (Italian) and Zuria (Basque).","White\n\nIn addition many names come from white flowers: Camille, Daisy, Lily, Lili, Magnolie, Jasmine, Yasemine, Leila, Marguerite, Rosalba, and others.","White\n\nOther names come from the white pearl; Pearl, Margarita (Latin), Margaret, Margarethe, Marga, Grete, Rita, Gitta, Marjorie, Margot.","White\n\nWhite in other cultures","White\n\nIn China, Korea, and some other Asian countries, white, or more precisely, the whitish color of undyed linen, is the color of mourning and funerals.","White\n\nIn traditional China, undyed linen clothing is worn at funerals. As time passes, the bereaved can gradually wear clothing dyed with colors, then with darker colors. Small sacks of quicklime, one for each year of the life of the deceased are placed around the body to protect it against impurity in the next world, and white paper flowers are placed around the body.","White\n\nIn China and other Asian counties, white is the color of reincarnation, showing that death is not a permanent separation from the world.","White\n\nIn China, white is associated with the masculine (the yang of the yin and yang); with the unicorn and tiger; with the fur of an animal; with the direction of west; with the element metal; and with the autumn season.","White\n\nIn Japan, undyed linen white robes are worn by pilgrims for rituals of purification, and bathing in sacred rivers. In the mountains, pilgrims wear costumes of undyed jute to symbolize purity. A white kimono is often placed in the casket with the deceased for the journey to the other world, as white represents death sometimes. Condolence gifts, or kooden, are tied with black and white ribbons and wrapped in white paper, protecting the contents from the impurities of the other world.","White\n\nIn India, the color white was traditionally reserved for the Brahmin caste. It is the color of purity, divinity, detachment and serenity. In Hindi, the name Sweta means white.","White\n\nIn Tibetan Buddhism, white robes were reserved for the lama of a monastery.","White\n\nIn the Bedouin and some other pastoral cultures, there is a strong connection between milk and white, which is considered the color of gratitude, esteem, joy, good fortune and fertility.","White\n\nFile:Iwamotoji PilgrimGirl.JPG|A pilgrim in Japan.\nFile:JapaneseFuneralEnvelope.jpg|In Japan, the traditional envelope for condolence gifts is wrapped in a black and white cord, and a white kimono is often placed in the coffin with the deceased.\nFile:Weisse tara mongolian art.jpg|The Buddhist deity Tara is often depicted with white skin.\nFile:Brahmin boy ritual.jpg|A Brahmin boy in India wears white for a religious ritual.\nFile:Bedouin.jpg|A Bedouin in the United Arab Emirates. White is the traditional costume for men, and the color of esteem and good fortune.","White\n\nTemples, churches and government buildings","White\n\nSince ancient times, temples, churches, and many government buildings in many countries have traditionally been white, the color associated with religious and civic virtue. The Parthenon and other ancient temples of Greece, and the buildings of the Roman forum were mostly made of or clad in white marble, though it is now known that some of these ancient buildings were actually brightly painted. The Roman tradition of using white stone for government buildings and churches was revived in the Renaissance and especially in the neoclassic style of the 18th and 19th centuries. White stone became the material of choice for government buildings in Washington D.C. and other American cities. European cathedrals were also usually built of white or light-colored stone, though many darkened over the centuries from smoke and soot.","White\n\nThe Renaissance architect and scholar Leon Battista Alberti wrote in 1452 that churches should be plastered white on the inside, since white was the only appropriate color for reflection and meditation. After the Reformation, Calvinist churches in the Netherlands were whitewashed and sober inside, a tradition that was also followed in the Protestant churches of New England, such as Old North Church in Boston.","White\n\nFile:Parthenon.jpg|Although the Parthenon in Athens (5th century BC) is white today, it was originally painted with many colors \nFile:858MilanoDuomo.JPG|The Cathedral of Milan (1386–1965)\nFile:Delft interieur Waalse Kerk.jpg|Dutch Reformed Church interior in Delft, the Netherlands (16th century)\nFile:2006Boston007.jpg|Interior of Old North Church, Boston (1723)\nFile:WhiteHouseSouthFacade.JPG|The White House (1801), Washington D.C.\nFile:United States Capitol dome daylight.jpg|The United States Capitol dome (1855–66)\nFile:Sacre-coeur-paris.jpg| Basilica of Sacré-Cœur, Paris (1919)\nFile:Palacio do Planalto.jpeg|The Palácio do Planalto in Brasília, official workplace of the President of Brazil (1960)\nFile:St Mary's Cathedral - San Francisco.jpg|Saint Mary's Cathedral in San Francisco (1971)\nFile:Den Haag stadhuis april 2004.JPG|The City Hall in The Hague, Netherlands, by architect Richard Meier (2004).","White\n\nGovernment and politics","White\n\nWhite is often associated with monarchism. The association originally came from the white flag of the Bourbon dynasty of France. White became the banner of the royalist rebellions against the French Revolution (see Revolt in the Vendée).","White\n\nDuring the Civil War which followed the Russian Revolution of 1917, the White Army, a coalition of monarchists, nationalists and liberals, fought unsuccessfully against the Red Army of the Bolsheviks. A similar battle between reds and whites took place during the Civil War in Finland in the same period.","White\n\nThe Ku Klux Klan is a racist and anti-immigrant organization which flourished in the Southern United States after the American Civil War. They wore white robes and hoods, burned crosses and violently attacked and murdered black Americans.","White\n\nIn Iran, the White Revolution was a series of social and political reforms launched in 1963 by the last Shah of Iran before his downfall.","White\n\nWhite is also associated with peace and passive resistance. The white ribbon is worn by movements denouncing violence against women and the White Rose was a non-violent resistance group in Nazi Germany.","White\n\nFile:Volunteer Army recruitment poster.jpg|A recruiting poster for the White Volunteer Army during the Russian Civil War (1919). The text says, \"Son, go save the motherland!\" \nFile:Klan-in-gainesville.jpg|A cross burning by the racist Ku Klux Klan in Florida in the early 20th century.","White\n\nReligion","White\n\nIn the Roman Catholic Church, white is associated with Jesus Christ, innocence and sacrifice. Since the Middle Ages, priests wear a white cassock in many of the most important ceremonies and religious services connected with events in the life of Christ. White is worn by priests at Christmas, during Easter, and during celebrations connected with the other events of the life of Christ, such as Corpus Christi Sunday, and Trinity Sunday. It is also worn at the services dedicated to the Virgin Mary, and to those Saints who were not martyred, as well as other special occasions, such as the ordination of priests and the installation of new bishops. Within the hierarchy of the church, the lighter the color, the higher the rank. Ordinary priests wear black; bishops wear violet, cardinals wear red, and outside a church, only the Pope will wear white. Popes occasionally wore white in the Middle Ages, but usually wore red. Popes have worn white regularly since 1566, when Pope Pius V, a member of the Dominican Order, began the practice. White is the color of the Dominican Order.","White\n\nIn Islam, white clothing is worn during required pilgrimage to Mecca, or Ihram pilgrimage (Hajj).Hajj. Called Ihram clothing, men's garments often consist of two white un-hemmed sheets (usually towelling material). The top (the riḍā) is draped over the torso and the bottom (the izār) is secured by a belt; plus a pair of sandals. Women's clothing varies considerably and reflects regional as well as religious influences. Ihram is typically worn during Dhu al-Hijjah, the last month in the Islamic calendar.","White\n\nIn Judaism, during the rituals of Yom Kippur, the ceremony of atonement, the rabbi dresses in white, as do the members of the congregation, to restore the bonds between God and his followers.","White\n\nIn the traditional Japanese religion of Shinto, an area of white gravel or stones marks a sacred place, called a niwa. These places were dedicated to the kami, spirits which had descended from the heavens or had come across the sea. Later, temples of Zen Buddhism in Japan often featured a Zen garden, where white sand or gravel was carefully raked to resemble rivers or streams, designed as objects of meditation.","White\n\nIn the temples of The Church of Jesus Christ of Latter-day Saints (LDS Church or also known as Mormon), White clothing is worn inside once they have been officially dedicated, due to white symbolizing purity.","White\n\nMany religions symbolize heaven by using a sky with white clouds. This phenomenon is not limited to western culture; in Yoruba religion, the orisha Obatala in the Ifá tradition is represented by white. Obatala is associated with calmness, morality, old age, and purity.","White\n\nIn Theosophy and similar religions, the deities called the Great White Brotherhood are said to have white auras.","White\n\nIn some Asian and Slavic cultures, white is considered to be a color that represents death. White also represented death in ancient Egypt, representing the lifeless desert that covered much of the country; black was held to be the color of life, representing the mud-covered fertile lands created by the flooding of the Nile and giving the country its name (Kemet, or \"black land\").","White\n\nFile:Al-Haram mosque - Flickr - Al Jazeera English.jpg|Thousands of pilgrims in white gather in Mecca for the beginning of their pilgrimage, or Haj.\nFile:Pope Francis in March 2013.jpg|Pope Francis (2013). The Pope wears white as a symbol of innocence and sacrifice.\nFile:Toufuku-ji kaizandou3.JPG|The zen garden of Tōfuku-ji temple in Japan. The Shinto religion uses white sand or gravel to symbolize a sacred place, while Zen Buddhism uses it to stimulate calm and meditation.","White\n\nEthnography","White\n\nPeople of the Caucasian race, most commonly those of European descent, are often referred to simply as white. The United States Census Bureau defines White people as those \"having origins in any of the original peoples of Europe, the Middle East, or North Africa. It includes people who reported “White” or wrote in entries such as Irish, German, Italian, Lebanese, Near Easterner, Arab, or Polish.\" Whites constitute the majority of the U.S. population, with a total of 223,553,265 or 72.4% of the population in the 2010 United States Census.","White\n\nThe white flag","White\n\nA white flag has long been used to represent either surrender or a request for a truce. It is believed to have originated in the 15th century, during the Hundred Years' War between France and England, when multicolored flags, as well as firearms, came into common use by European armies. The white flag was officially recognized as a request to cease hostilities by the Geneva Convention of 1949.","White\n\nVexillology and heraldry","White\n\nIn English heraldry, white or silver signified brightness, purity, virtue, and innocence.","White\n\nSelected national flags featuring white","White\n\nWhite is a common color in national flags, though its symbolism varies widely. The white in the flag of the United States and flag of the United Kingdom comes from traditional red St George's Cross on a white background of the historic flag of England. The white in the flag of France represents either the monarchy or \"white, the ancient French color\" according to the Marquis de Lafayette.","White\n\nMany flags in the Arab world use the colors of the flag of the Arab Revolt of 1916; red, white, green and black. These include the flags of Egypt, Bahrain, Jordan, Syria, Kuwait and Iraq.","White\n\nPhilippines also use white as their symbol for unity in their flag.","White\n\nFile:Pavillon royal de France.svg|Flag of the Bourbons, royal family of France until the French Revolution and during the restoration of the monarchy afterwards.\nFile:Flag of the Vatican City.svg|The Flag of Vatican City (1929). The white and gold colors symbolize the colors of the keys to heaven given by Jesus Christ to Saint Peter: the gold of spiritual power, the white of worldly power. The keys have been the Papal symbol since the 13th century.","White\n\nFile:Flag of the Netherlands.svg|The flag of the Netherlands (1572) was the first red, white and blue national flag. Peter the Great adopted the colors for the flag of Russia. \nFile:Flag of India.svg|The flag of India (1947). White represents \"light, the path of truth\". \nFile:Flag of Ireland.svg|The flag of Ireland. According to the Irish government press office, \"The green represents the older Gaelic tradition while the orange represents the supporters of William of Orange. The white in the centre signifies a lasting truce between the 'Orange' and the 'Green'. \" \nFile:Flag of Egypt.svg|The flag of Egypt (1984). \nFile:Flag of the Philippines.svg| The Flag of the Philippines use royal blue, scarlet , yellow, and white. \nThe colors come from the flag of the Arab Revolt in 1916.\nFile:Flag of Taliban.svg|The flag of the Taliban in Afghanistan from 1997-2001. It reverses the colors of the Black Standard, the flag of Muhammad. The text says 'There is no God but Allah, and Muhammad is his prophet.\"","White\n\nIdioms and expressions","White\n\n* To whitewash something is to conceal an unpleasant reality. * A white lie is an innocent lie told out of politeness. * White noise is the noise of all the frequencies of sound combined. It is used to cover up unwanted noise. * A white knight in finance is a friendly investor who steps in to rescue a company from a hostile takeover. * White-collar workers are those who work in offices, as opposed to blue-collar workers, who work with their hands in factories or workshops. * A white paper is an authoritative report on a major issue by a team of experts; a government report outlining policy; or a short treatise whose purpose is to educate industry customers. Associating a paper with white may signify clean facts and unbiased information. * The white feather is a symbol of cowardice, particularly in Britain. It supposedly comes from cockfighting and the belief that a cockerel sporting a white feather in its tail is likely to be a poor fighter. At the beginning of the First World War, women in England were encouraged to give white feathers to men who had not enlisted in the British Armed Forces.","White\n\n* In the US, a white shoe firm is an older, conservative firm, usually in a field such as banking or law. The phrase derives from the \"white bucks,\" laced suede or buckskin shoes with red soles, long popular in the Ivy League colleges. * In Russia, the nobility are sometimes described as white bone (белая кость, bélaya kost'), commoners as black bone."],"string":"[\n \"Color\\n\\nColor (American English) or colour (Commonwealth English) is the visual perceptual property corresponding in humans to the categories called red, blue, yellow, etc. Color derives from the spectrum of light (distribution of light power versus wavelength) interacting in the eye with the spectral sensitivities of the light receptors. Color categories and physical specifications of color are also associated with objects or materials based on their physical properties such as light absorption, reflection, or emission spectra. By defining a color space colors can be identified numerically by their coordinates.\",\n \"Color\\n\\nBecause perception of color stems from the varying spectral sensitivity of different types of cone cells in the retina to different parts of the spectrum, colors may be defined and quantified by the degree to which they stimulate these cells. These physical or physiological quantifications of color, however, do not fully explain the psychophysical perception of color appearance.\",\n \"Color\\n\\nThe science of color is sometimes called chromatics, colorimetry, or simply color science. It includes the perception of color by the human eye and brain, the origin of color in materials, color theory in art, and the physics of electromagnetic radiation in the visible range (that is, what we commonly refer to simply as light).\",\n \"Color\\n\\nPhysics of color\",\n \"Color\\n\\nElectromagnetic radiation is characterized by its wavelength (or frequency) and its intensity. When the wavelength is within the visible spectrum (the range of wavelengths humans can perceive, approximately from 390 nm to 700 nm), it is known as \\\"visible light\\\".\",\n \"Color\\n\\nMost light sources emit light at many different wavelengths; a source's spectrum is a distribution giving its intensity at each wavelength. Although the spectrum of light arriving at the eye from a given direction determines the color sensation in that direction, there are many more possible spectral combinations than color sensations. In fact, one may formally define a color as a class of spectra that give rise to the same color sensation, although such classes would vary widely among different species, and to a lesser extent among individuals within the same species. In each such class the members are called metamers of the color in question.\",\n \"Color\\n\\nSpectral colors\",\n \"Color\\n\\nThe familiar colors of the rainbow in the spectrum – named using the Latin word for appearance or apparition by Isaac Newton in 1671 – include all those colors that can be produced by visible light of a single wavelength only, the pure spectral or monochromatic colors. The table at right shows approximate frequencies (in terahertz) and wavelengths (in nanometers) for various pure spectral colors. The wavelengths listed are as measured in air or vacuum (see refractive index).\",\n \"Color\\n\\nThe color table should not be interpreted as a definitive list – the pure spectral colors form a continuous spectrum, and how it is divided into distinct colors linguistically is a matter of culture and historical contingency (although people everywhere have been shown to perceive colors in the same way ). A common list identifies six main bands: red, orange, yellow, green, blue, and violet. Newton's conception included a seventh color, indigo, between blue and violet. It is possible that what Newton referred to as blue is nearer to what today we call cyan, and that indigo was simply the dark blue of the indigo dye that was being imported at the time.\",\n \"Color\\n\\nThe intensity of a spectral color, relative to the context in which it is viewed, may alter its perception considerably; for example, a low-intensity orange-yellow is brown, and a low-intensity yellow-green is olive-green.\",\n \"Color\\n\\nColor of objects\",\n \"Color\\n\\nThe color of an object depends on both the physics of the object in its environment and the characteristics of the perceiving eye and brain. Physically, objects can be said to have the color of the light leaving their surfaces, which normally depends on the spectrum of the incident illumination and the reflectance properties of the surface, as well as potentially on the angles of illumination and viewing. Some objects not only reflect light, but also transmit light or emit light themselves, which also contribute to the color. A viewer's perception of the object's color depends not only on the spectrum of the light leaving its surface, but also on a host of contextual cues, so that color differences between objects can be discerned mostly independent of the lighting spectrum, viewing angle, etc. This effect is known as color constancy.\",\n \"Color\\n\\nSome generalizations of the physics can be drawn, neglecting perceptual effects for now:\",\n \"Color\\n\\n* Light arriving at an opaque surface is either reflected \\\"specularly\\\" (that is, in the manner of a mirror), scattered (that is, reflected with diffuse scattering), or absorbed – or some combination of these. * Opaque objects that do not reflect specularly (which tend to have rough surfaces) have their color determined by which wavelengths of light they scatter strongly (with the light that is not scattered being absorbed). If objects scatter all wavelengths with roughly equal strength, they appear white. If they absorb all wavelengths, they appear black. * Opaque objects that specularly reflect light of different wavelengths with different efficiencies look like mirrors tinted with colors determined by those differences. An object that reflects some fraction of impinging light and absorbs the rest may look black but also be faintly reflective; examples are black objects coated with layers of enamel or lacquer. * Objects that transmit light are either translucent (scattering the transmitted light) or transparent (not scattering the transmitted light). If they also absorb (or reflect) light of various wavelengths differentially, they appear tinted with a color determined by the nature of that absorption (or that reflectance).\",\n \"Color\\n\\n* Objects may emit light that they generate from having excited electrons, rather than merely reflecting or transmitting light. The electrons may be excited due to elevated temperature (incandescence), as a result of chemical reactions (chemoluminescence), after absorbing light of other frequencies (\\\"fluorescence\\\" or \\\"phosphorescence\\\") or from electrical contacts as in light emitting diodes, or other light sources.\",\n \"Color\\n\\nTo summarize, the color of an object is a complex result of its surface properties, its transmission properties, and its emission properties, all of which contribute to the mix of wavelengths in the light leaving the surface of the object. The perceived color is then further conditioned by the nature of the ambient illumination, and by the color properties of other objects nearby, and via other characteristics of the perceiving eye and brain.\",\n \"Color\\n\\nPerception\",\n \"Color\\n\\nDevelopment of theories of color vision\",\n \"Color\\n\\nAlthough Aristotle and other ancient scientists had already written on the nature of light and color vision, it was not until Newton that light was identified as the source of the color sensation. In 1810, Goethe published his comprehensive Theory of Colors in which he ascribed physiological effects to color that are now understood as psychological.\",\n \"Color\\n\\nIn 1801 Thomas Young proposed his trichromatic theory, based on the observation that any color could be matched with a combination of three lights. This theory was later refined by James Clerk Maxwell and Hermann von Helmholtz. As Helmholtz puts it, \\\"the principles of Newton's law of mixture were experimentally confirmed by Maxwell in 1856. Young's theory of color sensations, like so much else that this marvelous investigator achieved in advance of his time, remained unnoticed until Maxwell directed attention to it.\\\"\",\n \"Color\\n\\nAt the same time as Helmholtz, Ewald Hering developed the opponent process theory of color, noting that color blindness and afterimages typically come in opponent pairs (red-green, blue-orange, yellow-violet, and black-white). Ultimately these two theories were synthesized in 1957 by Hurvich and Jameson, who showed that retinal processing corresponds to the trichromatic theory, while processing at the level of the lateral geniculate nucleus corresponds to the opponent theory.\",\n \"Color\\n\\nIn 1931, an international group of experts known as the Commission internationale de l'éclairage (CIE) developed a mathematical color model, which mapped out the space of observable colors and assigned a set of three numbers to each.\",\n \"Color\\n\\nColor in the eye\",\n \"Color\\n\\nThe ability of the human eye to distinguish colors is based upon the varying sensitivity of different cells in the retina to light of different wavelengths. Humans being trichromatic, the retina contains three types of color receptor cells, or cones. One type, relatively distinct from the other two, is most responsive to light that we perceive as blue or blue-violet, with wavelengths around 450 nm; cones of this type are sometimes called short-wavelength cones, S cones, or blue cones. The other two types are closely related genetically and chemically: middle-wavelength cones, M cones, or green cones are most sensitive to light perceived as green, with wavelengths around 540 nm, while the long-wavelength cones, L cones, or red cones, are most sensitive to light we perceive as greenish yellow, with wavelengths around 570 nm.\",\n \"Color\\n\\nLight, no matter how complex its composition of wavelengths, is reduced to three color components by the eye. For each location in the visual field, the three types of cones yield three signals based on the extent to which each is stimulated. These amounts of stimulation are sometimes called tristimulus values.\",\n \"Color\\n\\nThe response curve as a function of wavelength varies for each type of cone. Because the curves overlap, some tristimulus values do not occur for any incoming light combination. For example, it is not possible to stimulate only the mid-wavelength (so-called \\\"green\\\") cones; the other cones will inevitably be stimulated to some degree at the same time. The set of all possible tristimulus values determines the human color space. It has been estimated that humans can distinguish roughly 10 million different colors.\",\n \"Color\\n\\nThe other type of light-sensitive cell in the eye, the rod, has a different response curve. In normal situations, when light is bright enough to strongly stimulate the cones, rods play virtually no role in vision at all. On the other hand, in dim light, the cones are understimulated leaving only the signal from the rods, resulting in a colorless response. (Furthermore, the rods are barely sensitive to light in the \\\"red\\\" range.) In certain conditions of intermediate illumination, the rod response and a weak cone response can together result in color discriminations not accounted for by cone responses alone. These effects, combined, are summarized also in the Kruithof curve, that describes the change of color perception and pleasingness of light as function of temperature and intensity.\",\n \"Color\\n\\nColor in the brain\",\n \"Color\\n\\nWhile the mechanisms of color vision at the level of the retina are well-described in terms of tristimulus values, color processing after that point is organized differently. A dominant theory of color vision proposes that color information is transmitted out of the eye by three opponent processes, or opponent channels, each constructed from the raw output of the cones: a red–green channel, a blue–yellow channel, and a black–white \\\"luminance\\\" channel. This theory has been supported by neurobiology, and accounts for the structure of our subjective color experience. Specifically, it explains why we cannot perceive a \\\"reddish green\\\" or \\\"yellowish blue\\\", and it predicts the color wheel: it is the collection of colors for which at least one of the two color channels measures a value at one of its extremes.\",\n \"Color\\n\\nThe exact nature of color perception beyond the processing already described, and indeed the status of color as a feature of the perceived world or rather as a feature of our perception of the world – a type of qualia – is a matter of complex and continuing philosophical dispute.\",\n \"Color\\n\\nNonstandard color perception\",\n \"Color\\n\\nColor deficiency\",\n \"Color\\n\\nIf one or more types of a person's color-sensing cones are missing or less responsive than normal to incoming light, that person can distinguish fewer colors and is said to be color deficient or color blind (though this latter term can be misleading; almost all color deficient individuals can distinguish at least some colors). Some kinds of color deficiency are caused by anomalies in the number or nature of cones in the retina. Others (like central or cortical achromatopsia) are caused by neural anomalies in those parts of the brain where visual processing takes place.\",\n \"Color\\n\\nTetrachromacy\",\n \"Color\\n\\nWhile most humans are trichromatic (having three types of color receptors), many animals, known as tetrachromats, have four types. These include some species of spiders, most marsupials, birds, reptiles, and many species of fish. Other species are sensitive to only two axes of color or do not perceive color at all; these are called dichromats and monochromats respectively. A distinction is made between retinal tetrachromacy (having four pigments in cone cells in the retina, compared to three in trichromats) and functional tetrachromacy (having the ability to make enhanced color discriminations based on that retinal difference). As many as half of all women are retinal tetrachromats. The phenomenon arises when an individual receives two slightly different copies of the gene for either the medium- or long-wavelength cones, which are carried on the x-chromosome. To have two different genes, a person must have two x-chromosomes, which is why the phenomenon only occurs in women. For some of these retinal tetrachromats, color discriminations are enhanced, making them functional tetrachromats.\",\n \"Color\\n\\nSynesthesia\",\n \"Color\\n\\nIn certain forms of synesthesia/ideasthesia, perceiving letters and numbers (grapheme–color synesthesia) or hearing musical sounds (music–color synesthesia) will lead to the unusual additional experiences of seeing colors. Behavioral and functional neuroimaging experiments have demonstrated that these color experiences lead to changes in behavioral tasks and lead to increased activation of brain regions involved in color perception, thus demonstrating their reality, and similarity to real color percepts, albeit evoked through a non-standard route.\",\n \"Color\\n\\nAfterimages\",\n \"Color\\n\\nAfter exposure to strong light in their sensitivity range, photoreceptors of a given type become desensitized. For a few seconds after the light ceases, they will continue to signal less strongly than they otherwise would. Colors observed during that period will appear to lack the color component detected by the desensitized photoreceptors. This effect is responsible for the phenomenon of afterimages, in which the eye may continue to see a bright figure after looking away from it, but in a complementary color.\",\n \"Color\\n\\nAfterimage effects have also been utilized by artists, including Vincent van Gogh.\",\n \"Color\\n\\nColor constancy\",\n \"Color\\n\\nWhen an artist uses a limited color palette, the eye tends to compensate by seeing any gray or neutral color as the color which is missing from the color wheel. For example, in a limited palette consisting of red, yellow, black, and white, a mixture of yellow and black will appear as a variety of green, a mixture of red and black will appear as a variety of purple, and pure gray will appear bluish.\",\n \"Color\\n\\nThe trichromatic theory is strictly true when the visual system is in a fixed state of adaptation. In reality, the visual system is constantly adapting to changes in the environment and compares the various colors in a scene to reduce the effects of the illumination. If a scene is illuminated with one light, and then with another, as long as the difference between the light sources stays within a reasonable range, the colors in the scene appear relatively constant to us. This was studied by Edwin Land in the 1970s and led to his retinex theory of color constancy.\",\n \"Color\\n\\nIt should be noted, that both phenomena are readily explained and mathematically modeled with modern theories of chromatic adaptation and color appearance (e.g. CIECAM02, iCAM). There is no need to dismiss the trichromatic theory of vision, but rather it can be enhanced with an understanding of how the visual system adapts to changes in the viewing environment.\",\n \"Color\\n\\nColor naming\",\n \"Color\\n\\nColors vary in several different ways, including hue (shades of red, orange, yellow, green, blue, and violet), saturation, brightness, and gloss. Some color words are derived from the name of an object of that color, such as \\\"orange\\\" or \\\"salmon\\\", while others are abstract, like \\\"red\\\".\",\n \"Color\\n\\nIn the 1969 study Basic Color Terms: Their Universality and Evolution, Brent Berlin and Paul Kay describe a pattern in naming \\\"basic\\\" colors (like \\\"red\\\" but not \\\"red-orange\\\" or \\\"dark red\\\" or \\\"blood red\\\", which are \\\"shades\\\" of red). All languages that have two \\\"basic\\\" color names distinguish dark/cool colors from bright/warm colors. The next colors to be distinguished are usually red and then yellow or green. All languages with six \\\"basic\\\" colors include black, white, red, green, blue, and yellow. The pattern holds up to a set of twelve: black, gray, white, pink, red, orange, yellow, green, blue, purple, brown, and azure (distinct from blue in Russian and Italian, but not English).\",\n \"Color\\n\\nAssociations\",\n \"Color\\n\\nIndividual colors have a variety of cultural associations such as national colors (in general described in individual color articles and color symbolism). The field of color psychology attempts to identify the effects of color on human emotion and activity. Chromotherapy is a form of alternative medicine attributed to various Eastern traditions. Colors have different associations in different countries and cultures.\",\n \"Color\\n\\nDifferent colors have been demonstrated to have effects on cognition. For example, researchers at the University of Linz in Austria demonstrated that the color red significantly decreases cognitive functioning in men.\",\n \"Color\\n\\nSpectral colors and color reproduction\",\n \"Color\\n\\nMost light sources are mixtures of various wavelengths of light. Many such sources can still effectively produce a spectral color, as the eye cannot distinguish them from single-wavelength sources. For example, most computer displays reproduce the spectral color orange as a combination of red and green light; it appears orange because the red and green are mixed in the right proportions to allow the eye's cones to respond the way they do to the spectral color orange.\",\n \"Color\\n\\nA useful concept in understanding the perceived color of a non-monochromatic light source is the dominant wavelength, which identifies the single wavelength of light that produces a sensation most similar to the light source. Dominant wavelength is roughly akin to hue.\",\n \"Color\\n\\nThere are many color perceptions that by definition cannot be pure spectral colors due to desaturation or because they are purples (mixtures of red and violet light, from opposite ends of the spectrum). Some examples of necessarily non-spectral colors are the achromatic colors (black, gray, and white) and colors such as pink, tan, and magenta.\",\n \"Color\\n\\nTwo different light spectra that have the same effect on the three color receptors in the human eye will be perceived as the same color. They are metamers of that color. This is exemplified by the white light emitted by fluorescent lamps, which typically has a spectrum of a few narrow bands, while daylight has a continuous spectrum. The human eye cannot tell the difference between such light spectra just by looking into the light source, although reflected colors from objects can look different. (This is often exploited; for example, to make fruit or tomatoes look more intensely red.)\",\n \"Color\\n\\nSimilarly, most human color perceptions can be generated by a mixture of three colors called primaries. This is used to reproduce color scenes in photography, printing, television, and other media. There are a number of methods or color spaces for specifying a color in terms of three particular primary colors. Each method has its advantages and disadvantages depending on the particular application.\",\n \"Color\\n\\nNo mixture of colors, however, can produce a response truly identical to that of a spectral color, although one can get close, especially for the longer wavelengths, where the CIE 1931 color space chromaticity diagram has a nearly straight edge. For example, mixing green light (530 nm) and blue light (460 nm) produces cyan light that is slightly desaturated, because response of the red color receptor would be greater to the green and blue light in the mixture than it would be to a pure cyan light at 485 nm that has the same intensity as the mixture of blue and green.\",\n \"Color\\n\\nBecause of this, and because the primaries in color printing systems generally are not pure themselves, the colors reproduced are never perfectly saturated spectral colors, and so spectral colors cannot be matched exactly. However, natural scenes rarely contain fully saturated colors, thus such scenes can usually be approximated well by these systems. The range of colors that can be reproduced with a given color reproduction system is called the gamut. The CIE chromaticity diagram can be used to describe the gamut.\",\n \"Color\\n\\nAnother problem with color reproduction systems is connected with the acquisition devices, like cameras or scanners. The characteristics of the color sensors in the devices are often very far from the characteristics of the receptors in the human eye. In effect, acquisition of colors can be relatively poor if they have special, often very \\\"jagged\\\", spectra caused for example by unusual lighting of the photographed scene.\\nA color reproduction system \\\"tuned\\\" to a human with normal color vision may give very inaccurate results for other observers.\",\n \"Color\\n\\nThe different color response of different devices can be problematic if not properly managed. For color information stored and transferred in digital form, color management techniques, such as those based on ICC profiles, can help to avoid distortions of the reproduced colors. Color management does not circumvent the gamut limitations of particular output devices, but can assist in finding good mapping of input colors into the gamut that can be reproduced.\",\n \"Color\\n\\nAdditive coloring\",\n \"Color\\n\\nAdditive color is light created by mixing together light of two or more different colors. Red, green, and blue are the additive primary colors normally used in additive color systems such as projectors and computer terminals.\",\n \"Color\\n\\nSubtractive coloring\",\n \"Color\\n\\nSubtractive coloring uses dyes, inks, pigments, or filters to absorb some wavelengths of light and not others. The color that a surface displays comes from the parts of the visible spectrum that are not absorbed and therefore remain visible. Without pigments or dye, fabric fibers, paint base and paper are usually made of particles that scatter white light (all colors) well in all directions. When a pigment or ink is added, wavelengths are absorbed or \\\"subtracted\\\" from white light, so light of another color reaches the eye.\",\n \"Color\\n\\nIf the light is not a pure white source (the case of nearly all forms of artificial lighting), the resulting spectrum will appear a slightly different color. Red paint, viewed under blue light, may appear black. Red paint is red because it scatters only the red components of the spectrum. If red paint is illuminated by blue light, it will be absorbed by the red paint, creating the appearance of a black object.\",\n \"Color\\n\\nStructural color\",\n \"Color\\n\\nStructural colors are colors caused by interference effects rather than by pigments. Color effects are produced when a material is scored with fine parallel lines, formed of one or more parallel thin layers, or otherwise composed of microstructures on the scale of the color's wavelength. If the microstructures are spaced randomly, light of shorter wavelengths will be scattered preferentially to produce Tyndall effect colors: the blue of the sky (Rayleigh scattering, caused by structures much smaller than the wavelength of light, in this case air molecules), the luster of opals, and the blue of human irises. If the microstructures are aligned in arrays, for example the array of pits in a CD, they behave as a diffraction grating: the grating reflects different wavelengths in different directions due to interference phenomena, separating mixed \\\"white\\\" light into light of different wavelengths. If the structure is one or more thin layers then it will reflect some wavelengths and transmit others, depending on the layers' thickness.\",\n \"Color\\n\\nStructural color is studied in the field of thin-film optics. A layman's term that describes particularly the most ordered or the most changeable structural colors is iridescence. Structural color is responsible for the blues and greens of the feathers of many birds (the blue jay, for example), as well as certain butterfly wings and beetle shells. Variations in the pattern's spacing often give rise to an iridescent effect, as seen in peacock feathers, soap bubbles, films of oil, and mother of pearl, because the reflected color depends upon the viewing angle. Numerous scientists have carried out research in butterfly wings and beetle shells, including Isaac Newton and Robert Hooke. Since 1942, electron micrography has been used, advancing the development of products that exploit structural color, such as \\\"photonic\\\" cosmetics.\",\n \"Color\\n\\nMentions of color in social media\",\n \"Color\\n\\nAccording to Pantone, the top three colors in social media for 2012 were red (186 million mentions; accredited to Taylor Swift's Red album, NASA's landing on Mars, and red carpet coverage), blue (125 million mentions; accredited to the United States presidential election, 2012, Mars rover Curiosity finding blue rocks, and blue sports teams), and Green (102 million mentions; accredited to \\\"environmental friendliness\\\", Green Bay Packers, and green eyed girls).\",\n \"Color\\n\\nAdditional terms\",\n \"Color\\n\\n* Color wheel: an illustrative organization of color hues in a circle that shows relationships.\\n* Colorfulness, chroma, purity, or saturation: how \\\"intense\\\" or \\\"concentrated\\\" a color is. Technical definitions distinguish between colorfulness, chroma, and saturation as distinct perceptual attributes and include purity as a physical quantity. These terms, and others related to light and color are internationally agreed upon and published in the CIE Lighting Vocabulary. More readily available texts on colorimetry also define and explain these terms. \\n* Dichromatism: a phenomenon where the hue is dependent on concentration and/or thickness of the absorbing substance.\\n* Hue: the color's direction from white, for example in a color wheel or chromaticity diagram.\\n* Shade: a color made darker by adding black.\\n* Tint: a color made lighter by adding white.\\n* Value, brightness, lightness, or luminosity: how light or dark a color is.\",\n \"Electromagnetic spectrum\\n\\nThe electromagnetic spectrum is the collective term for all known frequencies and their linked wave lengths of the known photons ( electromagnetic radiation ). The \\\"electromagnetic spectrum\\\" of an object has a different meaning, and is instead the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object.\",\n \"Electromagnetic spectrum\\n\\nThe electromagnetic spectrum extends from below the low frequencies used for modern radio communication to gamma radiation at the short-wavelength (high-frequency) end, thereby covering wavelengths from thousands of kilometers down to a fraction of the size of an atom. Visible light lies toward the shorter end, with wavelengths from 400 to 700 nanometres. The limit for long wavelengths is the size of the universe itself, while it is thought that the short wavelength limit is in the vicinity of the Planck length. Until the middle of the 20th century it was believed by most physicists that this spectrum was infinite and continuous.\",\n \"Electromagnetic spectrum\\n\\nNearly all types of electromagnetic radiation can be used for spectroscopy, to study and characterize matter. Other technological uses are described under electromagnetic radiation.\",\n \"Electromagnetic spectrum\\n\\nHistory of electromagnetic spectrum discovery\",\n \"Electromagnetic spectrum\\n\\nFor most of history, visible light was the only known part of the electromagnetic spectrum. The ancient Greeks recognized that light traveled in straight lines and studied some of its properties, including reflection and refraction. The study of light continued, and during the 16th and 17th centuries conflicting theories regarded light as either a wave or a particle.\",\n \"Electromagnetic spectrum\\n\\nThe first discovery of electromagnetic radiation other than visible light came in 1800, when William Herschel discovered infrared radiation. He was studying the temperature of different colors by moving a thermometer through light split by a prism. He noticed that the highest temperature was beyond red. He theorized that this temperature change was due to \\\"calorific rays\\\" that were a type of light ray that could not be seen.\",\n \"Electromagnetic spectrum\\n\\nThe next year, Johann Ritter, working at the other end of the spectrum, noticed what he called \\\"chemical rays\\\" (invisible light rays that induced certain chemical reactions). These behaved similarly to visible violet light rays, but were beyond them in the spectrum. They were later renamed ultraviolet radiation.\",\n \"Electromagnetic spectrum\\n\\nElectromagnetic radiation had been first linked to electromagnetism in 1845, when Michael Faraday noticed that the polarization of light traveling through a transparent material responded to a magnetic field (see Faraday effect). During the 1860s James Maxwell developed four partial differential equations for the electromagnetic field. Two of these equations predicted the possibility of, and behavior of, waves in the field. Analyzing the speed of these theoretical waves, Maxwell realized that they must travel at a speed that was about the known speed of light. This startling coincidence in value led Maxwell to make the inference that light itself is a type of electromagnetic wave.\",\n \"Electromagnetic spectrum\\n\\nMaxwell's equations predicted an infinite number of frequencies of electromagnetic waves, all traveling at the speed of light. This was the first indication of the existence of the entire electromagnetic spectrum.\",\n \"Electromagnetic spectrum\\n\\nMaxwell's predicted waves included waves at very low frequencies compared to infrared, which in theory might be created by oscillating charges in an ordinary electrical circuit of a certain type. Attempting to prove Maxwell's equations and detect such low frequency electromagnetic radiation, in 1886 the physicist Heinrich Hertz built an apparatus to generate and detect what are now called radio waves. Hertz found the waves and was able to infer (by measuring their wavelength and multiplying it by their frequency) that they traveled at the speed of light. Hertz also demonstrated that the new radiation could be both reflected and refracted by various dielectric media, in the same manner as light. For example, Hertz was able to focus the waves using a lens made of tree resin. In a later experiment, Hertz similarly produced and measured the properties of microwaves. These new types of waves paved the way for inventions such as the wireless telegraph and the radio.\",\n \"Electromagnetic spectrum\\n\\nIn 1895 Wilhelm Röntgen noticed a new type of radiation emitted during an experiment with an evacuated tube subjected to a high voltage. He called these radiations x-rays and found that they were able to travel through parts of the human body but were reflected or stopped by denser matter such as bones. Before long, many uses were found for them in the field of medicine.\",\n \"Electromagnetic spectrum\\n\\nThe last portion of the electromagnetic spectrum was filled in with the discovery of gamma rays. In 1900 Paul Villard was studying the radioactive emissions of radium when he identified a new type of radiation that he first thought consisted of particles similar to known alpha and beta particles, but with the power of being far more penetrating than either. However, in 1910, British physicist William Henry Bragg demonstrated that gamma rays are electromagnetic radiation, not particles, and in 1914, Ernest Rutherford (who had named them gamma rays in 1903 when he realized that they were fundamentally different from charged alpha and beta particles) and Edward Andrade measured their wavelengths, and found that gamma rays were similar to X-rays, but with shorter wavelengths and higher frequencies.\",\n \"Electromagnetic spectrum\\n\\nRange of the spectrum\",\n \"Electromagnetic spectrum\\n\\nElectromagnetic waves are typically described by any of the following three physical properties: the frequency f, wavelength λ, or photon energy E. Frequencies observed in astronomy range from (1 GeV gamma rays) down to the local plasma frequency of the ionized interstellar medium (~1 kHz). Wavelength is inversely proportional to the wave frequency, so gamma rays have very short wavelengths that are fractions of the size of atoms, where as wavelengths on the opposite end of the spectrum can be as long as the universe. Photon energy is directly proportional to the wave frequency, so gamma ray photons have the highest energy (around a billion electron volts), while radio wave photons have very low energy (around a femtoelectronvolt). These relations are illustrated by the following equations:\\nf \\\\frac{c}{\\\\lambda}, \\\\quad\\\\text{or}\\\\quad f \\n \\\\frac{E}{h}, \\\\quad\\\\text{or}\\\\quad E=\\\\frac{hc}{\\\\lambda},\\nwhere:\\n*c = is the speed of light in a vacuum\\n*h \\n is Planck's constant.\",\n \"Electromagnetic spectrum\\n\\nWhenever electromagnetic waves exist in a medium with matter, their wavelength is decreased. Wavelengths of electromagnetic radiation, no matter what medium they are traveling through, are usually quoted in terms of the vacuum wavelength, although this is not always explicitly stated.\",\n \"Electromagnetic spectrum\\n\\nGenerally, electromagnetic radiation is classified by wavelength into radio wave, microwave, terahertz (or sub-millimeter) radiation, infrared, the visible region that is perceived as light, ultraviolet, X-rays and gamma rays. The behavior of EM radiation depends on its wavelength. When EM radiation interacts with single atoms and molecules, its behavior also depends on the amount of energy per quantum (photon) it carries.\",\n \"Electromagnetic spectrum\\n\\nSpectroscopy can detect a much wider region of the EM spectrum than the visible range of 400 nm to 700 nm. A common laboratory spectroscope can detect wavelengths from 2 nm to 2500 nm. Detailed information about the physical properties of objects, gases, or even stars can be obtained from this type of device. Spectroscopes are widely used in astrophysics. For example, many hydrogen atoms emit a radio wave photon that has a wavelength of 21.12 cm. Also, frequencies of 30 Hz and below can be produced by and are important in the study of certain stellar nebulae and frequencies as high as have been detected from astrophysical sources.\",\n \"Electromagnetic spectrum\\n\\nRationale for spectrum regional names\",\n \"Electromagnetic spectrum\\n\\nElectromagnetic radiation interacts with matter in different ways across the spectrum. These types of interaction are so different that historically different names have been applied to different parts of the spectrum, as though these were different types of radiation. Thus, although these \\\"different kinds\\\" of electromagnetic radiation form a quantitatively continuous spectrum of frequencies and wavelengths, the spectrum remains divided for practical reasons related to these qualitative interaction differences.\",\n \"Electromagnetic spectrum\\n\\nTypes of radiation\",\n \"Electromagnetic spectrum\\n\\nBoundaries\",\n \"Electromagnetic spectrum\\n\\nA discussion of the regions (or bands or types) of the electromagnetic spectrum is given below. Note that there are no precisely defined boundaries between the bands of the electromagnetic spectrum; rather they fade into each other like the bands in a rainbow (which is the sub-spectrum of visible light). Radiation of each frequency and wavelength (or in each band) has a mix of properties of the two regions of the spectrum that bound it. For example, red light resembles infrared radiation in that it can excite and add energy to some chemical bonds and indeed must do so to power the chemical mechanisms responsible for photosynthesis and the working of the visual system.\",\n \"Electromagnetic spectrum\\n\\nRegions of the spectrum\",\n \"Electromagnetic spectrum\\n\\nThe types of electromagnetic radiation are broadly classified into the following classes:\\n# Gamma radiation\\n# X-ray radiation\\n# Ultraviolet radiation\\n# Visible radiation\\n# Infrared radiation\\n# Terahertz radiation\\n# Microwave radiation\\n# Radio waves\\nThis classification goes in the increasing order of wavelength, which is characteristic of the type of radiation.\\nWhile, in general, the classification scheme is accurate, in reality there is often some overlap between neighboring types of electromagnetic energy. For example, SLF radio waves at 60 Hz may be received and studied by astronomers, or may be ducted along wires as electric power, although the latter is, in the strict sense, not electromagnetic radiation at all (see near and far field).\",\n \"Electromagnetic spectrum\\n\\nThe distinction between X-rays and gamma rays is partly based on sources: the photons generated from nuclear decay or other nuclear and subnuclear/particle process, are always termed gamma rays, whereas X-rays are generated by electronic transitions involving highly energetic inner atomic electrons. In general, nuclear transitions are much more energetic than electronic transitions, so gamma-rays are more energetic than X-rays, but exceptions exist. By analogy to electronic transitions, muonic atom transitions are also said to produce X-rays, even though their energy may exceed 6 MeV, whereas there are many (77 known to be less than 10 keV) low-energy nuclear transitions (e.g., the nuclear transition of thorium-229), and, despite being one million-fold less energetic than some muonic X-rays, the emitted photons are still called gamma rays due to their nuclear origin.\",\n \"Electromagnetic spectrum\\n\\nThe convention that EM radiation that is known to come from the nucleus, is always called \\\"gamma ray\\\" radiation is the only convention that is universally respected, however. Many astronomical gamma ray sources (such as gamma ray bursts) are known to be too energetic (in both intensity and wavelength) to be of nuclear origin. Quite often, in high energy physics and in medical radiotherapy, very high energy EMR (in the >10 MeV region)—which is of higher energy than any nuclear gamma ray—is not called X-ray or gamma-ray, but instead by the generic term of \\\"high energy photons.\\\"\",\n \"Electromagnetic spectrum\\n\\nThe region of the spectrum where a particular observed electromagnetic radiation falls, is reference frame-dependent (due to the Doppler shift for light), so EM radiation that one observer would say is in one region of the spectrum could appear to an observer moving at a substantial fraction of the speed of light with respect to the first to be in another part of the spectrum. For example, consider the cosmic microwave background. It was produced, when matter and radiation decoupled, by the de-excitation of hydrogen atoms to the ground state. These photons were from Lyman series transitions, putting them in the ultraviolet (UV) part of the electromagnetic spectrum. Now this radiation has undergone enough cosmological red shift to put it into the microwave region of the spectrum for observers moving slowly (compared to the speed of light) with respect to the cosmos.\",\n \"Electromagnetic spectrum\\n\\nRadio frequency\",\n \"Electromagnetic spectrum\\n\\nRadio waves generally are utilized by antennas of appropriate size (according to the principle of resonance), with wavelengths ranging from hundreds of meters to about one millimeter. They are used for transmission of data, via modulation. Television, mobile phones, wireless networking, and amateur radio all use radio waves. The use of the radio spectrum is regulated by many governments through frequency allocation.\",\n \"Electromagnetic spectrum\\n\\nRadio waves can be made to carry information by varying a combination of the amplitude, frequency, and phase of the wave within a frequency band. When EM radiation impinges upon a conductor, it couples to the conductor, travels along it, and induces an electric current on the surface of that conductor by exciting the electrons of the conducting material. This effect (the skin effect) is used in antennas.\",\n \"Electromagnetic spectrum\\n\\nMicrowaves\",\n \"Electromagnetic spectrum\\n\\nThe super-high frequency (SHF) and extremely high frequency (EHF) of microwaves are on the short side of radio waves. Microwaves are waves that are typically short enough (measured in millimeters) to employ tubular metal waveguides of reasonable diameter. Microwave energy is produced with klystron and magnetron tubes, and with solid state diodes such as Gunn and IMPATT devices. Microwaves are absorbed by molecules that have a dipole moment in liquids. In a microwave oven, this effect is used to heat food. Low-intensity microwave radiation is used in Wi-Fi, although this is at intensity levels unable to cause thermal heating.\",\n \"Electromagnetic spectrum\\n\\nVolumetric heating, as used by microwave ovens, transfers energy through the material electromagnetically, not as a thermal heat flux. The benefit of this is a more uniform heating and reduced heating time; microwaves can heat material in less than 1% of the time of conventional heating methods.\",\n \"Electromagnetic spectrum\\n\\nWhen active, the average microwave oven is powerful enough to cause interference at close range with poorly shielded electromagnetic fields such as those found in mobile medical devices and poorly made consumer electronics.\",\n \"Electromagnetic spectrum\\n\\nTerahertz radiation\",\n \"Electromagnetic spectrum\\n\\nTerahertz radiation is a region of the spectrum between far infrared and microwaves. Until recently, the range was rarely studied and few sources existed for microwave energy at the high end of the band (sub-millimeter waves or so-called terahertz waves), but applications such as imaging and communications are now appearing. Scientists are also looking to apply terahertz technology in the armed forces, where high-frequency waves might be directed at enemy troops to incapacitate their electronic equipment.\",\n \"Electromagnetic spectrum\\n\\nInfrared radiation\",\n \"Electromagnetic spectrum\\n\\nThe infrared part of the electromagnetic spectrum covers the range from roughly 300 GHz to 400 THz (1 mm - 750 nm). It can be divided into three parts:\\n*Far-infrared, from 300 GHz to 30 THz (1 mm - 10 μm). The lower part of this range may also be called microwaves or terahertz waves. This radiation is typically absorbed by so-called rotational modes in gas-phase molecules, by molecular motions in liquids, and by phonons in solids. The water in Earth's atmosphere absorbs so strongly in this range that it renders the atmosphere in effect opaque. However, there are certain wavelength ranges (\\\"windows\\\") within the opaque range that allow partial transmission, and can be used for astronomy. The wavelength range from approximately 200 μm up to a few mm is often referred to as \\\"sub-millimeter\\\" in astronomy, reserving far infrared for wavelengths below 200 μm. *Mid-infrared, from 30 to 120 THz (10 - 2.5 μm). Hot objects (black-body radiators) can radiate strongly in this range, and human skin at normal body temperature radiates strongly at the lower end of this region. This radiation is absorbed by molecular vibrations, where the different atoms in a molecule vibrate around their equilibrium positions.\",\n \"Electromagnetic spectrum\\n\\nThis range is sometimes called the fingerprint region, since the mid-infrared absorption spectrum of a compound is very specific for that compound. *Near-infrared, from 120 to 400 THz (2,500 - 750 nm). Physical processes that are relevant for this range are similar to those for visible light. The highest frequences in this region can be detected directly by some types of photographic film, and by many types of solid state image sensors for infrared photography and videography.\",\n \"Electromagnetic spectrum\\n\\nVisible radiation (light)\",\n \"Electromagnetic spectrum\\n\\nAbove infrared in frequency comes visible light. The Sun emits its peak power in the visible region, although integrating the entire emission power spectrum through all wavelengths shows that the Sun emits slightly more infrared than visible light. By definition, visible light is the part of the EM spectrum the human eye is the most sensitive to. Visible light (and near-infrared light) is typically absorbed and emitted by electrons in molecules and atoms that move from one energy level to another. This action allows the chemical mechanisms that underlie human vision and plant photosynthesis. The light that excites the human visual system is a very small portion of the electromagnetic spectrum. A rainbow shows the optical (visible) part of the electromagnetic spectrum; infrared (if it could be seen) would be located just beyond the red side of the rainbow with ultraviolet appearing just beyond the violet end.\",\n \"Electromagnetic spectrum\\n\\nElectromagnetic radiation with a wavelength between 380 nm and 760 nm (400–790 terahertz) is detected by the human eye and perceived as visible light. Other wavelengths, especially near infrared (longer than 760 nm) and ultraviolet (shorter than 380 nm) are also sometimes referred to as light, especially when the visibility to humans is not relevant. White light is a combination of lights of different wavelengths in the visible spectrum. Passing white light through a prism splits it up into the several colors of light observed in the visible spectrum between 400 nm and 780 nm.\",\n \"Electromagnetic spectrum\\n\\nIf radiation having a frequency in the visible region of the EM spectrum reflects off an object, say, a bowl of fruit, and then strikes the eyes, this results in visual perception of the scene. The brain's visual system processes the multitude of reflected frequencies into different shades and hues, and through this insufficiently-understood psychophysical phenomenon, most people perceive a bowl of fruit.\",\n \"Electromagnetic spectrum\\n\\nAt most wavelengths, however, the information carried by electromagnetic radiation is not directly detected by human senses. Natural sources produce EM radiation across the spectrum, and technology can also manipulate a broad range of wavelengths. Optical fiber transmits light that, although not necessarily in the visible part of the spectrum (it is usually infrared), can carry information. The modulation is similar to that used with radio waves.\",\n \"Electromagnetic spectrum\\n\\nUltraviolet radiation\",\n \"Electromagnetic spectrum\\n\\nNext in frequency comes ultraviolet (UV). The wavelength of UV rays is shorter than the violet end of the visible spectrum but longer than the X-ray.\",\n \"Electromagnetic spectrum\\n\\nUV in the very shortest wavelength range (next to X-rays) is capable of ionizing atoms (see photoelectric effect), greatly changing their physical behavior.\",\n \"Electromagnetic spectrum\\n\\nAt the middle range of UV, UV rays cannot ionize but can break chemical bonds, making molecules unusually reactive. Sunburn, for example, is caused by the disruptive effects of middle range UV radiation on skin cells, which is the main cause of skin cancer. UV rays in the middle range can irreparably damage the complex DNA molecules in the cells producing thymine dimers making it a very potent mutagen.\",\n \"Electromagnetic spectrum\\n\\nThe Sun emits significant UV radiation (about 10% of its total power), including extremely short wavelength UV that could potentially destroy most life on land (ocean water would provide some protection for life there). However, most of the Sun's damaging UV wavelengths are absorbed by the atmosphere and ozone layer before they reach the surface. The higher energy (shortest wavelength) ranges of UV (called \\\"vacuum UV\\\") are absorbed by nitrogen and, at longer wavelengths, by simple diatomic oxygen in the air. Most of the UV in the mid-range of energy is blocked by the ozone layer, which absorbs strongly in the important 200–315 nm range, the lower energy part of which is too long for ordinary dioxygen in air to absorb. The very lowest energy range of UV between 315 nm and visible light (called UV-A) is not blocked well by the atmosphere, but does not cause sunburn and does less biological damage. However, it is not harmless and does create oxygen radicals, mutations and skin damage. See ultraviolet for more information.\",\n \"Electromagnetic spectrum\\n\\nX-rays\",\n \"Electromagnetic spectrum\\n\\nAfter UV come X-rays, which, like the upper ranges of UV are also ionizing. However, due to their higher energies, X-rays can also interact with matter by means of the Compton effect. Hard X-rays have shorter wavelengths than soft X-rays and as they can pass through many substances with little absorption, they can be used to 'see through' objects with 'thicknesses' less than that equivalent to a few meters of water. One notable use is diagnostic X-ray imaging in medicine (a process known as radiography). X-rays are useful as probes in high-energy physics. In astronomy, the accretion disks around neutron stars and black holes emit X-rays, enabling studies of these phenomena. X-rays are also emitted by the coronas of stars and are strongly emitted by some types of nebulae. However, X-ray telescopes must be placed outside the Earth's atmosphere to see astronomical X-rays, since the great depth of the atmosphere of Earth is opaque to X-rays (with areal density of 1000 grams per cm2), equivalent to 10 meters thickness of water. This is an amount sufficient to block almost all astronomical X-rays (and also astronomical gamma rays—see below).\",\n \"Electromagnetic spectrum\\n\\nGamma rays\",\n \"Electromagnetic spectrum\\n\\nAfter hard X-rays come gamma rays, which were discovered by Paul Villard in 1900. These are the most energetic photons, having no defined lower limit to their wavelength. In astronomy they are valuable for studying high-energy objects or regions, however as with X-rays this can only be done with telescopes outside the Earth's atmosphere. Gamma rays are used experimentally by physicists for their penetrating ability and are produced by a number of radioisotopes. They are used for irradiation of foods and seeds for sterilization, and in medicine they are occasionally used in radiation cancer therapy.[http://www.revisionworld.com/gcse-revision/physics/waves/uses-electromagnetic-waves Uses of Electromagnetic Waves | gcse-revision, physics, waves, uses-electromagnetic-waves | Revision World] More commonly, gamma rays are used for diagnostic imaging in nuclear medicine, an example being PET scans. The wavelength of gamma rays can be measured with high accuracy through the effects of Compton scattering.\",\n \"White\\n\\nWhite is an achromatic color, a color without hue. An incoming light to the human eye that stimulates all its three types of color sensitive cone cells in nearly equal amounts results in white. White is one of the most common colors in nature, the color of sunlight, snow, milk, chalk, limestone and other common minerals. In many cultures white represents or signifies purity, innocence, and light, and is the symbolic opposite of black, or darkness. According to surveys in Europe and the United States, white is the color most often associated with perfection, the good, honesty, cleanliness, the beginning, the new, neutrality, and exactitude.\",\n \"White\\n\\nIn ancient Egypt and ancient Rome, priestesses wore white as a symbol of purity, and Romans wore a white toga as a symbol of citizenship. In the Middle Ages and Renaissance a white unicorn symbolized chastity, and a white lamb sacrifice and purity; the widows of kings dressed in white rather than black as the color of mourning. It sometimes symbolizes royalty; it was the color of the French kings (black being the color of the queens) and of the monarchist movement after the French Revolution as well as of the movement called the White Russians (not to be confounded with Belarus, literally \\\"White Russia\\\") who fought the Bolsheviks during the Russian Civil War (1917–1922). Greek and Roman temples were faced with white marble, and beginning in the 18th century, with the advent of neoclassical architecture, white became the most common color of new churches, capitols and other government buildings, especially in the United States. It was also widely used in 20th century modern architecture as a symbol of modernity, simplicity and strength.\",\n \"White\\n\\nWhite is an important color for almost all world religions. The Pope, the head of the Roman Catholic Church, has worn white since 1566, as a symbol of purity and sacrifice. In Islam, and in the Shinto religion of Japan, it is worn by pilgrims; and by the Brahmins in India. In Western cultures and in Japan, white is the most common color for wedding dresses, symbolizing purity and virginity. In many Asian cultures, white is also the color of mourning.\",\n \"White\\n\\nThe white color on television screens and computer monitors is created with the RGB color model by mixing red, green and blue light at equal intensities.\",\n \"White\\n\\nWhite in nature and culture\",\n \"White\\n\\nFile:Alps.jpg|Ice and snow. The Weisshorn (\\\"white mountain\\\"), in the high Alps.\\nFile:Milk glass.jpg|A glass of milk\\nFile:Cloud.jpg|Cumulus clouds\\nFile:Taj Mahal (Edited).jpeg|White marble - the Taj Mahal.\\nFile: Ivory cover of the Lorsch Gospels, c. 810, Carolingian, Victoria and Albert Museum.jpg| Ivory cover of the Lorsch Gospels, circa 810 AD, (Victoria and Albert Museum, London.)\\nFile:Three Maries.jpg|Alabaster statue of the three Maries, (circa 1450), Warsaw Museum.\\nFile:Andalusian.jpg|A white Andalusian horse. White is commonly associated with innocence, perfection and purity.\\nFile:Polar bear with young - ANWR.jpg|Polar bear with young, Arctic National Wildlife Refuge, Alaska. \\nFile:Douvres (6).JPG|The White Cliffs of Dover are composed of chalk, or calcium carbonate.\",\n \"White\\n\\nIn nature, snow and clouds appear white because they are composed of water droplets or ice crystals mixed with air; when white sunlight enters snow, very little of the spectrum is absorbed; almost all of the light is reflected or scattered by the air and water molecules, so the snow appears to be the color of sunlight, white. Beaches with sand containing high amounts of quartz or eroded limestone also appear white, since quartz and limestone reflect or scatter sunlight, rather than absorbing it. Tropical white sand beaches may also have a high quantity of white calcium carbonate from tiny bits of seashells ground to fine sand by the action of the waves. An individual that has an aversion or hatred for the color white is called a leukophobe.\",\n \"White\\n\\nEtymology\",\n \"White\\n\\nThe word white continues Old English ', ultimately from a Common Germanic ' also reflected in OHG ', ON ', Goth. '. The root is ultimately from Proto-Indo-European language ', surviving also in Sanskrit ' \\\"to be white or bright\\\" and Slavonic ' \\\"light\\\". \\nThe Icelandic word for white, ', is directly derived from the Old Norse form of the word '.\\nCommon Germanic also had the word *blankaz (\\\"white, bright, blinding\\\"), borrowed into Late Latin as *blancus, which provided the source for Romance words for \\\"white\\\" (Catalan, Occitan and French blanc, Spanish blanco, Italian bianco, Galician-Portuguese branco, etc.). The antonym of white is black.\",\n \"White\\n\\nSome non-European languages have a wide variety of terms for white. The Inuit language has seven different words for seven different nuances of white. Sanskrit has specific words for bright white, the white of teeth, the white of sandalwood, the white of the autumn moon, the white of silver, the white of cow's milk, the white of pearls, the white of a ray of sunlight, and the white of stars. Japanese has six different words, depending upon brilliance or dullness, or if the color is inert or dynamic.\",\n \"White\\n\\nWhite in history and art\",\n \"White\\n\\nThe Ancient World\",\n \"White\\n\\nWhite was one of the first colors used by Paleolithic artists; they used calcite or chalk, sometimes as a background, sometimes as a highlight, along with charcoal and red and yellow ochre in their vivid cave paintings.\",\n \"White\\n\\nIn ancient Egypt, white was connected with the goddess Isis. The priests and priestesses of Isis dressed only in white linen, and it was used to wrap mummies.\",\n \"White\\n\\nIn Greece and other ancient civilizations, white was often associated with mother's milk. In Greek mythology, the chief god Zeus was nourished at the breast of the nymph Amalthea. In the Talmud, milk was one of four sacred substances, along with wine, honey, and the rose.\",\n \"White\\n\\nThe ancient Greeks saw the world in terms of darkness and light, so white was a fundamental color. According to Pliny the Elder in his Natural History, Apelles (4th century BC) and the other famous painters of ancient Greece used only four colors in their paintings; white, red, yellow and black; For painting, the Greeks used lead white, made by a long and laborious process.\",\n \"White\\n\\nA plain white toga, known as a toga virilis, was worn for ceremonial occasions by all Roman citizens over the age of 14–18. Magistrates and certain priests wore a toga praetexta, with a broad purple stripe.\\nIn the time of the Emperor Augustus, no Roman man was allowed to appear in the Roman forum without a toga.\",\n \"White\\n\\nThe ancient Romans had two words for white; albus, a plain white, (the source of the word albino); and candidus, a brighter white. A man who wanted public office in Rome wore a white toga brightened with chalk, called a toga candida, the origin of the word candidate. The Latin word candere meant to shine, to be bright. It was the origin of the words candle and candid.\",\n \"White\\n\\nIn ancient Rome, the priestesses of the goddess Vesta dressed in white linen robes, a white palla or shawl, and a white veil. They protected the sacred fire and the penates of Rome. White symbolized their purity, loyalty, and chastity.\",\n \"White\\n\\nFile:Paintings from the Chauvet cave (museum replica).jpg|Prehistoric paintings in Chauvet Cave, France (30,000 to 32,000 BC)\\nFile:Ägyptischer Maler um 1360 v. Chr. 001.jpg|Painting of the goddess Isis (1380–1385 BC). The priests of her cult wore white linen.\\nFile:Maler der Grabkammer des Thot 001.jpg|Paintings of women in white from a tomb (1448–1422 BC).\\nFile:Chief Vestal.jpg|Statue of the chief Vestal Virgin, wearing a white palla and a white veil.\",\n \"White\\n\\nThe Middle Ages and the Renaissance\",\n \"White\\n\\nThe early Christian church adopted the Roman symbolism of white as the color of purity, sacrifice and virtue. It became the color worn by priests during Mass, the color worn by monks of the Cistercian Order, and, under Pope Pius V, a former monk of the Dominican Order, it became the official color worn by the pope himself. Monks of the Order of Saint Benedict dressed in the white or gray of natural undyed wool, but later changed to black, the color of humility and penitence.\",\n \"White\\n\\nIn Medieval art, the white lamb became the symbol of the sacrifice of Christ on behalf of mankind. John the Baptist described Christ as the lamb of God, who took the sins of the world upon himself. The white lamb was the center of one of the most famous paintings of the Medieval period, the Ghent Altarpiece by Jan van Eyck.\",\n \"White\\n\\nWhite was also the symbolic color of the transfiguration. The Gospel of Saint Mark describes Jesus' clothing in this event as \\\"shining, exceeding white as snow.\\\" Artists such as Fra Angelico used their greatest skill to capture the whiteness of his garments. In his painting of the transfiguration at the Convent of Saint Mark in Florence, Fra Angelico emphasized the white garment by using a light gold background, placed in an almond-shaped halo.\",\n \"White\\n\\nThe white unicorn was a common subject of Medieval and Renaissance manuscripts, paintings and tapestries. It was a symbol of purity, chastity and grace, which could only be captured by a virgin. It was often portrayed in the lap of the Virgin Mary.\",\n \"White\\n\\nDuring the Middle Ages, painters rarely ever mixed colors; but in the Renaissance, the influential humanist and scholar Leon Battista Alberti encouraged artists to add white to their colors to make them lighter, brighter, and to add hilaritas, or gaiety. Many painters followed his advice, and the palette of the Renaissance was considerably brighter.\",\n \"White\\n\\nIn the Middle Ages and Renaissance, white was commonly worn by widows as a color of mourning. The widows of the kings of France wore white until Anne of Brittany in the 16th century. A white tunic was also worn by many knights, along with a red cloak, which showed the knights were willing to give their blood for the king or Church.\",\n \"White\\n\\nFile:Sodoma - Life of St Benedict, Scene 31 - Benedict Feeds the Monk - WGA21581.jpg|The monks of the order of Saint Benedict (circa 480-542) first dressed in undyed white or gray wool robes, here shown in painting by Sodoma on the life of Saint Benedict (1504). They later changed to black robes, the color of humility and penitence. File:Unicorn hunt - British Library Royal 12 F xiii f10v (detail).jpg|The white unicorn frequently appeared in Medieval art, often as a symbol of virginity and purity. This the unicorn hunt from the Rochester Bestiary, from about 1230, in the British Library. File:Bartolomeo Passarotti Pope Pius V.jpg|Under Pope Pius V (1504–1572), a former monk of the Dominican Order, white became the official color worn by the Pope. File:Ghent Altarpiece D - Adoration of the Lamb 2.jpg|The white lamb in the Ghent Altarpiece by Jan van Eyck. (1432)\\nFile:Transfiguration by fra Angelico (San Marco Cell 6).jpg|The Transfiguration by Fra Angelico (1440–1442)\\nFile:Leonardo da Vinci - Portrait of Cecilia Gallerani (Lady with an Ermine) - WGA12698.jpg|Lady with an ermine, by Leonardo da Vinci (1490). The ermine symbolized nobility and purity.\",\n \"White\\n\\nIt was believed that an ermine would rather die than allow its white fur to become dirty. File:Mary Queen of Scots in mourning.jpg|Mary Stuart wore white in mourning for her husband, King Francis II of France, who died in 1560.\",\n \"White\\n\\n18th and 19th centuries\",\n \"White\\n\\nWhite was the dominant color of architectural interiors in the Baroque period and especially the Rococo style that followed it in the 18th century. Church interiors were designed to show the power, glory and wealth of the church. They seemed to be alive, filled with curves, asymmetry, mirrors, gilding, statuary and reliefs, unified by white.\",\n \"White\\n\\nWhite was also a fashionable color for both men and women in the 18th century. Men in the aristocracy and upper classes wore powdered white wigs and white stockings, and women wore elaborate embroidered white and pastel gowns.\",\n \"White\\n\\nAfter the French Revolution, a more austere white (blanc cassé) became the most fashionable color in women's costumes which were modeled after the outfits of Ancient Greece and Republican Rome. Because of the rather revealing design of these dresses, the ladies wearing them were called les merveilleuses (the marvellous) by French men of that era. The Empire style under Emperor Napoléon I was modeled after the more conservative outfits of Ancient Imperial Rome. The dresses were high in fashion but low in warmth considering the more severe weather conditions of northern France; in 1814 the former wife of Napoleon, Joséphine de Beauharnais, caught pneumonia and died after taking a walk in the cold night air with Tsar Alexander I of Russia.\",\n \"White\\n\\nWhite was the universal color of both men and women's underwear and of sheets in the 18th and 19th centuries. It was unthinkable to have sheets or underwear of any other color. The reason was simple; the manner of washing linen in boiling water caused colors to fade. When linen was worn out, it was collected and turned into high-quality paper.\",\n \"White\\n\\nThe 19th-century American painter James McNeill Whistler (1834–1903), working at the same time as the French impressionists, created a series of paintings with musical titles where he used color to create moods, the way composers used music. His painting \\\"Symphony in White No. 1 - The White Girl\\\", which used his mistress Joanna Hiffernan as a model, used delicate colors to portray innocence and fragility, and a moment of uncertainty.\",\n \"White\\n\\nFile:BasilikaOttobeurenHauptschiff02.JPG|A highly theatrical white Rococo interior from the 18th century, at the Basilica at Ottobeuren, in Bavaria.\\nFile:Marie-Antoinette par Elisabeth Vigée-Lebrun - 1783.jpg|White gown of Marie Antoinette, painted by Elisabeth Vigée-Lebrun in 1783. \\nFile:Gilbert Stuart, George Washington (Lansdowne portrait, 1796).jpg|President George Washington in a white powdered wig. The first five Presidents of the United States wore dark suits with powdered wigs for formal occasions.\\nFile:Emprjose.jpg|Portrait of Joséphine de Beauharnais in a classic Empire gown, modeled after the clothing of ancient Rome. (1801), by François Gérard. (The State Hermitage Museum).\\nFile:Whistler James Symphony in White no 1 (The White Girl) 1862.jpg|Symphony in White No. 1 - The White Girl, by James McNeill Whistler (1862).\",\n \"White\\n\\n20th and 21st centuries\",\n \"White\\n\\nThe White movement was the opposition that formed against the Bolsheviks during the Russian Civil War, which followed the Russian Revolution in 1917. It was finally defeated by the Bolsheviks in 1921-22, and many of its members emigrated to Europe.\",\n \"White\\n\\nAt the end of the 19th century, lead white was still the most popular pigment; but between 1916 and 1918, chemical companies in Norway and the United States began to produce titanium white, made from titanium oxide. It had first been identified in the 18th century by the German chemist Martin Klaproth, who also discovered uranium. It had twice the covering power of lead white, and was the brightest white pigment known. By 1945, 80 percent of the white pigments sold were titanium white.\",\n \"White\\n\\nThe absoluteness of white appealed to modernist painters. It was used in its simplest form by the Russian suprematist painter Kazimir Malevich in his 1917 painting 'the white square,' the companion to his earlier 'black square.' It was also used by the Dutch modernist painter Piet Mondrian. His most famous paintings consisted of a pure white canvas with grid of vertical and horizontal black lines and rectangles of primary colors.\",\n \"White\\n\\nBlack and white also appealed to modernist architects, such as Le Corbusier (1887–1965). He said a house was \\\"a machine for living in\\\" and called for a \\\"calm and powerful architecture\\\" built of reinforced concrete and steel, without any ornament or frills. Almost all the buildings of contemporary architect Richard Meier, such as his museum in Rome to house the ancient Roman Ara Pacis, or Altar of Peace, are stark white, in the tradition of Le Corbusier.\",\n \"White\\n\\nFile:За единую Россію.jpg|Poster for the White Army during the Russian Civil War (1917–22). The poster says: \\\"for a United Russia.\\\" \\nFile:Kazimir_Malevich_-_%27Suprematist_Composition-_White_on_White%27,_oil_on_canvas,_1918,_Museum_of_Modern_Art.jpg|White on White (1917) by Kazimir Malevich, Museum of Modern Art, New York\\nFile:VillaSavoye.jpg|The Villa Savoye (1928–31) by Le Corbusier. Le Corbusier called for a \\\"calm and powerful\\\" architecture built of steel and reinforced concrete.\",\n \"White\\n\\nScience\",\n \"White\\n\\nOptics and white light\",\n \"White\\n\\nWhite is the color the human visual system senses when the incoming light to the eye stimulates all three types of color sensitive cone cells in the eye in nearly equal amounts. Materials that do not emit light themselves appear white if their surfaces reflect back most of the light that strikes them in a diffuse way.\",\n \"White\\n\\nIn 1666, Isaac Newton demonstrated that white light could be broken up into its composite colors by passing it through a prism, then using a second prism to reassemble them. Before Newton, most scientists believed that white was the fundamental color of light.\",\n \"White\\n\\nWhite light can be generated by the sun, by stars, or by earthbound sources such as fluorescent lamps, white LEDs and incandescent bulbs. On the screen of a color television or computer, white is produced by mixing the primary colors of light: red, green and blue (RGB) at full intensity, a process called additive mixing (see image below). White light can be fabricated using light with only two wavelengths, for instance by mixing light from a red and cyan laser or yellow and blue lasers. This light will however have very few practical applications since color rendering of objects will be greatly distorted.\",\n \"White\\n\\nThe fact that light sources with vastly different spectral power distributions can result in a similar sensory experience is due to the way the light is processed by the visual system. One color that arise from two different spectral power distributions is called a metamerism.\",\n \"White\\n\\nThe International Commission on Illumination defines white (adapted) as \\\"a color stimulus that an observer who is adapted to the viewing environment would judge to be perfectly achromatic and to have a luminance factor of unity. The color stimulus that is considered to be the adapted white may be different at different locations within a scene.\",\n \"White\\n\\nThe adaptation mentioned in the CIE definition above is the chromatic adaptation by which the same colored object in a scene experienced under very different illuminations will be perceived as having nearly the same color. The same principle is used in photography and cinematography where the choice of white point determines a transformation of all other color stimuli. Changes in or manipulation of the white point can be used to explain some optical illusions such as The dress.\",\n \"White\\n\\nFile:Synthese+.svg|In the RGB color model, used to create colors on TV and computer screens, white is made by mixing red, blue and green light at full intensity.\\nFile:Dispersion prism.jpg|White light refracted in a prism revealing the color components.\",\n \"White\\n\\nMany of the light sources that emit white light emit light at almost all visible wavelengths (sun light, incandescent lamps of various Color temperatures). This has led to the notion that white light can be defined as a mixture of \\\"all colors\\\" or \\\"all visible wavelengths\\\". This misconception is widespread and might originally stem from the fact that Newton discovered that sunlight is composed of light with wavelengths across the visible spectrum. Concluding that since \\\"all colors\\\" produce white light then white must be made up of \\\"all colors\\\" is a common logical error called affirming the consequent, which might be the cause of the misunderstanding.\",\n \"White\\n\\nWhy snow, clouds and beaches are white\",\n \"White\\n\\nSnow is a mixture of air and tiny ice crystals. When white sunlight enters snow, very little of the spectrum is absorbed; almost all of the light is reflected or scattered by the air and water molecules, so the snow appears to be the color of sunlight, white. Sometimes the light bounces around inside the ice crystals before being scattered, making the snow seem to sparkle.\",\n \"White\\n\\nIn the case of glaciers, the ice is more tightly pressed together and contains little air. As sunlight enters the ice, more light of the red spectrum is absorbed, so the light scattered will be bluish.\",\n \"White\\n\\nClouds are white for the same reason as ice. They are composed of water droplets or ice crystals mixed with air, very little light that strikes them is absorbed, and most of the light is scattered, appearing to the eye as white. Shadows of other clouds above can make clouds look gray, and some clouds have their own shadow on the bottom of the cloud.\",\n \"White\\n\\nMany mountains with winter or year-round snow cover are named accordingly: Mauna Kea means white mountain in Hawaiian, Mont Blanc means white mountain in French. Changbai Mountains literally meaning perpetually white mountains, marks the border between China and Korea.\",\n \"White\\n\\nBeaches with sand containing high amounts of quartz or eroded limestone also appear white, since quartz and limestone reflect or scatter sunlight, rather than absorbing it. Tropical white sand beaches may also have a high quantity of white calcium carbonate from tiny bits of seashells ground to fine sand by the action of the waves.\",\n \"White\\n\\nFile:Snow-covered fir trees.jpg|Snow is composed of ice and air; it scatters or reflects sunlight without absorbing other colors of the spectrum.\",\n \"White\\n\\nFile:MontBlanc2c.jpg|Mont Blanc in the Alps. It takes its name from the white snow on its summit.\\nFile:Cumulus clouds in fair weather.jpeg|Cumulus clouds look white because the water droplets reflect and scatter the sunlight without absorbing other colors.\\nFile:Pensacola Beach 1957 White Sand.jpg|Pensacola Beach, Florida. White sand beaches look white because the quartz or eroded limestone in the sand reflects or scatters sunlight without absorbing other colors.\",\n \"White\\n\\nChemistry- white pigments and dyes\",\n \"White\\n\\nChalk is a kind of limestone, made of the mineral calcite, or calcium carbonate. It was originally deposited under the sea as the scales or plates of tiny micro-organisms called Coccolithophore. It was the first white pigment used by prehistoric artists in cave paintings. The chalk used on blackboards today is usually made of gypsum or calcium sulphate, a powder pressed into sticks.\",\n \"White\\n\\nBianco di San Giovanni is a pigment used in the Renaissance, which was described by the painter Cennino Cennini in the 15th century. It is similar to chalk, made of calcium carbonate with calcium hydroxide. It was made of dried lime which was made into a powder, then soaked in water for eight days, with the water changed each day. It was then made into cakes and dried in the sun.\",\n \"White\\n\\nLead white was being produced during the 4th century BC; the process is described is Pliny the Elder, Vitruvius and the ancient Greek author Theophrastus. Pieces of lead were put into clay pots which had a separate compartment filled with vinegar. The pots in turn were piled on shelves close to cow dung. The combined fumes of the vinegar and the cow dung caused the lead to corrode into lead carbonate. It was a slow process which could take a month or more. It made an excellent white and was used by artists for centuries, but it was also toxic. It was replaced in the 19th century by zinc white and titanium white.\",\n \"White\\n\\nTitanium white is the most popular white for artists today; it is the brightest available white pigment, and has twice the coverage of lead white. It first became commercially available in 1921. It is made out of titanium dioxide, from the minerals brookite, anatase, rutile, or ilmenite, currently the major source. Because of its brilliant whiteness, it is used as a colorant for most toothpaste and sunscreen.\",\n \"White\\n\\nZinc white is made from zinc oxide. It is similar to but not as opaque as titanium white. It is added to some breakfast cereals, since zinc is an important nutrient.\",\n \"White\\n\\nSome materials can be made to look \\\"whiter than white\\\", this is achieved using optical brightener agents (OBA). These are chemical compounds that absorb light in the ultraviolet and violet region (usually 340-370 nm) of the electromagnetic spectrum, and re-emit light in the blue region (typically 420-470 nm). OBAs are often used in paper and clothing to create an impression of very bright white. This is due to the fact that the materials actually send out more visible light than they receive.\",\n \"White\\n\\nChinese white is a variety of zinc white made for artists.\",\n \"White\\n\\nFile:Titanium(IV) oxide.jpg|Titanium white, made with titanium dioxide, is the brightest white paint available. It also colors most toothpaste and sunscreen. \\nFile:Zinc oxide.jpg|Zinc white, made from zinc oxide.\",\n \"White\\n\\nBleach and bleaching\",\n \"White\\n\\nBleaching is a process for whitening fabrics which has been practiced for thousands of years. Sometimes it was simply a matter of leaving the fabric in the sun, to be faded by the bright light. In the 18th century several scientists developed varieties of chlorine bleach, including sodium hypochlorite and calcium hypochlorite (bleaching powder). Bleaching agents that do not contain chlorine most often are based on peroxides, such as hydrogen peroxide, sodium percarbonate and sodium perborate. While most bleaches are oxidizing agents, a fewer number are reducing agents such as sodium dithionite.\",\n \"White\\n\\nBleaches attack the chromophores, the part of a molecule which absorbs light and causes fabrics to have different colors. An oxidizing bleach works by breaking the chemical bonds that make up the chromophore. This changes the molecule into a different substance that either does not contain a chromophore, or contains a chromophore that does not absorb visible light. A reducing bleach works by converting double bonds in the chromophore into single bonds. This eliminates the ability of the chromophore to absorb visible light.\",\n \"White\\n\\nSunlight acts as a bleach through a similar process. High energy photons of light, often in the violet or ultraviolet range, can disrupt the bonds in the chromophore, rendering the resulting substance colorless.\",\n \"White\\n\\nSome detergents go one step further; they contain fluorescent chemicals which glow, making the fabric look literally whiter than white.\",\n \"White\\n\\nAstronomy\",\n \"White\\n\\nA white dwarf is a stellar remnant composed mostly of electron-degenerate matter. They are very dense; a white dwarf's mass is comparable to that of the Sun and its volume is comparable to that of the Earth. Its faint luminosity comes from the emission of stored thermal energy.\",\n \"White\\n\\nA white dwarf is very hot when it is formed, but since it has no source of energy, it will gradually radiate away its energy and cool down. This means that its radiation, which initially has a high color temperature, will lessen and redden with time. Over a very long time, a white dwarf will cool to temperatures at which it will no longer emit significant heat or light, and it will become a cold black dwarf. However, since no white dwarf can be older than the age of the Universe (approximately 13.8 billion years), even the oldest white dwarfs still radiate at temperatures of a few thousand kelvins, and no black dwarfs are thought to exist yet.\",\n \"White\\n\\nFile:Sirius A and B Hubble photo.jpg|Image of Sirius A and Sirius B taken by the Hubble Space Telescope. Sirius B, a white dwarf, is the faint pinprick of light to the lower left of the much brighter Sirius A.\",\n \"White\\n\\nBiology\",\n \"White\\n\\nMost white animals have their color as a form of camouflage in winter.\",\n \"White\\n\\nFile:Dove 001.JPG|The dove is an international symbol of peace.\\nFile:Ivory Gull Portrait.jpg|The ivory gull.\\nFile:Cygnus olor 2 (Marek Szczepanek).jpg|Mute swans. Swans of the Northern Hemisphere are white, while those of the Southern Hemisphere are black and white. \\nFile:Polarfuchs 1 2004-11-17.jpg|The Arctic fox\\nFile:Mustela erminea winter cropped.jpg|The ermine, or stoat. Once considered the most noble of animals because it would rather die than dirty its fur, it is now considered an invasive species.\\nFile:Uncia uncia.jpg|A snow leopard.\\nFile:Delphinapterus leucas 2.jpg|A beluga whale. Its color helps it hide from its chief enemies, the polar bear and killer whales.\\nFile:White pearl necklace.jpg|White pearls are hard objects produced within the soft tissue of a living shelled mollusk, like an oyster or clam. They are made of calcium carbonate in minute crystalline form. \\nFile:Betula pendula 001.jpg|The silver birch's bark is silvery-white.\\nFile:Proteus anguinus Postojnska Jama Slovenija.jpg|Olms in Postojna Cave, Slovenia. Their skin color is pale or whitish.\\nFile:Large white spread wings.jpg|A cabbage butterfly (Pieris brassicae).\",\n \"White\\n\\nAssociations and symbolism\",\n \"White\\n\\nInnocence and sacrifice\",\n \"White\\n\\nIn Western culture, white is the color most often associated with innocence. In Biblical times, lambs and other white animals were sacrificed to expiate sins. In Christianity Christ is considered the \\\"lamb of God,\\\" who died for the sins of mankind. The white lily is considered the flower of purity and innocence, and is often associated with the Virgin Mary.\",\n \"White\\n\\nThe beginning and the new\",\n \"White\\n\\nWhite is the color in Western culture most often associated with beginnings and the new. In Christianity, children are baptized wearing white, and, wear white for their first communion. Christ after his Resurrection is traditionally portrayed dressed in white. Eggs, another symbol of the new, are used to celebrate Easter.\",\n \"White\\n\\nThe Queen of the United Kingdom traditionally wears white when she opens the session of Parliament. In high society, debutantes traditionally wear white for their first ball.\",\n \"White\\n\\nWeddings\",\n \"White\\n\\nWhite has long been the traditional color worn by brides at royal weddings, but the white wedding gown for ordinary people appeared in the 19th century. Before that time, most brides wore their best Sunday clothing, of whatever color. The white lace wedding gown of Queen Victoria in 1840 had a large impact on the color and fashion of wedding dresses in both Europe and America down to the present day.\",\n \"White\\n\\nFile:Wedding of Queen Victoria and Prince Albert.jpg|The wedding dress of Queen Victoria (1840) set the fashion for wedding dresses of the Victorian era and for the 20th century.\\nFile:Wedding of Nicholas II and Alexandra Feodorovna by Laurits Tuxen (1895, Hermitage).jpg|The wedding of Czar Nicholas II of Russia and Alexandra Feodorovna (Alix of Hesse), the granddaughter of Queen Victoria, in 1894.\\nFile:Wedding kimono.jpg|Brides in China and other parts of Asia traditionally wear red, the color of happiness and good fortune, but in the Shinto religion of Japan brides traditionally wear a white wedding kimono.\\nFile:MyBarong created this Custom tailored Barong Tagalog for my wedding.jpg|The Barong Tagalog is a traditional Folk costume of the Philippines; this attire is worn on formal gatherings and weddings.\",\n \"White\\n\\nCleanliness\",\n \"White\\n\\nWhite is the color most associated with cleanliness. Objects which are expected to be clean, such as refrigerators and dishes, toilets and sinks, bed linen and towels, are traditionally white. White was the traditional color of the coats of doctors, nurses, scientists and laboratory technicians, though nowadays a pale blue or green is often used. White is also the color most often worn by chefs, bakers, and butchers, and the color of the aprons of waiters in French restaurants.\",\n \"White\\n\\nGhosts, phantoms and two of the Four Horsemen of the Apocalypse\",\n \"White\\n\\nWhite is the color associated with ghosts and phantoms. In the past the dead were traditionally buried in a white shroud. Ghosts are said to be the spirits of the dead who, for various reasons, are unable to rest or enter heaven, and so walk the earth in their white shrouds. White is also connected with the paleness of death. A common expression in English is \\\"pale as a ghost.\\\"\",\n \"White\\n\\nThe woman in white, Weiße Frau, or dame blanche is a familiar figure in English, German and French ghost stories. She is a spectral apparition of a female clad in white, in most cases the ghost of an ancestor, sometimes giving warning about death and disaster. The most notable Weiße Frau is the legendary ghost of the German Hohenzollern dynasty.\",\n \"White\\n\\nSeeing a white horse in a dream is said to be presentiment of death. \\nIn the Book of Revelation, the last book in the New Testament of the Bible, the Four Horsemen of the Apocalypse are supposed to announce the Apocalypse before the Last Judgement. The man on a white horse with a bow and arrow. according to different interpretations, represents either War and Conquest, the Antichrist, or Christ himself, cleansing the world of sin. Death rides a horse whose color is described in ancient Greek as khlōros (χλωρός) in the original Koine Greek, which can mean either green/greenish-yellow or pale/pallid. \\nFile:Apparition DB.JPG|The woman in white or dame blanche is a familiar figure in English, French and German ghost stories.\\nFile:Apocalypse vasnetsov.jpg|The biblical Four Horsemen of the Apocalypse. Conquest, with a bow, rides a white horse. Death rides a pale or light green horse. (Painting by Viktor Vasnetsov, 1887).\",\n \"White\\n\\nBlack and white\",\n \"White\\n\\nBlack and white often represent the contrast between light and darkness, day and night, good and evil.\",\n \"White\\n\\nIn taoism, the two opposite natures of the universe, yin and yang, are often symbolized in black and white, Ancient games of strategy, such as go and chess, use black and white to represent the two sides.\",\n \"White\\n\\nIn the French monarchy, white symbolized the King and his power par la grâce de Dieu (\\\"by the grace of God\\\") and in contrast black was the color of the queen who according to the Salic Law which excluded women from the throne (and thus from power) could never become the ruling monarch.\",\n \"White\\n\\nBlack and white also often represent formality and seriousness, as in the costumes of judges and priests, business suits, of formal evening dress. Monks of the Dominican Order wear a black cloak over a white habit. Until 1972 agents of the Federal Bureau of Investigation were required to wear white shirts with their suits, to project the correct image of the FBI.\",\n \"White\\n\\nFile:Yin and Yang.svg|In Taoism, white represents the yang, one of the two opposite natures of the universe.\",\n \"White\\n\\nNames taken from white\",\n \"White\\n\\nWhite is the source of more names for women in western countries than any other color. Names taken from white include Alba, Albine (Latin). Blanche and Blanchette (French); Bianca (Italian); Jennifer (Celt); Genevieve, Candice (from Latin Candida); Fenela, Fiona and Finola (Irish); Gwendoline, Gwenael, Nol(g)wen (white woman) (Celt), Nives (Italian) and Zuria (Basque).\",\n \"White\\n\\nIn addition many names come from white flowers: Camille, Daisy, Lily, Lili, Magnolie, Jasmine, Yasemine, Leila, Marguerite, Rosalba, and others.\",\n \"White\\n\\nOther names come from the white pearl; Pearl, Margarita (Latin), Margaret, Margarethe, Marga, Grete, Rita, Gitta, Marjorie, Margot.\",\n \"White\\n\\nWhite in other cultures\",\n \"White\\n\\nIn China, Korea, and some other Asian countries, white, or more precisely, the whitish color of undyed linen, is the color of mourning and funerals.\",\n \"White\\n\\nIn traditional China, undyed linen clothing is worn at funerals. As time passes, the bereaved can gradually wear clothing dyed with colors, then with darker colors. Small sacks of quicklime, one for each year of the life of the deceased are placed around the body to protect it against impurity in the next world, and white paper flowers are placed around the body.\",\n \"White\\n\\nIn China and other Asian counties, white is the color of reincarnation, showing that death is not a permanent separation from the world.\",\n \"White\\n\\nIn China, white is associated with the masculine (the yang of the yin and yang); with the unicorn and tiger; with the fur of an animal; with the direction of west; with the element metal; and with the autumn season.\",\n \"White\\n\\nIn Japan, undyed linen white robes are worn by pilgrims for rituals of purification, and bathing in sacred rivers. In the mountains, pilgrims wear costumes of undyed jute to symbolize purity. A white kimono is often placed in the casket with the deceased for the journey to the other world, as white represents death sometimes. Condolence gifts, or kooden, are tied with black and white ribbons and wrapped in white paper, protecting the contents from the impurities of the other world.\",\n \"White\\n\\nIn India, the color white was traditionally reserved for the Brahmin caste. It is the color of purity, divinity, detachment and serenity. In Hindi, the name Sweta means white.\",\n \"White\\n\\nIn Tibetan Buddhism, white robes were reserved for the lama of a monastery.\",\n \"White\\n\\nIn the Bedouin and some other pastoral cultures, there is a strong connection between milk and white, which is considered the color of gratitude, esteem, joy, good fortune and fertility.\",\n \"White\\n\\nFile:Iwamotoji PilgrimGirl.JPG|A pilgrim in Japan.\\nFile:JapaneseFuneralEnvelope.jpg|In Japan, the traditional envelope for condolence gifts is wrapped in a black and white cord, and a white kimono is often placed in the coffin with the deceased.\\nFile:Weisse tara mongolian art.jpg|The Buddhist deity Tara is often depicted with white skin.\\nFile:Brahmin boy ritual.jpg|A Brahmin boy in India wears white for a religious ritual.\\nFile:Bedouin.jpg|A Bedouin in the United Arab Emirates. White is the traditional costume for men, and the color of esteem and good fortune.\",\n \"White\\n\\nTemples, churches and government buildings\",\n \"White\\n\\nSince ancient times, temples, churches, and many government buildings in many countries have traditionally been white, the color associated with religious and civic virtue. The Parthenon and other ancient temples of Greece, and the buildings of the Roman forum were mostly made of or clad in white marble, though it is now known that some of these ancient buildings were actually brightly painted. The Roman tradition of using white stone for government buildings and churches was revived in the Renaissance and especially in the neoclassic style of the 18th and 19th centuries. White stone became the material of choice for government buildings in Washington D.C. and other American cities. European cathedrals were also usually built of white or light-colored stone, though many darkened over the centuries from smoke and soot.\",\n \"White\\n\\nThe Renaissance architect and scholar Leon Battista Alberti wrote in 1452 that churches should be plastered white on the inside, since white was the only appropriate color for reflection and meditation. After the Reformation, Calvinist churches in the Netherlands were whitewashed and sober inside, a tradition that was also followed in the Protestant churches of New England, such as Old North Church in Boston.\",\n \"White\\n\\nFile:Parthenon.jpg|Although the Parthenon in Athens (5th century BC) is white today, it was originally painted with many colors \\nFile:858MilanoDuomo.JPG|The Cathedral of Milan (1386–1965)\\nFile:Delft interieur Waalse Kerk.jpg|Dutch Reformed Church interior in Delft, the Netherlands (16th century)\\nFile:2006Boston007.jpg|Interior of Old North Church, Boston (1723)\\nFile:WhiteHouseSouthFacade.JPG|The White House (1801), Washington D.C.\\nFile:United States Capitol dome daylight.jpg|The United States Capitol dome (1855–66)\\nFile:Sacre-coeur-paris.jpg| Basilica of Sacré-Cœur, Paris (1919)\\nFile:Palacio do Planalto.jpeg|The Palácio do Planalto in Brasília, official workplace of the President of Brazil (1960)\\nFile:St Mary's Cathedral - San Francisco.jpg|Saint Mary's Cathedral in San Francisco (1971)\\nFile:Den Haag stadhuis april 2004.JPG|The City Hall in The Hague, Netherlands, by architect Richard Meier (2004).\",\n \"White\\n\\nGovernment and politics\",\n \"White\\n\\nWhite is often associated with monarchism. The association originally came from the white flag of the Bourbon dynasty of France. White became the banner of the royalist rebellions against the French Revolution (see Revolt in the Vendée).\",\n \"White\\n\\nDuring the Civil War which followed the Russian Revolution of 1917, the White Army, a coalition of monarchists, nationalists and liberals, fought unsuccessfully against the Red Army of the Bolsheviks. A similar battle between reds and whites took place during the Civil War in Finland in the same period.\",\n \"White\\n\\nThe Ku Klux Klan is a racist and anti-immigrant organization which flourished in the Southern United States after the American Civil War. They wore white robes and hoods, burned crosses and violently attacked and murdered black Americans.\",\n \"White\\n\\nIn Iran, the White Revolution was a series of social and political reforms launched in 1963 by the last Shah of Iran before his downfall.\",\n \"White\\n\\nWhite is also associated with peace and passive resistance. The white ribbon is worn by movements denouncing violence against women and the White Rose was a non-violent resistance group in Nazi Germany.\",\n \"White\\n\\nFile:Volunteer Army recruitment poster.jpg|A recruiting poster for the White Volunteer Army during the Russian Civil War (1919). The text says, \\\"Son, go save the motherland!\\\" \\nFile:Klan-in-gainesville.jpg|A cross burning by the racist Ku Klux Klan in Florida in the early 20th century.\",\n \"White\\n\\nReligion\",\n \"White\\n\\nIn the Roman Catholic Church, white is associated with Jesus Christ, innocence and sacrifice. Since the Middle Ages, priests wear a white cassock in many of the most important ceremonies and religious services connected with events in the life of Christ. White is worn by priests at Christmas, during Easter, and during celebrations connected with the other events of the life of Christ, such as Corpus Christi Sunday, and Trinity Sunday. It is also worn at the services dedicated to the Virgin Mary, and to those Saints who were not martyred, as well as other special occasions, such as the ordination of priests and the installation of new bishops. Within the hierarchy of the church, the lighter the color, the higher the rank. Ordinary priests wear black; bishops wear violet, cardinals wear red, and outside a church, only the Pope will wear white. Popes occasionally wore white in the Middle Ages, but usually wore red. Popes have worn white regularly since 1566, when Pope Pius V, a member of the Dominican Order, began the practice. White is the color of the Dominican Order.\",\n \"White\\n\\nIn Islam, white clothing is worn during required pilgrimage to Mecca, or Ihram pilgrimage (Hajj).Hajj. Called Ihram clothing, men's garments often consist of two white un-hemmed sheets (usually towelling material). The top (the riḍā) is draped over the torso and the bottom (the izār) is secured by a belt; plus a pair of sandals. Women's clothing varies considerably and reflects regional as well as religious influences. Ihram is typically worn during Dhu al-Hijjah, the last month in the Islamic calendar.\",\n \"White\\n\\nIn Judaism, during the rituals of Yom Kippur, the ceremony of atonement, the rabbi dresses in white, as do the members of the congregation, to restore the bonds between God and his followers.\",\n \"White\\n\\nIn the traditional Japanese religion of Shinto, an area of white gravel or stones marks a sacred place, called a niwa. These places were dedicated to the kami, spirits which had descended from the heavens or had come across the sea. Later, temples of Zen Buddhism in Japan often featured a Zen garden, where white sand or gravel was carefully raked to resemble rivers or streams, designed as objects of meditation.\",\n \"White\\n\\nIn the temples of The Church of Jesus Christ of Latter-day Saints (LDS Church or also known as Mormon), White clothing is worn inside once they have been officially dedicated, due to white symbolizing purity.\",\n \"White\\n\\nMany religions symbolize heaven by using a sky with white clouds. This phenomenon is not limited to western culture; in Yoruba religion, the orisha Obatala in the Ifá tradition is represented by white. Obatala is associated with calmness, morality, old age, and purity.\",\n \"White\\n\\nIn Theosophy and similar religions, the deities called the Great White Brotherhood are said to have white auras.\",\n \"White\\n\\nIn some Asian and Slavic cultures, white is considered to be a color that represents death. White also represented death in ancient Egypt, representing the lifeless desert that covered much of the country; black was held to be the color of life, representing the mud-covered fertile lands created by the flooding of the Nile and giving the country its name (Kemet, or \\\"black land\\\").\",\n \"White\\n\\nFile:Al-Haram mosque - Flickr - Al Jazeera English.jpg|Thousands of pilgrims in white gather in Mecca for the beginning of their pilgrimage, or Haj.\\nFile:Pope Francis in March 2013.jpg|Pope Francis (2013). The Pope wears white as a symbol of innocence and sacrifice.\\nFile:Toufuku-ji kaizandou3.JPG|The zen garden of Tōfuku-ji temple in Japan. The Shinto religion uses white sand or gravel to symbolize a sacred place, while Zen Buddhism uses it to stimulate calm and meditation.\",\n \"White\\n\\nEthnography\",\n \"White\\n\\nPeople of the Caucasian race, most commonly those of European descent, are often referred to simply as white. The United States Census Bureau defines White people as those \\\"having origins in any of the original peoples of Europe, the Middle East, or North Africa. It includes people who reported “White” or wrote in entries such as Irish, German, Italian, Lebanese, Near Easterner, Arab, or Polish.\\\" Whites constitute the majority of the U.S. population, with a total of 223,553,265 or 72.4% of the population in the 2010 United States Census.\",\n \"White\\n\\nThe white flag\",\n \"White\\n\\nA white flag has long been used to represent either surrender or a request for a truce. It is believed to have originated in the 15th century, during the Hundred Years' War between France and England, when multicolored flags, as well as firearms, came into common use by European armies. The white flag was officially recognized as a request to cease hostilities by the Geneva Convention of 1949.\",\n \"White\\n\\nVexillology and heraldry\",\n \"White\\n\\nIn English heraldry, white or silver signified brightness, purity, virtue, and innocence.\",\n \"White\\n\\nSelected national flags featuring white\",\n \"White\\n\\nWhite is a common color in national flags, though its symbolism varies widely. The white in the flag of the United States and flag of the United Kingdom comes from traditional red St George's Cross on a white background of the historic flag of England. The white in the flag of France represents either the monarchy or \\\"white, the ancient French color\\\" according to the Marquis de Lafayette.\",\n \"White\\n\\nMany flags in the Arab world use the colors of the flag of the Arab Revolt of 1916; red, white, green and black. These include the flags of Egypt, Bahrain, Jordan, Syria, Kuwait and Iraq.\",\n \"White\\n\\nPhilippines also use white as their symbol for unity in their flag.\",\n \"White\\n\\nFile:Pavillon royal de France.svg|Flag of the Bourbons, royal family of France until the French Revolution and during the restoration of the monarchy afterwards.\\nFile:Flag of the Vatican City.svg|The Flag of Vatican City (1929). The white and gold colors symbolize the colors of the keys to heaven given by Jesus Christ to Saint Peter: the gold of spiritual power, the white of worldly power. The keys have been the Papal symbol since the 13th century.\",\n \"White\\n\\nFile:Flag of the Netherlands.svg|The flag of the Netherlands (1572) was the first red, white and blue national flag. Peter the Great adopted the colors for the flag of Russia. \\nFile:Flag of India.svg|The flag of India (1947). White represents \\\"light, the path of truth\\\". \\nFile:Flag of Ireland.svg|The flag of Ireland. According to the Irish government press office, \\\"The green represents the older Gaelic tradition while the orange represents the supporters of William of Orange. The white in the centre signifies a lasting truce between the 'Orange' and the 'Green'. \\\" \\nFile:Flag of Egypt.svg|The flag of Egypt (1984). \\nFile:Flag of the Philippines.svg| The Flag of the Philippines use royal blue, scarlet , yellow, and white. \\nThe colors come from the flag of the Arab Revolt in 1916.\\nFile:Flag of Taliban.svg|The flag of the Taliban in Afghanistan from 1997-2001. It reverses the colors of the Black Standard, the flag of Muhammad. The text says 'There is no God but Allah, and Muhammad is his prophet.\\\"\",\n \"White\\n\\nIdioms and expressions\",\n \"White\\n\\n* To whitewash something is to conceal an unpleasant reality. * A white lie is an innocent lie told out of politeness. * White noise is the noise of all the frequencies of sound combined. It is used to cover up unwanted noise. * A white knight in finance is a friendly investor who steps in to rescue a company from a hostile takeover. * White-collar workers are those who work in offices, as opposed to blue-collar workers, who work with their hands in factories or workshops. * A white paper is an authoritative report on a major issue by a team of experts; a government report outlining policy; or a short treatise whose purpose is to educate industry customers. Associating a paper with white may signify clean facts and unbiased information. * The white feather is a symbol of cowardice, particularly in Britain. It supposedly comes from cockfighting and the belief that a cockerel sporting a white feather in its tail is likely to be a poor fighter. At the beginning of the First World War, women in England were encouraged to give white feathers to men who had not enlisted in the British Armed Forces.\",\n \"White\\n\\n* In the US, a white shoe firm is an older, conservative firm, usually in a field such as banking or law. The phrase derives from the \\\"white bucks,\\\" laced suede or buckskin shoes with red soles, long popular in the Ivy League colleges. * In Russia, the nobility are sometimes described as white bone (белая кость, bélaya kost'), commoners as black bone.\"\n]","isConversational":false}}},{"rowIdx":1791,"cells":{"id":{"kind":"string","value":"tc_2765"},"question":{"kind":"string","value":"The discovery of which law provoked the surprised cry 'Eureka!'?"},"answer":{"kind":"string","value":"Archimedes Principle"},"answer_aliases":{"kind":"list like","value":["principle of displacement","archimedes principle","archemedes principle","archemides principle"],"string":"[\n \"principle of displacement\",\n \"archimedes principle\",\n \"archemedes principle\",\n \"archemides principle\"\n]","isConversational":false},"documents":{"kind":"list like","value":["PHYSICS FOLIO |authorSTREAM\n\nPHYSICS FOLIO |authorSTREAM\nPHYSICS FOLIO\n Does not support media & animations\n Automatically changes to Flash or non-Flash embed\n The presentation is successfully added In Your Favorites . Views:\n This Presentation is Public Favorites: \n0\nENTRY NO. 1: Physics A Natural Philosophy:\nENTRY NO. 1: Physics A Natural Philosophy ENTRY NO. 1: Physics A Natural Philosophy\nPhysics A Natural Philosophy:\nPhysics A Natural Philosophy Physics as natural philosophy. Physics is present in our environment at all times. The gravitational theory is the perfect explanation for this natural philosophy. Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. In everyday life, gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped. ENTRY NO.2 PHYSICS REALLY WORKS:\nENTRY NO.2 PHYSICS REALLY WORKS\nPhysics Really Works:\nPhysics Really Works Physics really works. A branch of physics, which is electromagnetism, can be seen in modern inventions. Electromagnetism is the force that causes the interaction between electrically charged particles; the areas in which this happens are called electromagnetic fields. This is the set-up in a MICROPHONE.","PHYSICS FOLIO |authorSTREAM\n\nsound waves enter the microphone, which cause the microphone to vibrate back and forth. This subsequently causes the wire loops to oscillate, and the magnetic field through the plane of the loops subsequently changes, inducing a current in the wires. In this way sound or wave energy is converted into electrical energy. ENTRY NO. 3: TESTING TIME :\nENTRY NO. 3: TESTING TIME\nPHYSICS TRIVIAS::\nPHYSICS TRIVIAS: Q: What did scientists build in a squash court under a football stadium at the University of Chicago in 1942? A: A nuclear reactor. Slide 8:\nQ: Which Swedish scientist had a temperature scale named after him? A: Anders Celsius. Slide 9:\nQ :What is the term used to denote the tendency of an object to remain in a state of rest until acted upon by an external force? A: Inertia. Slide 10:\nQ: The discovery of which law provoked the surprised cry 'Eureka!'? A: Archimedes Principle. Slide 11:\nQ: Which electronic device magnifies the strength of a signal? A: Amplifier. Slide 12:\nQ :What is an unchanging position in which forces cancel each other out? A: Equilibrium. Slide 13:\nQ: What was the name of the unit of heat now replaced by the joule? A: Calorie.","PHYSICS FOLIO |authorSTREAM\n\nSlide 14:\nQ: What is described as an ionized gas with approximately equal numbers of positive and negative charges? A: Plasma. ENTRY NO. 4: EUREKA EXPERIENCE:\nENTRY NO. 4: EUREKA EXPERIENCE\nMy Eureka Experience..:\nMy Eureka Experience.. I have learned a lot of things in my fourth year life now. One of those lessons I’ve learned was the accuracy of measurement. Once we where able to measure using the Vernier caliper. First it was so hard because I’m not familiar with it but Aldrin teach me and now I know how to read its measurement. Eureka! Eureka! ENTRY NO. 5: MEDIA HYPE:\nENTRY NO. 5: MEDIA HYPE\nMedia Hype:\nMedia Hype The advertisement of the shampoos and conditioners are one of the best example of media hype. The commercial says that you will have a smoother and healthier hair just like when you go to the parlor. These models and endorsers have some hair treatment before the shoot and some are made by the camera tricks for the commercial so that it will look more beautiful and real. Slide 21:\nCommercials told us that their products can make our clothes whiter from having dirt after we washed them.","PHYSICS FOLIO |authorSTREAM\n\nThey illustrate their product and another product and compared it from one another. The t-shirt that been soaked in their product was much whiter than the other but it looks like it’s a new one and not the original one. Old Quill to Ordinary pen and now. Pen with USB.. At the early age they used the old quill just like Jose Rizal and now there's a lot of hi-tech pens. Pens with camera, with USB or sometimes made from gold.:\nOld Quill to Ordinary pen and now. Pen with USB.. At the early age they used the old quill just like Jose Rizal and now there's a lot of hi-tech pens. Pens with camera, with USB or sometimes made from gold. Slide 24:\nEven Electric Fan evolved. First we have a fan made from abaca then someone invented the electric fan for convenience and then because of technology, air conditioners are now existing. Slide 25:"],"string":"[\n \"PHYSICS FOLIO |authorSTREAM\\n\\nPHYSICS FOLIO |authorSTREAM\\nPHYSICS FOLIO\\n Does not support media & animations\\n Automatically changes to Flash or non-Flash embed\\n The presentation is successfully added In Your Favorites . Views:\\n This Presentation is Public Favorites: \\n0\\nENTRY NO. 1: Physics A Natural Philosophy:\\nENTRY NO. 1: Physics A Natural Philosophy ENTRY NO. 1: Physics A Natural Philosophy\\nPhysics A Natural Philosophy:\\nPhysics A Natural Philosophy Physics as natural philosophy. Physics is present in our environment at all times. The gravitational theory is the perfect explanation for this natural philosophy. Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. In everyday life, gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped. ENTRY NO.2 PHYSICS REALLY WORKS:\\nENTRY NO.2 PHYSICS REALLY WORKS\\nPhysics Really Works:\\nPhysics Really Works Physics really works. A branch of physics, which is electromagnetism, can be seen in modern inventions. Electromagnetism is the force that causes the interaction between electrically charged particles; the areas in which this happens are called electromagnetic fields. This is the set-up in a MICROPHONE.\",\n \"PHYSICS FOLIO |authorSTREAM\\n\\nsound waves enter the microphone, which cause the microphone to vibrate back and forth. This subsequently causes the wire loops to oscillate, and the magnetic field through the plane of the loops subsequently changes, inducing a current in the wires. In this way sound or wave energy is converted into electrical energy. ENTRY NO. 3: TESTING TIME :\\nENTRY NO. 3: TESTING TIME\\nPHYSICS TRIVIAS::\\nPHYSICS TRIVIAS: Q: What did scientists build in a squash court under a football stadium at the University of Chicago in 1942? A: A nuclear reactor. Slide 8:\\nQ: Which Swedish scientist had a temperature scale named after him? A: Anders Celsius. Slide 9:\\nQ :What is the term used to denote the tendency of an object to remain in a state of rest until acted upon by an external force? A: Inertia. Slide 10:\\nQ: The discovery of which law provoked the surprised cry 'Eureka!'? A: Archimedes Principle. Slide 11:\\nQ: Which electronic device magnifies the strength of a signal? A: Amplifier. Slide 12:\\nQ :What is an unchanging position in which forces cancel each other out? A: Equilibrium. Slide 13:\\nQ: What was the name of the unit of heat now replaced by the joule? A: Calorie.\",\n \"PHYSICS FOLIO |authorSTREAM\\n\\nSlide 14:\\nQ: What is described as an ionized gas with approximately equal numbers of positive and negative charges? A: Plasma. ENTRY NO. 4: EUREKA EXPERIENCE:\\nENTRY NO. 4: EUREKA EXPERIENCE\\nMy Eureka Experience..:\\nMy Eureka Experience.. I have learned a lot of things in my fourth year life now. One of those lessons I’ve learned was the accuracy of measurement. Once we where able to measure using the Vernier caliper. First it was so hard because I’m not familiar with it but Aldrin teach me and now I know how to read its measurement. Eureka! Eureka! ENTRY NO. 5: MEDIA HYPE:\\nENTRY NO. 5: MEDIA HYPE\\nMedia Hype:\\nMedia Hype The advertisement of the shampoos and conditioners are one of the best example of media hype. The commercial says that you will have a smoother and healthier hair just like when you go to the parlor. These models and endorsers have some hair treatment before the shoot and some are made by the camera tricks for the commercial so that it will look more beautiful and real. Slide 21:\\nCommercials told us that their products can make our clothes whiter from having dirt after we washed them.\",\n \"PHYSICS FOLIO |authorSTREAM\\n\\nThey illustrate their product and another product and compared it from one another. The t-shirt that been soaked in their product was much whiter than the other but it looks like it’s a new one and not the original one. Old Quill to Ordinary pen and now. Pen with USB.. At the early age they used the old quill just like Jose Rizal and now there's a lot of hi-tech pens. Pens with camera, with USB or sometimes made from gold.:\\nOld Quill to Ordinary pen and now. Pen with USB.. At the early age they used the old quill just like Jose Rizal and now there's a lot of hi-tech pens. Pens with camera, with USB or sometimes made from gold. Slide 24:\\nEven Electric Fan evolved. First we have a fan made from abaca then someone invented the electric fan for convenience and then because of technology, air conditioners are now existing. Slide 25:\"\n]","isConversational":false}}},{"rowIdx":1792,"cells":{"id":{"kind":"string","value":"tc_2768"},"question":{"kind":"string","value":"What is the study and use of frequencies above 20 khz?"},"answer":{"kind":"string","value":"Ultrasonic's"},"answer_aliases":{"kind":"list like","value":["from sound to image","ultrasonics","ultrasonic wave","ultrasound","ultra sound","ultrasonic s","biomedical ultrasonic","ultrasounds","industrial ultrasonography","ultrsound","ultrasound ct"],"string":"[\n \"from sound to image\",\n \"ultrasonics\",\n \"ultrasonic wave\",\n \"ultrasound\",\n \"ultra sound\",\n \"ultrasonic s\",\n \"biomedical ultrasonic\",\n \"ultrasounds\",\n \"industrial ultrasonography\",\n \"ultrsound\",\n \"ultrasound ct\"\n]","isConversational":false},"documents":{"kind":"list like","value":["Hertz\n\nThe hertz (symbol Hz) is the unit of frequency in the International System of Units (SI) and is defined as one cycle per second. It is named for Heinrich Rudolf Hertz, the first person to provide conclusive proof of the existence of electromagnetic waves.","Hertz\n\nSome of the unit's most common uses are in the description of sine waves and musical tones, particularly those used in radio- and audio-related applications. It is also used to describe the speeds at which computers and other electronics are driven.","Hertz\n\nDefinition","Hertz\n\nThe hertz is equivalent to cycles per second, i.e., \"1/second\" or \\text{s}^{-1}. The International Committee for Weights and Measures defined the second as \"the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom\" and then adds the obvious conclusion: \"It follows that the hyperfine splitting in the ground state of the caesium 133 atom is exactly 9 192 631 770 hertz, ν(hfs Cs) = 9 192 631 770 Hz.\"","Hertz\n\nIn English, \"hertz\" is also used as the plural form. As an SI unit, Hz can be prefixed; commonly used multiples are kHz (kilohertz, 103 Hz), MHz (megahertz, 106 Hz), GHz (gigahertz, 109 Hz) and THz (terahertz, 1012 Hz). One hertz simply means \"one cycle per second\" (typically that which is being counted is a complete cycle); 100 Hz means \"one hundred cycles per second\", and so on. The unit may be applied to any periodic event—for example, a clock might be said to tick at 1 Hz, or a human heart might be said to beat at 1.2 Hz. The rate of aperiodic or stochastic events occur is expressed in reciprocal second or inverse second (1/s or s−1) in general or, the specific case of radioactive decay, becquerels. Whereas 1 Hz is 1 cycle per second, 1 Bq is 1 aperiodic radionuclide event per second.","Hertz\n\nEven though angular velocity, angular frequency and the unit hertz all have the dimension 1/s, angular velocity and angular frequency are not expressed in hertz, but rather in an appropriate angular unit such as radians per second. Thus a disc rotating at 60 revolutions per minute (rpm) is said to be rotating at either 2 rad/s or 1 Hz, where the former measures the angular velocity and the latter reflects the number of complete revolutions per second. The conversion between a frequency f measured in hertz and an angular velocity ω measured in radians per second is","Hertz\n\n\\omega 2\\pi f \\, and f \n \\frac{\\omega}{2\\pi} \\,\n.","Hertz\n\nHistory","Hertz\n\nThe hertz is named after the German physicist Heinrich Hertz (1857–1894), who made important scientific contributions to the study of electromagnetism. The name was established by the International Electrotechnical Commission (IEC) in 1930. It was adopted by the General Conference on Weights and Measures (CGPM) (Conférence générale des poids et mesures) in 1960, replacing the previous name for the unit, cycles per second (cps), along with its related multiples, primarily kilocycles per second (kc/s) and megacycles per second (Mc/s), and occasionally kilomegacycles per second (kMc/s). The term cycles per second was largely replaced by hertz by the 1970s. One hobby magazine, Electronics Illustrated, declared their intention to stick with the traditional kc., Mc., etc. units.","Hertz\n\nApplications","Hertz\n\nVibration","Hertz\n\nSound is a traveling longitudinal wave which is an oscillation of pressure. Humans perceive frequency of sound waves as pitch. Each musical note corresponds to a particular frequency which can be measured in hertz. An infant's ear is able to perceive frequencies ranging from 20 Hz to 20,000 Hz; the average adult human can hear sounds between 20 Hz and 16,000 Hz. The range of ultrasound, infrasound and other physical vibrations such as molecular and atomic vibrations extends from a few femtoHz into the terahertz range and beyond.","Hertz\n\nElectromagnetic radiation","Hertz\n\nElectromagnetic radiation is often described by its frequency—the number of oscillations of the perpendicular electric and magnetic fields per second—expressed in hertz.","Hertz\n\nRadio frequency radiation is usually measured in kilohertz (kHz), megahertz (MHz), or gigahertz (GHz). Light is electromagnetic radiation that is even higher in frequency, and has frequencies in the range of tens (infrared) to thousands (ultraviolet) of terahertz. Electromagnetic radiation with frequencies in the low terahertz range, (intermediate between those of the highest normally usable radio frequencies and long-wave infrared light), is often called terahertz radiation. Even higher frequencies exist, such as that of gamma rays, which can be measured in exahertz. (For historical reasons, the frequencies of light and higher frequency electromagnetic radiation are more commonly specified in terms of their wavelengths or photon energies: for a more detailed treatment of this and the above frequency ranges, see electromagnetic spectrum.)","Hertz\n\nComputers","Hertz\n\nIn computers, most central processing units (CPU) are labeled in terms of their clock rate expressed in megahertz or gigahertz (106 or 109 hertz, respectively). This number refers to the frequency of the CPU's master clock signal (\"clock rate\"). This signal is a square wave, which is an electrical voltage that switches between low and high values at regular intervals. Hertz has become the primary unit of measurement accepted by the general populace to determine the performance of a CPU, but many experts have criticized this approach, which they claim is an easily manipulable benchmark as some processors use multiple clock periods to perform a single operation, while others can perform multiple operations in a single cycle. For home-based personal computers, CPU clock speeds have ranged from approximately 1 MHz in the late 1970s (Atari, Commodore, Apple computers) to up to 6 GHz in IBM POWER processors.","Hertz\n\nVarious computer buses, such as the front-side bus connecting the CPU and northbridge, also operate at various frequencies in the megahertz range.","Hertz\n\nThe \"speed\" or the more correct term bandwidth of networks, including wireless, such as Wi-Fi, 3G, 4G, LTE, etc. is not affected by the myth described above. In general, higher frequency means higher bandwidth or bit rates, that lower the times to download big files. In general, however, higher frequencies do not pass through walls, making lower frequencies an advantage e.g. indoors (most common equipment reports the highest frequency used, but usually also work at lower, making this often not a problem). Bandwidth is often equated with \"speed\", while latency (\"lag\"), is the perceived problem, that is a distinct measure from bandwidth, while higher bandwidth has an influence on latency.","Hertz\n\nSI multiples","Hertz\n\nHigher frequencies than the International System of Units provides prefixes for, are believed to occur naturally in the frequencies of the quantum-mechanical vibrations of high-energy, or, equivalently, massive particles, although these are not directly observable and must be inferred from their interactions with other phenomena. For practical reasons, these are typically not expressed in hertz, but in terms of the equivalent quantum energy, which is proportional to the frequency by the factor of Planck's constant."],"string":"[\n \"Hertz\\n\\nThe hertz (symbol Hz) is the unit of frequency in the International System of Units (SI) and is defined as one cycle per second. It is named for Heinrich Rudolf Hertz, the first person to provide conclusive proof of the existence of electromagnetic waves.\",\n \"Hertz\\n\\nSome of the unit's most common uses are in the description of sine waves and musical tones, particularly those used in radio- and audio-related applications. It is also used to describe the speeds at which computers and other electronics are driven.\",\n \"Hertz\\n\\nDefinition\",\n \"Hertz\\n\\nThe hertz is equivalent to cycles per second, i.e., \\\"1/second\\\" or \\\\text{s}^{-1}. The International Committee for Weights and Measures defined the second as \\\"the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom\\\" and then adds the obvious conclusion: \\\"It follows that the hyperfine splitting in the ground state of the caesium 133 atom is exactly 9 192 631 770 hertz, ν(hfs Cs) = 9 192 631 770 Hz.\\\"\",\n \"Hertz\\n\\nIn English, \\\"hertz\\\" is also used as the plural form. As an SI unit, Hz can be prefixed; commonly used multiples are kHz (kilohertz, 103 Hz), MHz (megahertz, 106 Hz), GHz (gigahertz, 109 Hz) and THz (terahertz, 1012 Hz). One hertz simply means \\\"one cycle per second\\\" (typically that which is being counted is a complete cycle); 100 Hz means \\\"one hundred cycles per second\\\", and so on. The unit may be applied to any periodic event—for example, a clock might be said to tick at 1 Hz, or a human heart might be said to beat at 1.2 Hz. The rate of aperiodic or stochastic events occur is expressed in reciprocal second or inverse second (1/s or s−1) in general or, the specific case of radioactive decay, becquerels. Whereas 1 Hz is 1 cycle per second, 1 Bq is 1 aperiodic radionuclide event per second.\",\n \"Hertz\\n\\nEven though angular velocity, angular frequency and the unit hertz all have the dimension 1/s, angular velocity and angular frequency are not expressed in hertz, but rather in an appropriate angular unit such as radians per second. Thus a disc rotating at 60 revolutions per minute (rpm) is said to be rotating at either 2 rad/s or 1 Hz, where the former measures the angular velocity and the latter reflects the number of complete revolutions per second. The conversion between a frequency f measured in hertz and an angular velocity ω measured in radians per second is\",\n \"Hertz\\n\\n\\\\omega 2\\\\pi f \\\\, and f \\n \\\\frac{\\\\omega}{2\\\\pi} \\\\,\\n.\",\n \"Hertz\\n\\nHistory\",\n \"Hertz\\n\\nThe hertz is named after the German physicist Heinrich Hertz (1857–1894), who made important scientific contributions to the study of electromagnetism. The name was established by the International Electrotechnical Commission (IEC) in 1930. It was adopted by the General Conference on Weights and Measures (CGPM) (Conférence générale des poids et mesures) in 1960, replacing the previous name for the unit, cycles per second (cps), along with its related multiples, primarily kilocycles per second (kc/s) and megacycles per second (Mc/s), and occasionally kilomegacycles per second (kMc/s). The term cycles per second was largely replaced by hertz by the 1970s. One hobby magazine, Electronics Illustrated, declared their intention to stick with the traditional kc., Mc., etc. units.\",\n \"Hertz\\n\\nApplications\",\n \"Hertz\\n\\nVibration\",\n \"Hertz\\n\\nSound is a traveling longitudinal wave which is an oscillation of pressure. Humans perceive frequency of sound waves as pitch. Each musical note corresponds to a particular frequency which can be measured in hertz. An infant's ear is able to perceive frequencies ranging from 20 Hz to 20,000 Hz; the average adult human can hear sounds between 20 Hz and 16,000 Hz. The range of ultrasound, infrasound and other physical vibrations such as molecular and atomic vibrations extends from a few femtoHz into the terahertz range and beyond.\",\n \"Hertz\\n\\nElectromagnetic radiation\",\n \"Hertz\\n\\nElectromagnetic radiation is often described by its frequency—the number of oscillations of the perpendicular electric and magnetic fields per second—expressed in hertz.\",\n \"Hertz\\n\\nRadio frequency radiation is usually measured in kilohertz (kHz), megahertz (MHz), or gigahertz (GHz). Light is electromagnetic radiation that is even higher in frequency, and has frequencies in the range of tens (infrared) to thousands (ultraviolet) of terahertz. Electromagnetic radiation with frequencies in the low terahertz range, (intermediate between those of the highest normally usable radio frequencies and long-wave infrared light), is often called terahertz radiation. Even higher frequencies exist, such as that of gamma rays, which can be measured in exahertz. (For historical reasons, the frequencies of light and higher frequency electromagnetic radiation are more commonly specified in terms of their wavelengths or photon energies: for a more detailed treatment of this and the above frequency ranges, see electromagnetic spectrum.)\",\n \"Hertz\\n\\nComputers\",\n \"Hertz\\n\\nIn computers, most central processing units (CPU) are labeled in terms of their clock rate expressed in megahertz or gigahertz (106 or 109 hertz, respectively). This number refers to the frequency of the CPU's master clock signal (\\\"clock rate\\\"). This signal is a square wave, which is an electrical voltage that switches between low and high values at regular intervals. Hertz has become the primary unit of measurement accepted by the general populace to determine the performance of a CPU, but many experts have criticized this approach, which they claim is an easily manipulable benchmark as some processors use multiple clock periods to perform a single operation, while others can perform multiple operations in a single cycle. For home-based personal computers, CPU clock speeds have ranged from approximately 1 MHz in the late 1970s (Atari, Commodore, Apple computers) to up to 6 GHz in IBM POWER processors.\",\n \"Hertz\\n\\nVarious computer buses, such as the front-side bus connecting the CPU and northbridge, also operate at various frequencies in the megahertz range.\",\n \"Hertz\\n\\nThe \\\"speed\\\" or the more correct term bandwidth of networks, including wireless, such as Wi-Fi, 3G, 4G, LTE, etc. is not affected by the myth described above. In general, higher frequency means higher bandwidth or bit rates, that lower the times to download big files. In general, however, higher frequencies do not pass through walls, making lower frequencies an advantage e.g. indoors (most common equipment reports the highest frequency used, but usually also work at lower, making this often not a problem). Bandwidth is often equated with \\\"speed\\\", while latency (\\\"lag\\\"), is the perceived problem, that is a distinct measure from bandwidth, while higher bandwidth has an influence on latency.\",\n \"Hertz\\n\\nSI multiples\",\n \"Hertz\\n\\nHigher frequencies than the International System of Units provides prefixes for, are believed to occur naturally in the frequencies of the quantum-mechanical vibrations of high-energy, or, equivalently, massive particles, although these are not directly observable and must be inferred from their interactions with other phenomena. For practical reasons, these are typically not expressed in hertz, but in terms of the equivalent quantum energy, which is proportional to the frequency by the factor of Planck's constant.\"\n]","isConversational":false}}},{"rowIdx":1793,"cells":{"id":{"kind":"string","value":"tc_2769"},"question":{"kind":"string","value":"What is an unchanging position in which forces cancel each other out?"},"answer":{"kind":"string","value":"Equilibrium"},"answer_aliases":{"kind":"list like","value":["equilibration","equilibrium disambiguation","equilibrium album","equilibrium","equilibria","position of equilibrium","equillibrium"],"string":"[\n \"equilibration\",\n \"equilibrium disambiguation\",\n \"equilibrium album\",\n \"equilibrium\",\n \"equilibria\",\n \"position of equilibrium\",\n \"equillibrium\"\n]","isConversational":false},"documents":{"kind":"list like","value":["Equilibria - definition of equilibria by The Free Dictionary\n\nEquilibria - definition of equilibria by The Free Dictionary\nEquilibria - definition of equilibria by The Free Dictionary\nhttp://www.thefreedictionary.com/equilibria\nRelated to equilibria: Punctuated equilibria\ne·qui·lib·ri·um\n (ē′kwə-lĭb′rē-əm, ĕk′wə-)\nn. pl. e·qui·lib·ri·ums or e·qui·lib·ri·a (-rē-ə)\n1. A condition in which all acting influences are canceled by others, resulting in a stable, balanced, or unchanging system. 2. Mental or emotional balance. 3. Physics The state of a body or physical system at rest or in unaccelerated motion in which the resultant of all forces acting on it is zero and the sum of all torques about any axis is zero. 4. Chemistry\na. The state of a chemical reaction in which its forward and reverse reactions occur at equal rates so that the concentration of the reactants and products does not change with time. b. The state of a system in which more than one phase exists and exchange between phases occurs at equal rates so that there is no net change in the composition of the system. [Latin aequilībrium : aequi-, equi- + lībra, balance.]\nequilibrium\nn, pl -riums or -ria (-rɪə)\n1. a stable condition in which forces cancel one another\n2. a state or feeling of mental balance; composure\n3.","Equilibria - definition of equilibria by The Free Dictionary\n\n(General Physics) any unchanging condition or state of a body, system, etc, resulting from the balance or cancelling out of the influences or processes to which it is subjected. See thermodynamic equilibrium\n4. (General Physics) physics a state of rest or uniform motion in which there is no resultant force on a body\n5. (Chemistry) chem the condition existing when a chemical reaction and its reverse reaction take place at equal rates\n6. (General Physics) physics the condition of a system that has its total energy distributed among its component parts in the statistically most probable manner\n7. (Physiology) physiol a state of bodily balance, maintained primarily by special receptors in the inner ear\n8. (Economics) the economic condition in which there is neither excess demand nor excess supply in a market\n[C17: from Latin aequilībrium, from aequi- equi- + lībra pound, balance]\ne•qui•lib•ri•um\n(ˌi kwəˈlɪb ri əm, ˌɛk wə-)\nn., pl. -ri•ums, -ri•a (-ri ə)\n1. a state of rest or balance due to the equal action of opposing forces. 2. equal balance between any powers, influences, etc.; equality of effect. 3. mental or emotional balance; equanimity. 4. a state or sense of steadiness and proper orientation of the body.","Equilibria - definition of equilibria by The Free Dictionary\n\n5. the condition existing when a chemical reaction and its reverse reaction proceed at equal rates. [1600–10; < Latin aequilībrium=aequi- equi - + lībr(a) balance]\ne•quil′i•bra•to`ry (ɪˈkwɪl ə brəˌtɔr i, -ˌtoʊr i) adj. e·qui·lib·ri·um\n(ē′kwə-lĭb′rē-əm)\n1. Physics The state of a body or physical system that is at rest or in constant and unchanging motion. The sum of all forces acting on a body that is in equilibrium is zero (because opposing forces balance each other). A system that is in equilibrium shows no tendency to alter over time. 2. Chemistry The state of a reversible chemical reaction in which its forward and reverse reactions occur at equal rates so that the concentration of the reactants and products remains the same. equilibrium\nThe state of a reversible chemical reaction at which the forward and backward reactions take place at the same rate\nThesaurusAntonymsRelated WordsSynonymsLegend:","Equilibrium dictionary definition | equilibrium defined\n\nEquilibrium dictionary definition | equilibrium defined\n» more...\nShe squinted through her fingers and braced herself against one wall to counter the effects the drugs had on her equilibrium as she moved down the long hallway.\nIn 1879 C. Nageli formulated his well-known molecularphysical theory, which supported Liebig's chemical theory on the one hand and Pasteur's physiological hypothesis on the other: \"Fermentation is the transference of the condition of motion of the molecules, atomic groups and atoms of the various compounds constituting the living plasma, to the fermenting material, in consequence of which equilibrium in the molecules of the latter is destroyed, the result being their disintegration.\"\n(5) On the Equilibrium of Planes or Centres of Gravity of Planes (Peri epipedon isorropeon e kentra baron epipedon).\nThe earth, or other planet, does not actually move round the sun; yet it is carried round the sun in the subtle matter of the great vortex, where it lies in equilibrium, - carried like the passenger in a boat, who may cross the sea and yet not rise from his berth.\nHis marvellous physical and moral equilibrium gave him an evenness of temper which always renaered his society charming.\nRelated","Equilibrium | Define Equilibrium at Dictionary.com\n\nEquilibrium | Define Equilibrium at Dictionary.com\nequilibrium\n[ee-kwuh-lib-ree-uh m, ek-wuh-] /ˌi kwəˈlɪb ri əm, ˌɛk wə-/\nSpell\n[ee-kwuh-lib-ree-uh, ek-wuh-] /ˌi kwəˈlɪb ri ə, ˌɛk wə-/ (Show IPA)\n1. a state of rest or balance due to the equal action of opposing forces. 2. equal balance between any powers, influences, etc.; equality of effect. 3. mental or emotional balance; equanimity:\nThe pressures of the situation caused her to lose her equilibrium. 4. Chemistry. the condition existing when a chemical reaction and its reverse reaction proceed at equal rates. Origin of equilibrium\n1600-10; < Latin aequilībrium, equivalent to aequi- equi- + lībr(a) balance + -ium -ium\nRelated forms\nExpand\nequilibratory\n[ih-kwil-uh-bruh-tawr-ee, -tohr-ee, ee-kwuh-lib-ruh-, ek-wuh-] /ɪˈkwɪl ə brəˌtɔr i, -ˌtoʊr i, ˌi kwəˈlɪb rə-, ˌɛk wə-/ (Show IPA), adjective\nnonequilibrium, noun\nExamples from the Web for equilibrium\nExpand\nContemporary Examples\nBut how many of us, thus sunk in despair, have not been vaulted back to equilibrium by another look at Groundhog Day? Is Syria Being 'Lebanized' or is Lebanon Being 'Syrianized'? Hussein Ibish August 28, 2013\nHistorical Examples\nMrs. Gray turned with a degree of eagerness that threatened to destroy the equilibrium of her stately person. Fashion and Famine Ann S.","Equilibrium | Define Equilibrium at Dictionary.com\n\nStephens\n\"equilibrium is an equality between two forces,\" replied Forester. Forests of Maine Jacob S. Abbott\nCharles had disturbed the equilibrium of her heart by his warmth, and had not restored it again by a word of recompense. The Longest Journey E. M. Forster\nThe equilibrium of the figures composing the group is the same as that of the \"Saint John the Baptist.\"\nBritish Dictionary definitions for equilibrium\nExpand\nnoun (pl) -riums, -ria (-rɪə)\n1. a stable condition in which forces cancel one another\n2. a state or feeling of mental balance; composure\n3. any unchanging condition or state of a body, system, etc, resulting from the balance or cancelling out of the influences or processes to which it is subjected See thermodynamic equilibrium\n4. (physics) a state of rest or uniform motion in which there is no resultant force on a body\n5. (chem) the condition existing when a chemical reaction and its reverse reaction take place at equal rates\n6. (physics) the condition of a system that has its total energy distributed among its component parts in the statistically most probable manner\n7. (physiol) a state of bodily balance, maintained primarily by special receptors in the inner ear\n8.","Equilibrium | Define Equilibrium at Dictionary.com\n\nthe economic condition in which there is neither excess demand nor excess supply in a market\nWord Origin\nC17: from Latin aequilībrium, from aequi-equi- + lībra pound, balance\nCollins English Dictionary - Complete & Unabridged 2012 Digital Edition\n© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins\nPublishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012\nWord Origin and History for equilibrium\nExpand\nn. c.1600, from Latin aequilibrium, from aequus \"equal\" (see equal ) + libra \"a balance, scale, plummet\" (see Libra ). Online Etymology Dictionary, © 2010 Douglas Harper\nequilibrium e·qui·lib·ri·um (ē'kwə-lĭb'rē-əm, ěk'wə-)\nn. A condition in which all influences acting upon it are canceled by others, resulting in a stable, balanced, or unchanging system. The state of a chemical reaction in which its forward and reverse reactions occur at equal rates so that the concentration of the reactants and products does not change with time. Also called dynamic equilibrium. Mental or emotional balance. The American Heritage® Stedman's Medical Dictionary\nCopyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company.","Equilibrium | Define Equilibrium at Dictionary.com\n\n(ē'kwə-lĭb'rē-əm) \nPlural equilibriums or equilibria\nPhysics The state of a body or physical system that is at rest or in constant and unchanging motion. A system that is in equilibrium shows no tendency to alter over time. ◇ If a system is in static equilibrium, there are no net forces and no net torque in the system. ◇ If a system is in stable equilibrium, small disturbances to the system cause only a temporary change before it returns to its original state. Chemistry The state of a reversible chemical reaction in which its forward and reverse reactions occur at equal rates so that the concentration of the reactants and products remains the same. The American Heritage® Science Dictionary\nCopyright © 2002. Published by Houghton Mifflin. All rights reserved. Expand\nequilibrium definition\nIn economics , a state of the economy in which for every commodity or service (including labor), total supply and demand are exactly equal. Equilibrium is never actually attained; it is approximated by movements of the market. Note: Keynesian economics departed from conventional economic theory in demonstrating that economic equilibrium and full employment need not occur together. Therefore, as a system tends toward equilibrium, it might not eliminate unemployment.","Equilibrium | Define Equilibrium at Dictionary.com\n\nequilibrium definition\nA condition in which all influences acting cancel each other, so that a static or balanced situation results. In physics , equilibrium results from the cancellation of forces acting on an object. In chemistry , it occurs when chemical reactions are proceeding in such a way that the amount of each substance in a system remains the same. (See chemical equilibrium .)\nThe American Heritage® New Dictionary of Cultural Literacy, Third Edition\nCopyright © 2005 by Houghton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved."],"string":"[\n \"Equilibria - definition of equilibria by The Free Dictionary\\n\\nEquilibria - definition of equilibria by The Free Dictionary\\nEquilibria - definition of equilibria by The Free Dictionary\\nhttp://www.thefreedictionary.com/equilibria\\nRelated to equilibria: Punctuated equilibria\\ne·qui·lib·ri·um\\n (ē′kwə-lĭb′rē-əm, ĕk′wə-)\\nn. pl. e·qui·lib·ri·ums or e·qui·lib·ri·a (-rē-ə)\\n1. A condition in which all acting influences are canceled by others, resulting in a stable, balanced, or unchanging system. 2. Mental or emotional balance. 3. Physics The state of a body or physical system at rest or in unaccelerated motion in which the resultant of all forces acting on it is zero and the sum of all torques about any axis is zero. 4. Chemistry\\na. The state of a chemical reaction in which its forward and reverse reactions occur at equal rates so that the concentration of the reactants and products does not change with time. b. The state of a system in which more than one phase exists and exchange between phases occurs at equal rates so that there is no net change in the composition of the system. [Latin aequilībrium : aequi-, equi- + lībra, balance.]\\nequilibrium\\nn, pl -riums or -ria (-rɪə)\\n1. a stable condition in which forces cancel one another\\n2. a state or feeling of mental balance; composure\\n3.\",\n \"Equilibria - definition of equilibria by The Free Dictionary\\n\\n(General Physics) any unchanging condition or state of a body, system, etc, resulting from the balance or cancelling out of the influences or processes to which it is subjected. See thermodynamic equilibrium\\n4. (General Physics) physics a state of rest or uniform motion in which there is no resultant force on a body\\n5. (Chemistry) chem the condition existing when a chemical reaction and its reverse reaction take place at equal rates\\n6. (General Physics) physics the condition of a system that has its total energy distributed among its component parts in the statistically most probable manner\\n7. (Physiology) physiol a state of bodily balance, maintained primarily by special receptors in the inner ear\\n8. (Economics) the economic condition in which there is neither excess demand nor excess supply in a market\\n[C17: from Latin aequilībrium, from aequi- equi- + lībra pound, balance]\\ne•qui•lib•ri•um\\n(ˌi kwəˈlɪb ri əm, ˌɛk wə-)\\nn., pl. -ri•ums, -ri•a (-ri ə)\\n1. a state of rest or balance due to the equal action of opposing forces. 2. equal balance between any powers, influences, etc.; equality of effect. 3. mental or emotional balance; equanimity. 4. a state or sense of steadiness and proper orientation of the body.\",\n \"Equilibria - definition of equilibria by The Free Dictionary\\n\\n5. the condition existing when a chemical reaction and its reverse reaction proceed at equal rates. [1600–10; < Latin aequilībrium=aequi- equi - + lībr(a) balance]\\ne•quil′i•bra•to`ry (ɪˈkwɪl ə brəˌtɔr i, -ˌtoʊr i) adj. e·qui·lib·ri·um\\n(ē′kwə-lĭb′rē-əm)\\n1. Physics The state of a body or physical system that is at rest or in constant and unchanging motion. The sum of all forces acting on a body that is in equilibrium is zero (because opposing forces balance each other). A system that is in equilibrium shows no tendency to alter over time. 2. Chemistry The state of a reversible chemical reaction in which its forward and reverse reactions occur at equal rates so that the concentration of the reactants and products remains the same. equilibrium\\nThe state of a reversible chemical reaction at which the forward and backward reactions take place at the same rate\\nThesaurusAntonymsRelated WordsSynonymsLegend:\",\n \"Equilibrium dictionary definition | equilibrium defined\\n\\nEquilibrium dictionary definition | equilibrium defined\\n» more...\\nShe squinted through her fingers and braced herself against one wall to counter the effects the drugs had on her equilibrium as she moved down the long hallway.\\nIn 1879 C. Nageli formulated his well-known molecularphysical theory, which supported Liebig's chemical theory on the one hand and Pasteur's physiological hypothesis on the other: \\\"Fermentation is the transference of the condition of motion of the molecules, atomic groups and atoms of the various compounds constituting the living plasma, to the fermenting material, in consequence of which equilibrium in the molecules of the latter is destroyed, the result being their disintegration.\\\"\\n(5) On the Equilibrium of Planes or Centres of Gravity of Planes (Peri epipedon isorropeon e kentra baron epipedon).\\nThe earth, or other planet, does not actually move round the sun; yet it is carried round the sun in the subtle matter of the great vortex, where it lies in equilibrium, - carried like the passenger in a boat, who may cross the sea and yet not rise from his berth.\\nHis marvellous physical and moral equilibrium gave him an evenness of temper which always renaered his society charming.\\nRelated\",\n \"Equilibrium | Define Equilibrium at Dictionary.com\\n\\nEquilibrium | Define Equilibrium at Dictionary.com\\nequilibrium\\n[ee-kwuh-lib-ree-uh m, ek-wuh-] /ˌi kwəˈlɪb ri əm, ˌɛk wə-/\\nSpell\\n[ee-kwuh-lib-ree-uh, ek-wuh-] /ˌi kwəˈlɪb ri ə, ˌɛk wə-/ (Show IPA)\\n1. a state of rest or balance due to the equal action of opposing forces. 2. equal balance between any powers, influences, etc.; equality of effect. 3. mental or emotional balance; equanimity:\\nThe pressures of the situation caused her to lose her equilibrium. 4. Chemistry. the condition existing when a chemical reaction and its reverse reaction proceed at equal rates. Origin of equilibrium\\n1600-10; < Latin aequilībrium, equivalent to aequi- equi- + lībr(a) balance + -ium -ium\\nRelated forms\\nExpand\\nequilibratory\\n[ih-kwil-uh-bruh-tawr-ee, -tohr-ee, ee-kwuh-lib-ruh-, ek-wuh-] /ɪˈkwɪl ə brəˌtɔr i, -ˌtoʊr i, ˌi kwəˈlɪb rə-, ˌɛk wə-/ (Show IPA), adjective\\nnonequilibrium, noun\\nExamples from the Web for equilibrium\\nExpand\\nContemporary Examples\\nBut how many of us, thus sunk in despair, have not been vaulted back to equilibrium by another look at Groundhog Day? Is Syria Being 'Lebanized' or is Lebanon Being 'Syrianized'? Hussein Ibish August 28, 2013\\nHistorical Examples\\nMrs. Gray turned with a degree of eagerness that threatened to destroy the equilibrium of her stately person. Fashion and Famine Ann S.\",\n \"Equilibrium | Define Equilibrium at Dictionary.com\\n\\nStephens\\n\\\"equilibrium is an equality between two forces,\\\" replied Forester. Forests of Maine Jacob S. Abbott\\nCharles had disturbed the equilibrium of her heart by his warmth, and had not restored it again by a word of recompense. The Longest Journey E. M. Forster\\nThe equilibrium of the figures composing the group is the same as that of the \\\"Saint John the Baptist.\\\"\\nBritish Dictionary definitions for equilibrium\\nExpand\\nnoun (pl) -riums, -ria (-rɪə)\\n1. a stable condition in which forces cancel one another\\n2. a state or feeling of mental balance; composure\\n3. any unchanging condition or state of a body, system, etc, resulting from the balance or cancelling out of the influences or processes to which it is subjected See thermodynamic equilibrium\\n4. (physics) a state of rest or uniform motion in which there is no resultant force on a body\\n5. (chem) the condition existing when a chemical reaction and its reverse reaction take place at equal rates\\n6. (physics) the condition of a system that has its total energy distributed among its component parts in the statistically most probable manner\\n7. (physiol) a state of bodily balance, maintained primarily by special receptors in the inner ear\\n8.\",\n \"Equilibrium | Define Equilibrium at Dictionary.com\\n\\nthe economic condition in which there is neither excess demand nor excess supply in a market\\nWord Origin\\nC17: from Latin aequilībrium, from aequi-equi- + lībra pound, balance\\nCollins English Dictionary - Complete & Unabridged 2012 Digital Edition\\n© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins\\nPublishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012\\nWord Origin and History for equilibrium\\nExpand\\nn. c.1600, from Latin aequilibrium, from aequus \\\"equal\\\" (see equal ) + libra \\\"a balance, scale, plummet\\\" (see Libra ). Online Etymology Dictionary, © 2010 Douglas Harper\\nequilibrium e·qui·lib·ri·um (ē'kwə-lĭb'rē-əm, ěk'wə-)\\nn. A condition in which all influences acting upon it are canceled by others, resulting in a stable, balanced, or unchanging system. The state of a chemical reaction in which its forward and reverse reactions occur at equal rates so that the concentration of the reactants and products does not change with time. Also called dynamic equilibrium. Mental or emotional balance. The American Heritage® Stedman's Medical Dictionary\\nCopyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company.\",\n \"Equilibrium | Define Equilibrium at Dictionary.com\\n\\n(ē'kwə-lĭb'rē-əm) \\nPlural equilibriums or equilibria\\nPhysics The state of a body or physical system that is at rest or in constant and unchanging motion. A system that is in equilibrium shows no tendency to alter over time. ◇ If a system is in static equilibrium, there are no net forces and no net torque in the system. ◇ If a system is in stable equilibrium, small disturbances to the system cause only a temporary change before it returns to its original state. Chemistry The state of a reversible chemical reaction in which its forward and reverse reactions occur at equal rates so that the concentration of the reactants and products remains the same. The American Heritage® Science Dictionary\\nCopyright © 2002. Published by Houghton Mifflin. All rights reserved. Expand\\nequilibrium definition\\nIn economics , a state of the economy in which for every commodity or service (including labor), total supply and demand are exactly equal. Equilibrium is never actually attained; it is approximated by movements of the market. Note: Keynesian economics departed from conventional economic theory in demonstrating that economic equilibrium and full employment need not occur together. Therefore, as a system tends toward equilibrium, it might not eliminate unemployment.\",\n \"Equilibrium | Define Equilibrium at Dictionary.com\\n\\nequilibrium definition\\nA condition in which all influences acting cancel each other, so that a static or balanced situation results. In physics , equilibrium results from the cancellation of forces acting on an object. In chemistry , it occurs when chemical reactions are proceeding in such a way that the amount of each substance in a system remains the same. (See chemical equilibrium .)\\nThe American Heritage® New Dictionary of Cultural Literacy, Third Edition\\nCopyright © 2005 by Houghton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved.\"\n]","isConversational":false}}},{"rowIdx":1794,"cells":{"id":{"kind":"string","value":"tc_2770"},"question":{"kind":"string","value":"Which physicist's law states that equal volumes of all gases, measured at the same temperature and pressure, contain the same number of molecules?"},"answer":{"kind":"string","value":"Amadeo Avogadro"},"answer_aliases":{"kind":"list like","value":["avogadro amadeo","conte di quaregna e ceretto","amedeo avogadro","lorenzo romano amedeo carlo avogadro","count lorenzo romano amedeo carlo avogadro di quaregna e cerreto","amedeo avogadro conte de quaregna","lorenzo romano amedeo carlo avogadro di quaregna e cerreto","amadeo avogadro","avogadro amedeo conte di quaregna e ceretto","lorenzo romano amedeo carlo avogadro di quaregna e di cerreto","avogadro amedeo conte di quaregna","amedeo conte di quaregna e ceretto avogadro","lorenzo romano amedeo carlo demarkus avogadro di quaregna e di cerreto","amadeo avogradro","amedeo conte de quaregna avogadro","avagadro","conte di quaregna e ceretto avogadro amedeo"],"string":"[\n \"avogadro amadeo\",\n \"conte di quaregna e ceretto\",\n \"amedeo avogadro\",\n \"lorenzo romano amedeo carlo avogadro\",\n \"count lorenzo romano amedeo carlo avogadro di quaregna e cerreto\",\n \"amedeo avogadro conte de quaregna\",\n \"lorenzo romano amedeo carlo avogadro di quaregna e cerreto\",\n \"amadeo avogadro\",\n \"avogadro amedeo conte di quaregna e ceretto\",\n \"lorenzo romano amedeo carlo avogadro di quaregna e di cerreto\",\n \"avogadro amedeo conte di quaregna\",\n \"amedeo conte di quaregna e ceretto avogadro\",\n \"lorenzo romano amedeo carlo demarkus avogadro di quaregna e di cerreto\",\n \"amadeo avogradro\",\n \"amedeo conte de quaregna avogadro\",\n \"avagadro\",\n \"conte di quaregna e ceretto avogadro amedeo\"\n]","isConversational":false},"documents":{"kind":"list like","value":["Gas\n\nGas is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or compound molecules made from a variety of atoms (e.g. carbon dioxide). A gas mixture would contain a variety of pure gases much like the air. What distinguishes a gas from liquids and solids is the vast separation of the individual gas particles. This separation usually makes a colorless gas invisible to the human observer. The interaction of gas particles in the presence of electric and gravitational fields are considered negligible as indicated by the constant velocity vectors in the image. One type of commonly known gas is steam.","Gas\n\nThe gaseous state of matter is found between the liquid and plasma states, the latter of which provides the upper temperature boundary for gases. Bounding the lower end of the temperature scale lie degenerative quantum gases which are gaining increasing attention. High-density atomic gases super cooled to incredibly low temperatures are classified by their statistical behavior as either a Bose gas or a Fermi gas. For a comprehensive listing of these exotic states of matter see list of states of matter.","Gas\n\nElemental gases","Gas\n\nThe only chemical elements which are stable multi atom homonuclear molecules at standard temperature and pressure (STP), are hydrogen (H2), nitrogen (N2) and oxygen (O2); \nplus two halogens, fluorine (F2) and chlorine (Cl2). \nThese gases, when grouped together with the monatomic noble gases; which are helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe) and radon (Rn) ; are called \"elemental gases\". Alternatively they are sometimes known as \"molecular gases\" to distinguish them from molecules that are also chemical compounds.","Gas\n\nEtymology","Gas\n\nThe word gas is a neologism first used by the early 17th-century Flemish chemist J.B. van Helmont. Van Helmont's word appears to have been simply a phonetic transcription of the Greek word χάος Chaos – the g in Dutch being pronounced like ch in \"loch\" – in which case Van Helmont was simply following the established alchemical usage first attested in the works of Paracelsus. According to Paracelsus's terminology, chaos meant something like \"ultra-rarefied water\".","Gas\n\nAn alternative story is that Van Helmont's word is corrupted from gahst (or geist), signifying a ghost or spirit. This was because certain gases suggested a supernatural origin, such as from their ability to cause death, extinguish flames, and to occur in \"mines, bottom of wells, churchyards and other lonely places\".","Gas\n\nPhysical characteristics","Gas\n\nBecause most gases are difficult to observe directly, they are described through the use of four physical properties or macroscopic characteristics: pressure, volume, number of particles (chemists group them by moles) and temperature. These four characteristics were repeatedly observed by scientists such as Robert Boyle, Jacques Charles, John Dalton, Joseph Gay-Lussac and Amedeo Avogadro for a variety of gases in various settings. Their detailed studies ultimately led to a mathematical relationship among these properties expressed by the ideal gas law (see simplified models section below).","Gas\n\nGas particles are widely separated from one another, and consequently have weaker intermolecular bonds than liquids or solids. These intermolecular forces result from electrostatic interactions between gas particles. Like-charged areas of different gas particles repel, while oppositely charged regions of different gas particles attract one another; gases that contain permanently charged ions are known as plasmas. Gaseous compounds with polar covalent bonds contain permanent charge imbalances and so experience relatively strong intermolecular forces, although the molecule while the compound's net charge remains neutral. Transient, randomly induced charges exist across non-polar covalent bonds of molecules and electrostatic interactions caused by them are referred to as Van der Waals forces. The interaction of these intermolecular forces varies within a substance which determines many of the physical properties unique to each gas. A comparison of boiling points for compounds formed by ionic and covalent bonds leads us to this conclusion. The drifting smoke particles in the image provides some insight into low pressure gas behavior.","Gas\n\nCompared to the other states of matter, gases have low density and viscosity. Pressure and temperature influence the particles within a certain volume. This variation in particle separation and speed is referred to as compressibility. This particle separation and size influences optical properties of gases as can be found in the following list of refractive indices. Finally, gas particles spread apart or diffuse in order to homogeneously distribute themselves throughout any container.","Gas\n\nMacroscopic","Gas\n\nWhen observing a gas, it is typical to specify a frame of reference or length scale. A larger length scale corresponds to a macroscopic or global point of view of the gas. This region (referred to as a volume) must be sufficient in size to contain a large sampling of gas particles. The resulting statistical analysis of this sample size produces the \"average\" behavior (i.e. velocity, temperature or pressure) of all the gas particles within the region. In contrast, a smaller length scale corresponds to a microscopic or particle point of view.","Gas\n\nMacroscopically, the gas characteristics measured are either in terms of the gas particles themselves (velocity, pressure, or temperature) or their surroundings (volume). For example, Robert Boyle studied pneumatic chemistry for a small portion of his career. One of his experiments related the macroscopic properties of pressure and volume of a gas. His experiment used a J-tube manometer which looks like a test tube in the shape of the letter J. Boyle trapped an inert gas in the closed end of the test tube with a column of mercury, thereby making the number of particles and the temperature constant. He observed that when the pressure was increased in the gas, by adding more mercury to the column, the trapped gas' volume decreased (this is known as an inverse relationship). Furthermore, when Boyle multiplied the pressure and volume of each observation, the product was constant. This relationship held for every gas that Boyle observed leading to the law, (PV=k), named to honor his work in this field.","Gas\n\nThere are many mathematical tools available for analyzing gas properties. As gases are subjected to extreme conditions, these tools become a bit more complex, from the Euler equations for inviscid flow to the Navier–Stokes equations that fully account for viscous effects. These equations are adapted to the conditions of the gas system in question. Boyle's lab equipment allowed the use of algebra to obtain his analytical results. His results were possible because he was studying gases in relatively low pressure situations where they behaved in an \"ideal\" manner. These ideal relationships apply to safety calculations for a variety of flight conditions on the materials in use. The high technology equipment in use today was designed to help us safely explore the more exotic operating environments where the gases no longer behave in an \"ideal\" manner. This advanced math, including statistics and multivariable calculus, makes possible the solution to such complex dynamic situations as space vehicle reentry. An example is the analysis of the space shuttle reentry pictured to ensure the material properties under this loading condition are appropriate. In this flight regime, the gas is no longer behaving ideally.","Gas\n\nPressure","Gas\n\nThe symbol used to represent pressure in equations is \"p\" or \"P\" with SI units of pascals.","Gas\n\nWhen describing a container of gas, the term pressure (or absolute pressure) refers to the average force per unit area that the gas exerts on the surface of the container. Within this volume, it is sometimes easier to visualize the gas particles moving in straight lines until they collide with the container (see diagram at top of the article). The force imparted by a gas particle into the container during this collision is the change in momentum of the particle. During a collision only the normal component of velocity changes. A particle traveling parallel to the wall does not change its momentum. Therefore, the average force on a surface must be the average change in linear momentum from all of these gas particle collisions.","Gas\n\nPressure is the sum of all the normal components of force exerted by the particles impacting the walls of the container divided by the surface area of the wall.","Gas\n\nTemperature","Gas\n\nThe symbol used to represent temperature in equations is T with SI units of kelvins.","Gas\n\nThe speed of a gas particle is proportional to its absolute temperature. The volume of the balloon in the video shrinks when the trapped gas particles slow down with the addition of extremely cold nitrogen. The temperature of any physical system is related to the motions of the particles (molecules and atoms) which make up the [gas] system. In statistical mechanics, temperature is the measure of the average kinetic energy stored in a particle. The methods of storing this energy are dictated by the degrees of freedom of the particle itself (energy modes). Kinetic energy added (endothermic process) to gas particles by way of collisions produces linear, rotational, and vibrational motion. In contrast, a molecule in a solid can only increase its vibrational modes with the addition of heat as the lattice crystal structure prevents both linear and rotational motions. These heated gas molecules have a greater speed range which constantly varies due to constant collisions with other particles. The speed range can be described by the Maxwell–Boltzmann distribution. Use of this distribution implies ideal gases near thermodynamic equilibrium for the system of particles being considered.","Gas\n\nSpecific volume","Gas\n\nThe symbol used to represent specific volume in equations is \"v\" with SI units of cubic meters per kilogram.","Gas\n\nThe symbol used to represent volume in equations is \"V\" with SI units of cubic meters.","Gas\n\nWhen performing a thermodynamic analysis, it is typical to speak of intensive and extensive properties. Properties which depend on the amount of gas (either by mass or volume) are called extensive properties, while properties that do not depend on the amount of gas are called intensive properties. Specific volume is an example of an intensive property because it is the ratio of volume occupied by a unit of mass of a gas that is identical throughout a system at equilibrium. 1000 atoms a gas occupy the same space as any other 1000 atoms for any given temperature and pressure. This concept is easier to visualize for solids such as iron which are incompressible compared to gases. Since a gas fills any container in which it is placed, volume is an extensive property.","Gas\n\nDensity","Gas\n\nThe symbol used to represent density in equations is ρ (rho) with SI units of kilograms per cubic meter. This term is the reciprocal of specific volume.","Gas\n\nSince gas molecules can move freely within a container, their mass is normally characterized by density. Density is the amount of mass per unit volume of a substance, or the inverse of specific volume. For gases, the density can vary over a wide range because the particles are free to move closer together when constrained by pressure or volume. This variation of density is referred to as compressibility. Like pressure and temperature, density is a state variable of a gas and the change in density during any process is governed by the laws of thermodynamics. For a static gas, the density is the same throughout the entire container. Density is therefore a scalar quantity. It can be shown by kinetic theory that the density is inversely proportional to the size of the container in which a fixed mass of gas is confined. In this case of a fixed mass, the density decreases as the volume increases.","Gas\n\nMicroscopic","Gas\n\nIf one could observe a gas under a powerful microscope, one would see a collection of particles (molecules, atoms, ions, electrons, etc.) without any definite shape or volume that are in more or less random motion. These neutral gas particles only change direction when they collide with another particle or with the sides of the container. In an ideal gas, these collisions are perfectly elastic. This particle or microscopic view of a gas is described by the Kinetic-molecular theory. The assumptions behind this theory can be found in the postulates section of Kinetic Theory.","Gas\n\nKinetic theory","Gas\n\nKinetic theory provides insight into the macroscopic properties of gases by considering their molecular composition and motion. Starting with the definitions of momentum and kinetic energy, one can use the conservation of momentum and geometric relationships of a cube to relate macroscopic system properties of temperature and pressure to the microscopic property of kinetic energy per molecule. The theory provides averaged values for these two properties.","Gas\n\nThe theory also explains how the gas system responds to change. For example, as a gas is heated from absolute zero, when it is (in theory) perfectly still, its internal energy (temperature) is increased. As a gas is heated, the particles speed up and its temperature rises. This results in greater numbers of collisions with the container per unit time due to the higher particle speeds associated with elevated temperatures. The pressure increases in proportion to the number of collisions per unit time.","Gas\n\nBrownian motion","Gas\n\nBrownian motion is the mathematical model used to describe the random movement of particles suspended in a fluid. The gas particle animation, using pink and green particles, illustrates how this behavior results in the spreading out of gases (entropy). These events are also described by particle theory.","Gas\n\nSince it is at the limit of (or beyond) current technology to observe individual gas particles (atoms or molecules), only theoretical calculations give suggestions about how they move, but their motion is different from Brownian motion because Brownian motion involves a smooth drag due to the frictional force of many gas molecules, punctuated by violent collisions of an individual (or several) gas molecule(s) with the particle. The particle (generally consisting of millions or billions of atoms) thus moves in a jagged course, yet not so jagged as would be expected if an individual gas molecule were examined.","Gas\n\nIntermolecular forces","Gas\n\nAs discussed earlier, momentary attractions (or repulsions) between particles have an effect on gas dynamics. In physical chemistry, the name given to these intermolecular forces is van der Waals force. These forces play a key role in determining physical properties of a gas such as viscosity and flow rate (see physical characteristics section). Ignoring these forces in certain conditions (see Kinetic-molecular theory) allows a real gas to be treated like an ideal gas. This assumption allows the use of ideal gas laws which greatly simplifies calculations.","Gas\n\nProper use of these gas relationships requires the Kinetic-molecular theory (KMT). When gas particles possess a magnetic charge or Intermolecular force they gradually influence one another as the spacing between them is reduced (the hydrogen bond model illustrates one example). In the absence of any charge, at some point when the spacing between gas particles is greatly reduced they can no longer avoid collisions between themselves at normal gas temperatures. Another case for increased collisions among gas particles would include a fixed volume of gas, which upon heating would contain very fast particles. This means that these ideal equations provide reasonable results except for extremely high pressure (compressible) or high temperature (ionized) conditions. Notice that all of these excepted conditions allow energy transfer to take place within the gas system. The absence of these internal transfers is what is referred to as ideal conditions in which the energy exchange occurs only at the boundaries of the system. Real gases experience some of these collisions and intermolecular forces. When these collisions are statistically negligible (incompressible), results from these ideal equations are still meaningful.","Gas\n\nIf the gas particles are compressed into close proximity they behave more like a liquid (see fluid dynamics).","Gas\n\nSimplified models","Gas\n\nAn equation of state (for gases) is a mathematical model used to roughly describe or predict the state properties of a gas. At present, there is no single equation of state that accurately predicts the properties of all gases under all conditions. Therefore, a number of much more accurate equations of state have been developed for gases in specific temperature and pressure ranges. The \"gas models\" that are most widely discussed are \"perfect gas\", \"ideal gas\" and \"real gas\". Each of these models has its own set of assumptions to facilitate the analysis of a given thermodynamic system. Each successive model expands the temperature range of coverage to which it applies.","Gas\n\nIdeal and perfect gas models","Gas\n\nThe equation of state for an ideal or perfect gas is the ideal gas law and reads\nPV=nRT,\nwhere P is the pressure, V is the volume, n is amount of gas (in mol units), R is the universal gas constant, 8.314 J/(mol K), and T is the temperature. Written this way, it is sometimes called the \"chemist's version\", since it emphasizes the number of molecules n. It can also be written as\nP=\\rho R_s T,\nwhere R_s is the specific gas constant for a particular gas, in units J/(kg K), and ρ = m/V is density. This notation is the \"gas dynamicist's\" version, which is more practical in modeling of gas flows involving acceleration without chemical reactions.","Gas\n\nThe ideal gas law does not make an assumption about the specific heat of a gas. In the most general case, the specific heat is a function of both temperature and pressure. If the pressure-dependence is neglected (and possibly the temperature-dependence as well) in a particular application, sometimes the gas is said to be a perfect gas, although the exact assumptions may vary depending on the author and/or field of science.","Gas\n\nFor an ideal gas, the ideal gas law applies without restrictions on the specific heat. An ideal gas is a simplified \"real gas\" with the assumption that the compressibility factor Z is set to 1 meaning that this pneumatic ratio remains constant. A compressibility factor of one also requires the four state variables to follow the ideal gas law.","Gas\n\nThis approximation is more suitable for applications in engineering although simpler models can be used to produce a \"ball-park\" range as to where the real solution should lie. An example where the \"ideal gas approximation\" would be suitable would be inside a combustion chamber of a jet engine. It may also be useful to keep the elementary reactions and chemical dissociations for calculating emissions.","Gas\n\nReal gas","Gas\n\nEach one of the assumptions listed below adds to the complexity of the problem's solution. As the density of a gas increases with rising pressure, the intermolecular forces play a more substantial role in gas behavior which results in the ideal gas law no longer providing \"reasonable\" results. At the upper end of the engine temperature ranges (e.g. combustor sections – 1300 K), the complex fuel particles absorb internal energy by means of rotations and vibrations that cause their specific heats to vary from those of diatomic molecules and noble gases. At more than double that temperature, electronic excitation and dissociation of the gas particles begins to occur causing the pressure to adjust to a greater number of particles (transition from gas to plasma). Finally, all of the thermodynamic processes were presumed to describe uniform gases whose velocities varied according to a fixed distribution. Using a non-equilibrium situation implies the flow field must be characterized in some manner to enable a solution.","Gas\n\nOne of the first attempts to expand the boundaries of the ideal gas law was to include coverage for different thermodynamic processes by adjusting the equation to read pVn = constant and then varying the n through different values such as the specific heat ratio, γ.","Gas\n\nReal gas effects include those adjustments made to account for a greater range of gas behavior:\n*Compressibility effects (Z allowed to vary from 1.0)\n*Variable heat capacity (specific heats vary with temperature)\n*Van der Waals forces (related to compressibility, can substitute other equations of state)\n*Non-equilibrium thermodynamic effects\n*Issues with molecular dissociation and elementary reactions with variable composition.","Gas\n\nFor most applications, such a detailed analysis is excessive. Examples where \"Real Gas effects\" would have a significant impact would be on the Space Shuttle re-entry where extremely high temperatures and pressures are present or the gases produced during geological events as in the image of the 1990 eruption of Mount Redoubt.","Gas\n\nHistorical synthesis","Gas\n\nBoyle's law","Gas\n\nBoyle's Law was perhaps the first expression of an equation of state. In 1662 Robert Boyle performed a series of experiments employing a J-shaped glass tube, which was sealed on one end. Mercury was added to the tube, trapping a fixed quantity of air in the short, sealed end of the tube. Then the volume of gas was carefully measured as additional mercury was added to the tube. The pressure of the gas could be determined by the difference between the mercury level in the short end of the tube and that in the long, open end. The image of Boyle's Equipment shows some of the exotic tools used by Boyle during his study of gases.","Gas\n\nThrough these experiments, Boyle noted that the pressure exerted by a gas held at a constant temperature varies inversely with the volume of the gas. For example, if the volume is halved, the pressure is doubled; and if the volume is doubled, the pressure is halved. Given the inverse relationship between pressure and volume, the product of pressure (P) and volume (V) is a constant (k) for a given mass of confined gas as long as the temperature is constant. Stated as a formula, thus is:","Gas\n\nPV = k","Gas\n\nBecause the before and after volumes and pressures of the fixed amount of gas, where the before and after temperatures are the same both equal the constant k, they can be related by the equation:","Gas\n\n\\qquad P_1 V_1 = P_2 V_2.","Gas\n\nCharles's Law","Gas\n\nIn 1787, the French physicist and balloon pioneer, Jacques Charles, found that oxygen, nitrogen, hydrogen, carbon dioxide, and air expand to the same extent over the same 80 kelvin interval. He noted that, for an ideal gas at constant pressure, the volume is directly proportional to its temperature:","Gas\n\n\\frac{V_1}{T_1} = \\frac{V_2}{T_2}","Gas\n\nGay-Lussac's Law","Gas\n\nIn 1802, Joseph Louis Gay-Lussac published results of similar, though more extensive experiments. Gay-Lussac credited Charle's earlier work by naming the law in his honor. Gay-Lussac himself is credited with the law describing pressure, which he found in 1809. It states that the pressure exerted on a container's sides by an ideal gas is proportional to its temperature.\n \\frac{P_1}{T_1}=\\frac{P_2}{T_2} \\,","Gas\n\nAvogadro's law","Gas\n\nIn 1811, Amedeo Avogadro verified that equal volumes of pure gases contain the same number of particles. His theory was not generally accepted until 1858 when another Italian chemist Stanislao Cannizzaro was able to explain non-ideal exceptions. For his work with gases a century prior, the number that bears his name Avogadro's constant represents the number of atoms found in 12 grams of elemental carbon-12 (6.022×1023 mol−1). This specific number of gas particles, at standard temperature and pressure (ideal gas law) occupies 22.40 liters, which is referred to as the molar volume.","Gas\n\nAvogadro's law states that the volume occupied by an ideal gas is proportional to the number of moles (or molecules) present in the container. This gives rise to the molar volume of a gas, which at STP is 22.4 dm3 (or litres). The relation is given by","Gas\n\n\\frac{V_1}{n_1}=\\frac{V_2}{n_2} \\,","Gas\n\nwhere n is equal to the number of moles of gas (the number of molecules divided by Avogadro's Number).","Gas\n\nDalton's law","Gas\n\nIn 1801, John Dalton published the Law of Partial Pressures from his work with ideal gas law relationship: The pressure of a mixture of non reactive gases is equal to the sum of the pressures of all of the constituent gases alone. Mathematically, this can be represented for n species as:","Gas\n\nPressuretotal = Pressure1 + Pressure2 + ... + Pressuren","Gas\n\nThe image of Dalton's journal depicts symbology he used as shorthand to record the path he followed. Among his key journal observations upon mixing unreactive \"elastic fluids\" (gases) were the following: \n*Unlike liquids, heavier gases did not drift to the bottom upon mixing.\n*Gas particle identity played no role in determining final pressure (they behaved as if their size was negligible).","Gas\n\nSpecial topics","Gas\n\nCompressibility","Gas\n\nThermodynamicists use this factor (Z) to alter the ideal gas equation to account for compressibility effects of real gases. This factor represents the ratio of actual to ideal specific volumes. It is sometimes referred to as a \"fudge-factor\" or correction to expand the useful range of the ideal gas law for design purposes. Usually this Z value is very close to unity. The compressibility factor image illustrates how Z varies over a range of very cold temperatures.","Gas\n\nReynolds number","Gas\n\nIn fluid mechanics, the Reynolds number is the ratio of inertial forces (vsρ) to viscous forces (μ/L). It is one of the most important dimensionless numbers in fluid dynamics and is used, usually along with other dimensionless numbers, to provide a criterion for determining dynamic similitude. As such, the Reynolds number provides the link between modeling results (design) and the full-scale actual conditions. It can also be used to characterize the flow.","Gas\n\nViscosity","Gas\n\nViscosity, a physical property, is a measure of how well adjacent molecules stick to one another. A solid can withstand a shearing force due to the strength of these sticky intermolecular forces. A fluid will continuously deform when subjected to a similar load. While a gas has a lower value of viscosity than a liquid, it is still an observable property. If gases had no viscosity, then they would not stick to the surface of a wing and form a boundary layer. A study of the delta wing in the Schlieren image reveals that the gas particles stick to one another (see Boundary layer section).","Gas\n\nTurbulence","Gas\n\nIn fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic, stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time. The Satellite view of weather around Robinson Crusoe Islands illustrates just one example.","Gas\n\nBoundary layer","Gas\n\nParticles will, in effect, \"stick\" to the surface of an object moving through it. This layer of particles is called the boundary layer. At the surface of the object, it is essentially static due to the friction of the surface. The object, with its boundary layer is effectively the new shape of the object that the rest of the molecules \"see\" as the object approaches. This boundary layer can separate from the surface, essentially creating a new surface and completely changing the flow path. The classical example of this is a stalling airfoil. The delta wing image clearly shows the boundary layer thickening as the gas flows from right to left along the leading edge.","Gas\n\nMaximum entropy principle","Gas\n\nAs the total number of degrees of freedom approaches infinity, the system will be found in the macrostate that corresponds to the highest multiplicity. In order to illustrate this principle, observe the skin temperature of a frozen metal bar. Using a thermal image of the skin temperature, note the temperature distribution on the surface. This initial observation of temperature represents a \"microstate.\" At some future time, a second observation of the skin temperature produces a second microstate. By continuing this observation process, it is possible to produce a series of microstates that illustrate the thermal history of the bar's surface. Characterization of this historical series of microstates is possible by choosing the macrostate that successfully classifies them all into a single grouping.","Gas\n\nThermodynamic equilibrium","Gas\n\nWhen energy transfer ceases from a system, this condition is referred to as thermodynamic equilibrium. Usually this condition implies the system and surroundings are at the same temperature so that heat no longer transfers between them. It also implies that external forces are balanced (volume does not change), and all chemical reactions within the system are complete. The timeline varies for these events depending on the system in question. A container of ice allowed to melt at room temperature takes hours, while in semiconductors the heat transfer that occurs in the device transition from an on to off state could be on the order of a few nanoseconds."],"string":"[\n \"Gas\\n\\nGas is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or compound molecules made from a variety of atoms (e.g. carbon dioxide). A gas mixture would contain a variety of pure gases much like the air. What distinguishes a gas from liquids and solids is the vast separation of the individual gas particles. This separation usually makes a colorless gas invisible to the human observer. The interaction of gas particles in the presence of electric and gravitational fields are considered negligible as indicated by the constant velocity vectors in the image. One type of commonly known gas is steam.\",\n \"Gas\\n\\nThe gaseous state of matter is found between the liquid and plasma states, the latter of which provides the upper temperature boundary for gases. Bounding the lower end of the temperature scale lie degenerative quantum gases which are gaining increasing attention. High-density atomic gases super cooled to incredibly low temperatures are classified by their statistical behavior as either a Bose gas or a Fermi gas. For a comprehensive listing of these exotic states of matter see list of states of matter.\",\n \"Gas\\n\\nElemental gases\",\n \"Gas\\n\\nThe only chemical elements which are stable multi atom homonuclear molecules at standard temperature and pressure (STP), are hydrogen (H2), nitrogen (N2) and oxygen (O2); \\nplus two halogens, fluorine (F2) and chlorine (Cl2). \\nThese gases, when grouped together with the monatomic noble gases; which are helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe) and radon (Rn) ; are called \\\"elemental gases\\\". Alternatively they are sometimes known as \\\"molecular gases\\\" to distinguish them from molecules that are also chemical compounds.\",\n \"Gas\\n\\nEtymology\",\n \"Gas\\n\\nThe word gas is a neologism first used by the early 17th-century Flemish chemist J.B. van Helmont. Van Helmont's word appears to have been simply a phonetic transcription of the Greek word χάος Chaos – the g in Dutch being pronounced like ch in \\\"loch\\\" – in which case Van Helmont was simply following the established alchemical usage first attested in the works of Paracelsus. According to Paracelsus's terminology, chaos meant something like \\\"ultra-rarefied water\\\".\",\n \"Gas\\n\\nAn alternative story is that Van Helmont's word is corrupted from gahst (or geist), signifying a ghost or spirit. This was because certain gases suggested a supernatural origin, such as from their ability to cause death, extinguish flames, and to occur in \\\"mines, bottom of wells, churchyards and other lonely places\\\".\",\n \"Gas\\n\\nPhysical characteristics\",\n \"Gas\\n\\nBecause most gases are difficult to observe directly, they are described through the use of four physical properties or macroscopic characteristics: pressure, volume, number of particles (chemists group them by moles) and temperature. These four characteristics were repeatedly observed by scientists such as Robert Boyle, Jacques Charles, John Dalton, Joseph Gay-Lussac and Amedeo Avogadro for a variety of gases in various settings. Their detailed studies ultimately led to a mathematical relationship among these properties expressed by the ideal gas law (see simplified models section below).\",\n \"Gas\\n\\nGas particles are widely separated from one another, and consequently have weaker intermolecular bonds than liquids or solids. These intermolecular forces result from electrostatic interactions between gas particles. Like-charged areas of different gas particles repel, while oppositely charged regions of different gas particles attract one another; gases that contain permanently charged ions are known as plasmas. Gaseous compounds with polar covalent bonds contain permanent charge imbalances and so experience relatively strong intermolecular forces, although the molecule while the compound's net charge remains neutral. Transient, randomly induced charges exist across non-polar covalent bonds of molecules and electrostatic interactions caused by them are referred to as Van der Waals forces. The interaction of these intermolecular forces varies within a substance which determines many of the physical properties unique to each gas. A comparison of boiling points for compounds formed by ionic and covalent bonds leads us to this conclusion. The drifting smoke particles in the image provides some insight into low pressure gas behavior.\",\n \"Gas\\n\\nCompared to the other states of matter, gases have low density and viscosity. Pressure and temperature influence the particles within a certain volume. This variation in particle separation and speed is referred to as compressibility. This particle separation and size influences optical properties of gases as can be found in the following list of refractive indices. Finally, gas particles spread apart or diffuse in order to homogeneously distribute themselves throughout any container.\",\n \"Gas\\n\\nMacroscopic\",\n \"Gas\\n\\nWhen observing a gas, it is typical to specify a frame of reference or length scale. A larger length scale corresponds to a macroscopic or global point of view of the gas. This region (referred to as a volume) must be sufficient in size to contain a large sampling of gas particles. The resulting statistical analysis of this sample size produces the \\\"average\\\" behavior (i.e. velocity, temperature or pressure) of all the gas particles within the region. In contrast, a smaller length scale corresponds to a microscopic or particle point of view.\",\n \"Gas\\n\\nMacroscopically, the gas characteristics measured are either in terms of the gas particles themselves (velocity, pressure, or temperature) or their surroundings (volume). For example, Robert Boyle studied pneumatic chemistry for a small portion of his career. One of his experiments related the macroscopic properties of pressure and volume of a gas. His experiment used a J-tube manometer which looks like a test tube in the shape of the letter J. Boyle trapped an inert gas in the closed end of the test tube with a column of mercury, thereby making the number of particles and the temperature constant. He observed that when the pressure was increased in the gas, by adding more mercury to the column, the trapped gas' volume decreased (this is known as an inverse relationship). Furthermore, when Boyle multiplied the pressure and volume of each observation, the product was constant. This relationship held for every gas that Boyle observed leading to the law, (PV=k), named to honor his work in this field.\",\n \"Gas\\n\\nThere are many mathematical tools available for analyzing gas properties. As gases are subjected to extreme conditions, these tools become a bit more complex, from the Euler equations for inviscid flow to the Navier–Stokes equations that fully account for viscous effects. These equations are adapted to the conditions of the gas system in question. Boyle's lab equipment allowed the use of algebra to obtain his analytical results. His results were possible because he was studying gases in relatively low pressure situations where they behaved in an \\\"ideal\\\" manner. These ideal relationships apply to safety calculations for a variety of flight conditions on the materials in use. The high technology equipment in use today was designed to help us safely explore the more exotic operating environments where the gases no longer behave in an \\\"ideal\\\" manner. This advanced math, including statistics and multivariable calculus, makes possible the solution to such complex dynamic situations as space vehicle reentry. An example is the analysis of the space shuttle reentry pictured to ensure the material properties under this loading condition are appropriate. In this flight regime, the gas is no longer behaving ideally.\",\n \"Gas\\n\\nPressure\",\n \"Gas\\n\\nThe symbol used to represent pressure in equations is \\\"p\\\" or \\\"P\\\" with SI units of pascals.\",\n \"Gas\\n\\nWhen describing a container of gas, the term pressure (or absolute pressure) refers to the average force per unit area that the gas exerts on the surface of the container. Within this volume, it is sometimes easier to visualize the gas particles moving in straight lines until they collide with the container (see diagram at top of the article). The force imparted by a gas particle into the container during this collision is the change in momentum of the particle. During a collision only the normal component of velocity changes. A particle traveling parallel to the wall does not change its momentum. Therefore, the average force on a surface must be the average change in linear momentum from all of these gas particle collisions.\",\n \"Gas\\n\\nPressure is the sum of all the normal components of force exerted by the particles impacting the walls of the container divided by the surface area of the wall.\",\n \"Gas\\n\\nTemperature\",\n \"Gas\\n\\nThe symbol used to represent temperature in equations is T with SI units of kelvins.\",\n \"Gas\\n\\nThe speed of a gas particle is proportional to its absolute temperature. The volume of the balloon in the video shrinks when the trapped gas particles slow down with the addition of extremely cold nitrogen. The temperature of any physical system is related to the motions of the particles (molecules and atoms) which make up the [gas] system. In statistical mechanics, temperature is the measure of the average kinetic energy stored in a particle. The methods of storing this energy are dictated by the degrees of freedom of the particle itself (energy modes). Kinetic energy added (endothermic process) to gas particles by way of collisions produces linear, rotational, and vibrational motion. In contrast, a molecule in a solid can only increase its vibrational modes with the addition of heat as the lattice crystal structure prevents both linear and rotational motions. These heated gas molecules have a greater speed range which constantly varies due to constant collisions with other particles. The speed range can be described by the Maxwell–Boltzmann distribution. Use of this distribution implies ideal gases near thermodynamic equilibrium for the system of particles being considered.\",\n \"Gas\\n\\nSpecific volume\",\n \"Gas\\n\\nThe symbol used to represent specific volume in equations is \\\"v\\\" with SI units of cubic meters per kilogram.\",\n \"Gas\\n\\nThe symbol used to represent volume in equations is \\\"V\\\" with SI units of cubic meters.\",\n \"Gas\\n\\nWhen performing a thermodynamic analysis, it is typical to speak of intensive and extensive properties. Properties which depend on the amount of gas (either by mass or volume) are called extensive properties, while properties that do not depend on the amount of gas are called intensive properties. Specific volume is an example of an intensive property because it is the ratio of volume occupied by a unit of mass of a gas that is identical throughout a system at equilibrium. 1000 atoms a gas occupy the same space as any other 1000 atoms for any given temperature and pressure. This concept is easier to visualize for solids such as iron which are incompressible compared to gases. Since a gas fills any container in which it is placed, volume is an extensive property.\",\n \"Gas\\n\\nDensity\",\n \"Gas\\n\\nThe symbol used to represent density in equations is ρ (rho) with SI units of kilograms per cubic meter. This term is the reciprocal of specific volume.\",\n \"Gas\\n\\nSince gas molecules can move freely within a container, their mass is normally characterized by density. Density is the amount of mass per unit volume of a substance, or the inverse of specific volume. For gases, the density can vary over a wide range because the particles are free to move closer together when constrained by pressure or volume. This variation of density is referred to as compressibility. Like pressure and temperature, density is a state variable of a gas and the change in density during any process is governed by the laws of thermodynamics. For a static gas, the density is the same throughout the entire container. Density is therefore a scalar quantity. It can be shown by kinetic theory that the density is inversely proportional to the size of the container in which a fixed mass of gas is confined. In this case of a fixed mass, the density decreases as the volume increases.\",\n \"Gas\\n\\nMicroscopic\",\n \"Gas\\n\\nIf one could observe a gas under a powerful microscope, one would see a collection of particles (molecules, atoms, ions, electrons, etc.) without any definite shape or volume that are in more or less random motion. These neutral gas particles only change direction when they collide with another particle or with the sides of the container. In an ideal gas, these collisions are perfectly elastic. This particle or microscopic view of a gas is described by the Kinetic-molecular theory. The assumptions behind this theory can be found in the postulates section of Kinetic Theory.\",\n \"Gas\\n\\nKinetic theory\",\n \"Gas\\n\\nKinetic theory provides insight into the macroscopic properties of gases by considering their molecular composition and motion. Starting with the definitions of momentum and kinetic energy, one can use the conservation of momentum and geometric relationships of a cube to relate macroscopic system properties of temperature and pressure to the microscopic property of kinetic energy per molecule. The theory provides averaged values for these two properties.\",\n \"Gas\\n\\nThe theory also explains how the gas system responds to change. For example, as a gas is heated from absolute zero, when it is (in theory) perfectly still, its internal energy (temperature) is increased. As a gas is heated, the particles speed up and its temperature rises. This results in greater numbers of collisions with the container per unit time due to the higher particle speeds associated with elevated temperatures. The pressure increases in proportion to the number of collisions per unit time.\",\n \"Gas\\n\\nBrownian motion\",\n \"Gas\\n\\nBrownian motion is the mathematical model used to describe the random movement of particles suspended in a fluid. The gas particle animation, using pink and green particles, illustrates how this behavior results in the spreading out of gases (entropy). These events are also described by particle theory.\",\n \"Gas\\n\\nSince it is at the limit of (or beyond) current technology to observe individual gas particles (atoms or molecules), only theoretical calculations give suggestions about how they move, but their motion is different from Brownian motion because Brownian motion involves a smooth drag due to the frictional force of many gas molecules, punctuated by violent collisions of an individual (or several) gas molecule(s) with the particle. The particle (generally consisting of millions or billions of atoms) thus moves in a jagged course, yet not so jagged as would be expected if an individual gas molecule were examined.\",\n \"Gas\\n\\nIntermolecular forces\",\n \"Gas\\n\\nAs discussed earlier, momentary attractions (or repulsions) between particles have an effect on gas dynamics. In physical chemistry, the name given to these intermolecular forces is van der Waals force. These forces play a key role in determining physical properties of a gas such as viscosity and flow rate (see physical characteristics section). Ignoring these forces in certain conditions (see Kinetic-molecular theory) allows a real gas to be treated like an ideal gas. This assumption allows the use of ideal gas laws which greatly simplifies calculations.\",\n \"Gas\\n\\nProper use of these gas relationships requires the Kinetic-molecular theory (KMT). When gas particles possess a magnetic charge or Intermolecular force they gradually influence one another as the spacing between them is reduced (the hydrogen bond model illustrates one example). In the absence of any charge, at some point when the spacing between gas particles is greatly reduced they can no longer avoid collisions between themselves at normal gas temperatures. Another case for increased collisions among gas particles would include a fixed volume of gas, which upon heating would contain very fast particles. This means that these ideal equations provide reasonable results except for extremely high pressure (compressible) or high temperature (ionized) conditions. Notice that all of these excepted conditions allow energy transfer to take place within the gas system. The absence of these internal transfers is what is referred to as ideal conditions in which the energy exchange occurs only at the boundaries of the system. Real gases experience some of these collisions and intermolecular forces. When these collisions are statistically negligible (incompressible), results from these ideal equations are still meaningful.\",\n \"Gas\\n\\nIf the gas particles are compressed into close proximity they behave more like a liquid (see fluid dynamics).\",\n \"Gas\\n\\nSimplified models\",\n \"Gas\\n\\nAn equation of state (for gases) is a mathematical model used to roughly describe or predict the state properties of a gas. At present, there is no single equation of state that accurately predicts the properties of all gases under all conditions. Therefore, a number of much more accurate equations of state have been developed for gases in specific temperature and pressure ranges. The \\\"gas models\\\" that are most widely discussed are \\\"perfect gas\\\", \\\"ideal gas\\\" and \\\"real gas\\\". Each of these models has its own set of assumptions to facilitate the analysis of a given thermodynamic system. Each successive model expands the temperature range of coverage to which it applies.\",\n \"Gas\\n\\nIdeal and perfect gas models\",\n \"Gas\\n\\nThe equation of state for an ideal or perfect gas is the ideal gas law and reads\\nPV=nRT,\\nwhere P is the pressure, V is the volume, n is amount of gas (in mol units), R is the universal gas constant, 8.314 J/(mol K), and T is the temperature. Written this way, it is sometimes called the \\\"chemist's version\\\", since it emphasizes the number of molecules n. It can also be written as\\nP=\\\\rho R_s T,\\nwhere R_s is the specific gas constant for a particular gas, in units J/(kg K), and ρ = m/V is density. This notation is the \\\"gas dynamicist's\\\" version, which is more practical in modeling of gas flows involving acceleration without chemical reactions.\",\n \"Gas\\n\\nThe ideal gas law does not make an assumption about the specific heat of a gas. In the most general case, the specific heat is a function of both temperature and pressure. If the pressure-dependence is neglected (and possibly the temperature-dependence as well) in a particular application, sometimes the gas is said to be a perfect gas, although the exact assumptions may vary depending on the author and/or field of science.\",\n \"Gas\\n\\nFor an ideal gas, the ideal gas law applies without restrictions on the specific heat. An ideal gas is a simplified \\\"real gas\\\" with the assumption that the compressibility factor Z is set to 1 meaning that this pneumatic ratio remains constant. A compressibility factor of one also requires the four state variables to follow the ideal gas law.\",\n \"Gas\\n\\nThis approximation is more suitable for applications in engineering although simpler models can be used to produce a \\\"ball-park\\\" range as to where the real solution should lie. An example where the \\\"ideal gas approximation\\\" would be suitable would be inside a combustion chamber of a jet engine. It may also be useful to keep the elementary reactions and chemical dissociations for calculating emissions.\",\n \"Gas\\n\\nReal gas\",\n \"Gas\\n\\nEach one of the assumptions listed below adds to the complexity of the problem's solution. As the density of a gas increases with rising pressure, the intermolecular forces play a more substantial role in gas behavior which results in the ideal gas law no longer providing \\\"reasonable\\\" results. At the upper end of the engine temperature ranges (e.g. combustor sections – 1300 K), the complex fuel particles absorb internal energy by means of rotations and vibrations that cause their specific heats to vary from those of diatomic molecules and noble gases. At more than double that temperature, electronic excitation and dissociation of the gas particles begins to occur causing the pressure to adjust to a greater number of particles (transition from gas to plasma). Finally, all of the thermodynamic processes were presumed to describe uniform gases whose velocities varied according to a fixed distribution. Using a non-equilibrium situation implies the flow field must be characterized in some manner to enable a solution.\",\n \"Gas\\n\\nOne of the first attempts to expand the boundaries of the ideal gas law was to include coverage for different thermodynamic processes by adjusting the equation to read pVn = constant and then varying the n through different values such as the specific heat ratio, γ.\",\n \"Gas\\n\\nReal gas effects include those adjustments made to account for a greater range of gas behavior:\\n*Compressibility effects (Z allowed to vary from 1.0)\\n*Variable heat capacity (specific heats vary with temperature)\\n*Van der Waals forces (related to compressibility, can substitute other equations of state)\\n*Non-equilibrium thermodynamic effects\\n*Issues with molecular dissociation and elementary reactions with variable composition.\",\n \"Gas\\n\\nFor most applications, such a detailed analysis is excessive. Examples where \\\"Real Gas effects\\\" would have a significant impact would be on the Space Shuttle re-entry where extremely high temperatures and pressures are present or the gases produced during geological events as in the image of the 1990 eruption of Mount Redoubt.\",\n \"Gas\\n\\nHistorical synthesis\",\n \"Gas\\n\\nBoyle's law\",\n \"Gas\\n\\nBoyle's Law was perhaps the first expression of an equation of state. In 1662 Robert Boyle performed a series of experiments employing a J-shaped glass tube, which was sealed on one end. Mercury was added to the tube, trapping a fixed quantity of air in the short, sealed end of the tube. Then the volume of gas was carefully measured as additional mercury was added to the tube. The pressure of the gas could be determined by the difference between the mercury level in the short end of the tube and that in the long, open end. The image of Boyle's Equipment shows some of the exotic tools used by Boyle during his study of gases.\",\n \"Gas\\n\\nThrough these experiments, Boyle noted that the pressure exerted by a gas held at a constant temperature varies inversely with the volume of the gas. For example, if the volume is halved, the pressure is doubled; and if the volume is doubled, the pressure is halved. Given the inverse relationship between pressure and volume, the product of pressure (P) and volume (V) is a constant (k) for a given mass of confined gas as long as the temperature is constant. Stated as a formula, thus is:\",\n \"Gas\\n\\nPV = k\",\n \"Gas\\n\\nBecause the before and after volumes and pressures of the fixed amount of gas, where the before and after temperatures are the same both equal the constant k, they can be related by the equation:\",\n \"Gas\\n\\n\\\\qquad P_1 V_1 = P_2 V_2.\",\n \"Gas\\n\\nCharles's Law\",\n \"Gas\\n\\nIn 1787, the French physicist and balloon pioneer, Jacques Charles, found that oxygen, nitrogen, hydrogen, carbon dioxide, and air expand to the same extent over the same 80 kelvin interval. He noted that, for an ideal gas at constant pressure, the volume is directly proportional to its temperature:\",\n \"Gas\\n\\n\\\\frac{V_1}{T_1} = \\\\frac{V_2}{T_2}\",\n \"Gas\\n\\nGay-Lussac's Law\",\n \"Gas\\n\\nIn 1802, Joseph Louis Gay-Lussac published results of similar, though more extensive experiments. Gay-Lussac credited Charle's earlier work by naming the law in his honor. Gay-Lussac himself is credited with the law describing pressure, which he found in 1809. It states that the pressure exerted on a container's sides by an ideal gas is proportional to its temperature.\\n \\\\frac{P_1}{T_1}=\\\\frac{P_2}{T_2} \\\\,\",\n \"Gas\\n\\nAvogadro's law\",\n \"Gas\\n\\nIn 1811, Amedeo Avogadro verified that equal volumes of pure gases contain the same number of particles. His theory was not generally accepted until 1858 when another Italian chemist Stanislao Cannizzaro was able to explain non-ideal exceptions. For his work with gases a century prior, the number that bears his name Avogadro's constant represents the number of atoms found in 12 grams of elemental carbon-12 (6.022×1023 mol−1). This specific number of gas particles, at standard temperature and pressure (ideal gas law) occupies 22.40 liters, which is referred to as the molar volume.\",\n \"Gas\\n\\nAvogadro's law states that the volume occupied by an ideal gas is proportional to the number of moles (or molecules) present in the container. This gives rise to the molar volume of a gas, which at STP is 22.4 dm3 (or litres). The relation is given by\",\n \"Gas\\n\\n\\\\frac{V_1}{n_1}=\\\\frac{V_2}{n_2} \\\\,\",\n \"Gas\\n\\nwhere n is equal to the number of moles of gas (the number of molecules divided by Avogadro's Number).\",\n \"Gas\\n\\nDalton's law\",\n \"Gas\\n\\nIn 1801, John Dalton published the Law of Partial Pressures from his work with ideal gas law relationship: The pressure of a mixture of non reactive gases is equal to the sum of the pressures of all of the constituent gases alone. Mathematically, this can be represented for n species as:\",\n \"Gas\\n\\nPressuretotal = Pressure1 + Pressure2 + ... + Pressuren\",\n \"Gas\\n\\nThe image of Dalton's journal depicts symbology he used as shorthand to record the path he followed. Among his key journal observations upon mixing unreactive \\\"elastic fluids\\\" (gases) were the following: \\n*Unlike liquids, heavier gases did not drift to the bottom upon mixing.\\n*Gas particle identity played no role in determining final pressure (they behaved as if their size was negligible).\",\n \"Gas\\n\\nSpecial topics\",\n \"Gas\\n\\nCompressibility\",\n \"Gas\\n\\nThermodynamicists use this factor (Z) to alter the ideal gas equation to account for compressibility effects of real gases. This factor represents the ratio of actual to ideal specific volumes. It is sometimes referred to as a \\\"fudge-factor\\\" or correction to expand the useful range of the ideal gas law for design purposes. Usually this Z value is very close to unity. The compressibility factor image illustrates how Z varies over a range of very cold temperatures.\",\n \"Gas\\n\\nReynolds number\",\n \"Gas\\n\\nIn fluid mechanics, the Reynolds number is the ratio of inertial forces (vsρ) to viscous forces (μ/L). It is one of the most important dimensionless numbers in fluid dynamics and is used, usually along with other dimensionless numbers, to provide a criterion for determining dynamic similitude. As such, the Reynolds number provides the link between modeling results (design) and the full-scale actual conditions. It can also be used to characterize the flow.\",\n \"Gas\\n\\nViscosity\",\n \"Gas\\n\\nViscosity, a physical property, is a measure of how well adjacent molecules stick to one another. A solid can withstand a shearing force due to the strength of these sticky intermolecular forces. A fluid will continuously deform when subjected to a similar load. While a gas has a lower value of viscosity than a liquid, it is still an observable property. If gases had no viscosity, then they would not stick to the surface of a wing and form a boundary layer. A study of the delta wing in the Schlieren image reveals that the gas particles stick to one another (see Boundary layer section).\",\n \"Gas\\n\\nTurbulence\",\n \"Gas\\n\\nIn fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic, stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time. The Satellite view of weather around Robinson Crusoe Islands illustrates just one example.\",\n \"Gas\\n\\nBoundary layer\",\n \"Gas\\n\\nParticles will, in effect, \\\"stick\\\" to the surface of an object moving through it. This layer of particles is called the boundary layer. At the surface of the object, it is essentially static due to the friction of the surface. The object, with its boundary layer is effectively the new shape of the object that the rest of the molecules \\\"see\\\" as the object approaches. This boundary layer can separate from the surface, essentially creating a new surface and completely changing the flow path. The classical example of this is a stalling airfoil. The delta wing image clearly shows the boundary layer thickening as the gas flows from right to left along the leading edge.\",\n \"Gas\\n\\nMaximum entropy principle\",\n \"Gas\\n\\nAs the total number of degrees of freedom approaches infinity, the system will be found in the macrostate that corresponds to the highest multiplicity. In order to illustrate this principle, observe the skin temperature of a frozen metal bar. Using a thermal image of the skin temperature, note the temperature distribution on the surface. This initial observation of temperature represents a \\\"microstate.\\\" At some future time, a second observation of the skin temperature produces a second microstate. By continuing this observation process, it is possible to produce a series of microstates that illustrate the thermal history of the bar's surface. Characterization of this historical series of microstates is possible by choosing the macrostate that successfully classifies them all into a single grouping.\",\n \"Gas\\n\\nThermodynamic equilibrium\",\n \"Gas\\n\\nWhen energy transfer ceases from a system, this condition is referred to as thermodynamic equilibrium. Usually this condition implies the system and surroundings are at the same temperature so that heat no longer transfers between them. It also implies that external forces are balanced (volume does not change), and all chemical reactions within the system are complete. The timeline varies for these events depending on the system in question. A container of ice allowed to melt at room temperature takes hours, while in semiconductors the heat transfer that occurs in the device transition from an on to off state could be on the order of a few nanoseconds.\"\n]","isConversational":false}}},{"rowIdx":1795,"cells":{"id":{"kind":"string","value":"tc_2771"},"question":{"kind":"string","value":"What is the ability of fluids to offer resistance to flow?"},"answer":{"kind":"string","value":"Viscosity"},"answer_aliases":{"kind":"list like","value":["inviscid","coefficient of viscosity","dynamic kinematic viscosity","viscous shear","viscosity","kinematic viscosity","pa·s","pascal second","sutherland s formula","eddy viscosity","centistoke","viscous force","rhe","inviscid fluid","millipoiseuille","centistokes","pa s","viscosity of amorphous materials","viscous","shear viscosity","viscousity","dynamic viscosity","inviscid fluids","stokes unit","viscous friction","bulk viscosity","viscous forces","viscocity","absolute viscosity"],"string":"[\n \"inviscid\",\n \"coefficient of viscosity\",\n \"dynamic kinematic viscosity\",\n \"viscous shear\",\n \"viscosity\",\n \"kinematic viscosity\",\n \"pa·s\",\n \"pascal second\",\n \"sutherland s formula\",\n \"eddy viscosity\",\n \"centistoke\",\n \"viscous force\",\n \"rhe\",\n \"inviscid fluid\",\n \"millipoiseuille\",\n \"centistokes\",\n \"pa s\",\n \"viscosity of amorphous materials\",\n \"viscous\",\n \"shear viscosity\",\n \"viscousity\",\n \"dynamic viscosity\",\n \"inviscid fluids\",\n \"stokes unit\",\n \"viscous friction\",\n \"bulk viscosity\",\n \"viscous forces\",\n \"viscocity\",\n \"absolute viscosity\"\n]","isConversational":false},"documents":{"kind":"list like","value":["Fluid\n\nIn physics, a fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids. Fluids are substances that have zero shear modulus or, in simpler terms, a fluid is a substance which cannot resist any shear force applied to it.","Fluid\n\nAlthough the term \"fluid\" includes both the liquid and gas phases, in common usage, \"fluid\" is often used as a synonym for \"liquid\", with no implication that gas could also be present. For example, \"brake fluid\" is hydraulic oil and will not perform its required incompressible function if there is gas in it. This colloquial usage of the term is also common in medicine and in nutrition (\"take plenty of fluids\").","Fluid\n\nLiquids form a free surface (that is, a surface not created by the container) while gases do not. The distinction between solids and fluid is not entirely obvious. The distinction is made by evaluating the viscosity of the substance. Silly Putty can be considered to behave like a solid or a fluid, depending on the time period over which it is observed. It is best described as a viscoelastic fluid. There are many examples of substances proving difficult to classify. A particularly interesting one is pitch, as demonstrated in the pitch drop experiment currently running at the University of Queensland.","Fluid\n\nPhysics","Fluid\n\nFluids display properties such as:\n* not resisting deformation, or resisting it only slightly (viscosity), and\n* the ability to flow (also described as the ability to take on the shape of the container).This also means that all liquids have the property of fluidity.\nThese properties are typically a function of their inability to support a shear stress in static equilibrium.","Fluid\n\nSolids can be subjected to shear stresses, and to normal stresses—both compressive and tensile. In contrast, ideal fluids can only be subjected to normal, compressive stress which is called pressure. Real fluids display viscosity and so are capable of being subjected to low levels of shear stress.","Fluid\n\nModelling","Fluid\n\nIn a solid, shear stress is a function of strain, but in a fluid, shear stress is a function of strain rate. A consequence of this behavior is Pascal's law which describes the role of pressure in characterizing a fluid's state.","Fluid\n\nDepending on the relationship between shear stress, and the rate of strain and its derivatives, fluids can be characterized as one of the following:\n*Newtonian fluids: where stress is directly proportional to rate of strain\n*Non-Newtonian fluids: where stress is not proportional to rate of strain, its higher powers and derivatives.","Fluid\n\nThe behavior of fluids can be described by the Navier–Stokes equations—a set of partial differential equations which are based on:\n* continuity (conservation of mass),\n* conservation of linear momentum,\n* conservation of angular momentum,\n* conservation of energy.","Fluid\n\nThe study of fluids is fluid mechanics, which is subdivided into fluid dynamics and fluid statics depending on whether the fluid is in motion.","Fluid dynamics\n\nIn physics, fluid dynamics is a subdiscipline of fluid mechanics that deals with fluid flow—the natural science of fluids (liquids and gases) in motion. It has several subdisciplines itself, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation. Some of its principles are even used in traffic engineering, where traffic is treated as a continuous fluid, and crowd dynamics.","Fluid dynamics\n\nFluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves calculating various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time.","Fluid dynamics\n\nBefore the twentieth century, hydrodynamics was synonymous with fluid dynamics. This is still reflected in names of some fluid dynamics topics, like magnetohydrodynamics and hydrodynamic stability, both of which can also be applied to gases.","Fluid dynamics\n\nEquations of fluid dynamics","Fluid dynamics\n\nThe foundational axioms of fluid dynamics are the conservation laws, specifically, conservation of mass, conservation of linear momentum (also known as Newton's Second Law of Motion), and conservation of energy (also known as First Law of Thermodynamics). These are based on classical mechanics and are modified in quantum mechanics and general relativity. They are expressed using the Reynolds Transport Theorem.","Fluid dynamics\n\nIn addition to the above, fluids are assumed to obey the continuum assumption. Fluids are composed of molecules that collide with one another and solid objects. However, the continuum assumption considers fluids as continuous, rather than discrete. Consequently, properties such as density, pressure, temperature, and flow velocity are assumed well-defined at infinitesimally small points, and are assumed to vary continuously from one point to another. The fact that the fluid is made up of discrete molecules is ignored.","Fluid dynamics\n\nFor fluids that are sufficiently dense to be a continuum, do not contain ionized species, and have flow velocities small in relation to the speed of light, the momentum equations for Newtonian fluids are the Navier–Stokes equations—which is a non-linear set of differential equations that describes the flow of a fluid whose stress depends linearly on flow velocity gradients and pressure. The unsimplified equations do not have a general closed-form solution, so they are primarily of use in Computational Fluid Dynamics. The equations can be simplified in a number of ways, all of which make them easier to solve. Some of them allow appropriate fluid dynamics problems be solved in closed form.","Fluid dynamics\n\nIn addition to the mass, momentum, and energy conservation equations, a thermodynamical equation of state giving the pressure as a function of other thermodynamic variables for the fluid is required to completely specify the problem. An example of this would be the perfect gas equation of state:","Fluid dynamics\n\np= \\frac{\\rho R_u T}{M}","Fluid dynamics\n\nwhere p is pressure, ρ is density, Ru is the gas constant, M is molar mass and T is temperature.\nConservation laws","Fluid dynamics\n\nThree conservation laws are used to solve fluid dynamics problems, and may be written in integral or differential form. Mathematical formulations of these conservation laws may be interpreted by considering the concept of a control volume. A control volume is a specified volume in space through which air can flow in and out. Integral formulations of the conservation laws consider the change in mass, momentum, or energy within the control volume. Differential formulations of the conservation laws apply Stokes' theorem to yield an expression which may be interpreted as the integral form of the law applied to an infinitesimal volume at a point within the flow.","Fluid dynamics\n\n*Mass continuity (conservation of mass): The rate of change of fluid mass inside a control volume must be equal to the net rate of fluid flow into the volume. Physically, this statement requires that mass is neither created nor destroyed in the control volume, and can be translated into the integral form of the continuity equation:\n:{\\partial \\over \\partial t} \\iiint_V \\rho \\, dV = - \\, {}","Fluid dynamics\n\nAbove, \\rho is the fluid density, u is the flow velocity vector, and t is time. The left-hand side of the above expression contains a triple integral over the control volume, whereas the right-hand side contains a surface integral over the surface of the control volume. The differential form of the continuity equation is, by the divergence theorem:","Fluid dynamics\n\n:\\ {\\partial \\rho \\over \\partial t} + \\nabla \\cdot (\\rho \\mathbf{u}) = 0 \n*Conservation of momentum: This equation applies Newton's second law of motion to the control volume, requiring that any change in momentum of the air within a control volume be due to the net flow of air into the volume and the action of external forces on the air within the volume. In the integral formulation of this equation, body forces here are represented by fbody, the body force per unit mass. Surface forces, such as viscous forces, are represented by \\mathbf{F}_\\text{surf}, the net force due to stresses on the control volume surface.","Fluid dynamics\n\n: \\frac{\\partial}{\\partial t} \\iiint_{\\scriptstyle V} \\rho\\mathbf{u} \\, dV = -\\, {} (\\rho\\mathbf{u}\\cdot d\\mathbf{S}) \\mathbf{u} -{} \\displaystyle{}+ \\iiint_{\\scriptstyle V} \\rho \\mathbf{f}_\\text{body} \\, dV + \\mathbf{F}_\\text{surf}","Fluid dynamics\n\nThe differential form of the momentum conservation equation is as follows. Here, both surface and body forces are accounted for in one total force, F. For example, F may be expanded into an expression for the frictional and gravitational forces acting on an internal flow.\n:\\ {D \\mathbf{u} \\over D t} = \\mathbf{F} - {\\nabla p \\over \\rho}","Fluid dynamics\n\nIn aerodynamics, air is assumed to be a Newtonian fluid, which posits a linear relationship between the shear stress (due to internal friction forces) and the rate of strain of the fluid. The equation above is a vector equation: in a three-dimensional flow, it can be expressed as three scalar equations. The conservation of momentum equations for the compressible, viscous flow case are called the Navier–Stokes equations. \n*Conservation of energy: Although energy can be converted from one form to another, the total energy in a given closed system remains constant.","Fluid dynamics\n\n:\\ \\rho {Dh \\over Dt} = {D p \\over D t} + \\nabla \\cdot \\left( k \\nabla T\\right) + \\Phi","Fluid dynamics\n\nAbove, h is enthalpy, k is the thermal conductivity of the fluid, T is temperature, and \\Phi is the viscous dissipation function. The viscous dissipation function governs the rate at which mechanical energy of the flow is converted to heat. The second law of thermodynamics requires that the dissipation term is always positive: viscosity cannot create energy within the control volume. The expression on the left side is a material derivative.","Fluid dynamics\n\nCompressible vs incompressible flow","Fluid dynamics\n\nAll fluids are compressible to some extent, that is, changes in pressure or temperature cause changes in density. However, in many situations the changes in pressure and temperature are sufficiently small that the changes in density are negligible. In this case the flow can be modelled as an incompressible flow. Otherwise the more general compressible flow equations must be used.","Fluid dynamics\n\nMathematically, incompressibility is expressed by saying that the density ρ of a fluid parcel does not change as it moves in the flow field, i.e.,\n\\frac{\\mathrm{D} \\rho}{\\mathrm{D}t} = 0 \\, ,\nwhere D/Dt is the substantial derivative, which is the sum of local and convective derivatives. This additional constraint simplifies the governing equations, especially in the case when the fluid has a uniform density.","Fluid dynamics\n\nFor flow of gases, to determine whether to use compressible or incompressible fluid dynamics, the Mach number of the flow is evaluated. As a rough guide, compressible effects can be ignored at Mach numbers below approximately 0.3. For liquids, whether the incompressible assumption is valid depends on the fluid properties (specifically the critical pressure and temperature of the fluid) and the flow conditions (how close to the critical pressure the actual flow pressure becomes). Acoustic problems always require allowing compressibility, since sound waves are compression waves involving changes in pressure and density of the medium through which they propagate.","Fluid dynamics\n\nInviscid vs Newtonian and non-Newtonian fluids","Fluid dynamics\n\nAll fluids are viscous, meaning that they exert some resistance to deformation: neighbouring parcels of fluid moving at different velocities exert viscous forces on each other. The velocity gradient is referred to as a strain rate; it has dimensions T^{-1}. Isaac Newton showed that for many familiar fluids such as water and air, the stress due to these viscous forces is linearly related to the strain rate. Such fluids are called Newtonian fluids. The coefficient of proportionality is called the fluid's viscosity; for Newtonian fluids, it is a fluid property independent of the strain rate.","Fluid dynamics\n\nNon-Newtonian fluids have a more complicated, non-linear stress-strain behaviour. The sub-discipline of rheology studies the stress-strain behaviours of these fluids, which include emulsions and slurries, some viscoelastic materials such as blood and some polymers, and sticky liquids such as latex, honey and lubricants.","Fluid dynamics\n\nThe dynamic of fluid parcels is described with the help of Newton's second law. An accelerating parcel of fluid is subject to inertial effects.","Fluid dynamics\n\nThe Reynolds number is a dimensionless quantity which characterises the magnitude of inertial effects compared to the magnitude of viscous effects. A low Reynolds number (Re>1) indicate that the inertial effects have more effect on the velocity field than the viscous (friction) effects. In high Reynolds number flows, the flow is often modeled as an inviscid flow, an approximation in which viscosity is completely neglected. The Navier-Stokes equations then simplify into the Euler equations. Integrating these along a streamline in an inviscid flow yields Bernoulli's equation. When in addition to being inviscid, the flow is everywhere irrotational, Bernoulli's equation can be used throughout the flow field. Such flows are called potential flows, because the velocity field may be expressed as the gradient of a potential.","Fluid dynamics\n\nThis idea can work fairly well when the Reynolds number is high. However, problems such as those involving solid boundaries may require that the viscosity be included. Viscosity cannot be neglected near solid boundaries because the no-slip condition generates a thin region of large strain rate, the boundary layer, in which viscosity effects dominate and which thus generates vorticity. Therefore, to calculate net forces on bodies (such as wings), viscous flow equations must be used: inviscid flow theory fails to predict drag forces, a limitation known as the d'Alembert's paradox.","Fluid dynamics\n\nA commonly used model, especially in computational fluid dynamics, is to use two flow models: the Euler equations away from the body, and boundary layer equations in a region close to the body. The two solutions can then be matched with each other, using the method of matched asymptotic expansions.","Fluid dynamics\n\nSteady vs unsteady flow","Fluid dynamics\n\nWhen all the time derivatives of a flow field vanish, the flow is considered steady flow. Steady-state flow refers to the condition where the fluid properties at a point in the system do not change over time. Otherwise, flow is called unsteady (also called transient ). Whether a particular flow is steady or unsteady, can depend on the chosen frame of reference. For instance, laminar flow over a sphere is steady in the frame of reference that is stationary with respect to the sphere. In a frame of reference that is stationary with respect to a background flow, the flow is unsteady.","Fluid dynamics\n\nTurbulent flows are unsteady by definition. A turbulent flow can, however, be statistically stationary. According to Pope:","Fluid dynamics\n\nThis roughly means that all statistical properties are constant in time. Often, the mean field is the object of interest, and this is constant too in a statistically stationary flow.","Fluid dynamics\n\nSteady flows are often more tractable than otherwise similar unsteady flows. The governing equations of a steady problem have one dimension fewer (time) than the governing equations of the same problem without taking advantage of the steadiness of the flow field.","Fluid dynamics\n\nLaminar vs turbulent flow","Fluid dynamics\n\nTurbulence is flow characterized by recirculation, eddies, and apparent randomness. Flow in which turbulence is not exhibited is called laminar. It should be noted, however, that the presence of eddies or recirculation alone does not necessarily indicate turbulent flow—these phenomena may be present in laminar flow as well. Mathematically, turbulent flow is often represented via a Reynolds decomposition, in which the flow is broken down into the sum of an average component and a perturbation component.","Fluid dynamics\n\nIt is believed that turbulent flows can be described well through the use of the Navier–Stokes equations. Direct numerical simulation (DNS), based on the Navier–Stokes equations, makes it possible to simulate turbulent flows at moderate Reynolds numbers. Restrictions depend on the power of the computer used and the efficiency of the solution algorithm. The results of DNS have been found to agree well with experimental data for some flows.","Fluid dynamics\n\nMost flows of interest have Reynolds numbers much too high for DNS to be a viable option, given the state of computational power for the next few decades. Any flight vehicle large enough to carry a human (L > 3 m), moving faster than 72 km/h (20 m/s) is well beyond the limit of DNS simulation (Re = 4 million). Transport aircraft wings (such as on an Airbus A300 or Boeing 747) have Reynolds numbers of 40 million (based on the wing chord). Solving these real-life flow problems requires turbulence models for the foreseeable future. Reynolds-averaged Navier–Stokes equations (RANS) combined with turbulence modelling provides a model of the effects of the turbulent flow. Such a modelling mainly provides the additional momentum transfer by the Reynolds stresses, although the turbulence also enhances the heat and mass transfer. Another promising methodology is large eddy simulation (LES), especially in the guise of detached eddy simulation (DES)—which is a combination of RANS turbulence modelling and large eddy simulation.","Fluid dynamics\n\nSubsonic vs transonic, supersonic and hypersonic flows","Fluid dynamics\n\nWhile many terrestrial flows (e.g. flow of water through a pipe) occur at low mach numbers, many flows of practical interest (e.g. in aerodynamics) occur at high fractions of the Mach Number M=1 or in excess of it (supersonic flows). New phenomena occur at these Mach number regimes (e.g. shock waves for supersonic flow, transonic instability in a regime of flows with M nearly equal to 1, non-equilibrium chemical behaviour due to ionization in hypersonic flows) and it is necessary to treat each of these flow regimes separately.","Fluid dynamics\n\nMagnetohydrodynamics","Fluid dynamics\n\nMagnetohydrodynamics is the multi-disciplinary study of the flow of electrically conducting fluids in electromagnetic fields. Examples of such fluids include plasmas, liquid metals, and salt water. The fluid flow equations are solved simultaneously with Maxwell's equations of electromagnetism.","Fluid dynamics\n\nOther approximations","Fluid dynamics\n\nThere are a large number of other possible approximations to fluid dynamic problems. Some of the more commonly used are listed below.\n* The Boussinesq approximation neglects variations in density except to calculate buoyancy forces. It is often used in free convection problems where density changes are small.\n* Lubrication theory and Hele–Shaw flow exploits the large aspect ratio of the domain to show that certain terms in the equations are small and so can be neglected.\n* Slender-body theory is a methodology used in Stokes flow problems to estimate the force on, or flow field around, a long slender object in a viscous fluid.\n* The shallow-water equations can be used to describe a layer of relatively inviscid fluid with a free surface, in which surface gradients are small.\n* The Boussinesq equations are applicable to surface waves on thicker layers of fluid and with steeper surface slopes.\n* Darcy's law is used for flow in porous media, and works with variables averaged over several pore-widths.\n* In rotating systems, the quasi-geostrophic equations assume an almost perfect balance between pressure gradients and the Coriolis force. It is useful in the study of atmospheric dynamics.","Fluid dynamics\n\nTerminology in fluid dynamics","Fluid dynamics\n\nThe concept of pressure is central to the study of both fluid statics and fluid dynamics. A pressure can be identified for every point in a body of fluid, regardless of whether the fluid is in motion or not. Pressure can be measured using an aneroid, Bourdon tube, mercury column, or various other methods.","Fluid dynamics\n\nSome of the terminology that is necessary in the study of fluid dynamics is not found in other similar areas of study. In particular, some of the terminology used in fluid dynamics is not used in fluid statics.","Fluid dynamics\n\nTerminology in incompressible fluid dynamics","Fluid dynamics\n\nThe concepts of total pressure and dynamic pressure arise from Bernoulli's equation and are significant in the study of all fluid flows. (These two pressures are not pressures in the usual sense—they cannot be measured using an aneroid, Bourdon tube or mercury column.) To avoid potential ambiguity when referring to pressure in fluid dynamics, many authors use the term static pressure to distinguish it from total pressure and dynamic pressure. Static pressure is identical to pressure and can be identified for every point in a fluid flow field.","Fluid dynamics\n\nIn Aerodynamics, L.J. Clancy writes: To distinguish it from the total and dynamic pressures, the actual pressure of the fluid, which is associated not with its motion but with its state, is often referred to as the static pressure, but where the term pressure alone is used it refers to this static pressure.","Fluid dynamics\n\nA point in a fluid flow where the flow has come to rest (i.e. speed is equal to zero adjacent to some solid body immersed in the fluid flow) is of special significance. It is of such importance that it is given a special name—a stagnation point. The static pressure at the stagnation point is of special significance and is given its own name—stagnation pressure. In incompressible flows, the stagnation pressure at a stagnation point is equal to the total pressure throughout the flow field.","Fluid dynamics\n\nTerminology in compressible fluid dynamics","Fluid dynamics\n\nIn a compressible fluid, such as air, the temperature and density are essential when determining the state of the fluid. In addition to the concept of total pressure (also known as stagnation pressure), the concepts of total (or stagnation) temperature and total (or stagnation) density are also essential in any study of compressible fluid flows. To avoid potential ambiguity when referring to temperature and density, many authors use the terms static temperature and static density. Static temperature is identical to temperature; and static density is identical to density; and both can be identified for every point in a fluid flow field.","Fluid dynamics\n\nThe temperature and density at a stagnation point are called stagnation temperature and stagnation density.","Fluid dynamics\n\nA similar approach is also taken with the thermodynamic properties of compressible fluids. Many authors use the terms total (or stagnation) enthalpy and total (or stagnation) entropy. The terms static enthalpy and static entropy appear less common, but where they are used they mean enthalpy and entropy respectively, using the prefix \"static\" to avoid ambiguity with their 'total' or 'stagnation' counterparts. Because the 'total' flow conditions are defined by isentropically bringing the fluid to rest, the total (or stagnation) entropy is by definition always equal to the \"static\" entropy."],"string":"[\n \"Fluid\\n\\nIn physics, a fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids. Fluids are substances that have zero shear modulus or, in simpler terms, a fluid is a substance which cannot resist any shear force applied to it.\",\n \"Fluid\\n\\nAlthough the term \\\"fluid\\\" includes both the liquid and gas phases, in common usage, \\\"fluid\\\" is often used as a synonym for \\\"liquid\\\", with no implication that gas could also be present. For example, \\\"brake fluid\\\" is hydraulic oil and will not perform its required incompressible function if there is gas in it. This colloquial usage of the term is also common in medicine and in nutrition (\\\"take plenty of fluids\\\").\",\n \"Fluid\\n\\nLiquids form a free surface (that is, a surface not created by the container) while gases do not. The distinction between solids and fluid is not entirely obvious. The distinction is made by evaluating the viscosity of the substance. Silly Putty can be considered to behave like a solid or a fluid, depending on the time period over which it is observed. It is best described as a viscoelastic fluid. There are many examples of substances proving difficult to classify. A particularly interesting one is pitch, as demonstrated in the pitch drop experiment currently running at the University of Queensland.\",\n \"Fluid\\n\\nPhysics\",\n \"Fluid\\n\\nFluids display properties such as:\\n* not resisting deformation, or resisting it only slightly (viscosity), and\\n* the ability to flow (also described as the ability to take on the shape of the container).This also means that all liquids have the property of fluidity.\\nThese properties are typically a function of their inability to support a shear stress in static equilibrium.\",\n \"Fluid\\n\\nSolids can be subjected to shear stresses, and to normal stresses—both compressive and tensile. In contrast, ideal fluids can only be subjected to normal, compressive stress which is called pressure. Real fluids display viscosity and so are capable of being subjected to low levels of shear stress.\",\n \"Fluid\\n\\nModelling\",\n \"Fluid\\n\\nIn a solid, shear stress is a function of strain, but in a fluid, shear stress is a function of strain rate. A consequence of this behavior is Pascal's law which describes the role of pressure in characterizing a fluid's state.\",\n \"Fluid\\n\\nDepending on the relationship between shear stress, and the rate of strain and its derivatives, fluids can be characterized as one of the following:\\n*Newtonian fluids: where stress is directly proportional to rate of strain\\n*Non-Newtonian fluids: where stress is not proportional to rate of strain, its higher powers and derivatives.\",\n \"Fluid\\n\\nThe behavior of fluids can be described by the Navier–Stokes equations—a set of partial differential equations which are based on:\\n* continuity (conservation of mass),\\n* conservation of linear momentum,\\n* conservation of angular momentum,\\n* conservation of energy.\",\n \"Fluid\\n\\nThe study of fluids is fluid mechanics, which is subdivided into fluid dynamics and fluid statics depending on whether the fluid is in motion.\",\n \"Fluid dynamics\\n\\nIn physics, fluid dynamics is a subdiscipline of fluid mechanics that deals with fluid flow—the natural science of fluids (liquids and gases) in motion. It has several subdisciplines itself, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation. Some of its principles are even used in traffic engineering, where traffic is treated as a continuous fluid, and crowd dynamics.\",\n \"Fluid dynamics\\n\\nFluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves calculating various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time.\",\n \"Fluid dynamics\\n\\nBefore the twentieth century, hydrodynamics was synonymous with fluid dynamics. This is still reflected in names of some fluid dynamics topics, like magnetohydrodynamics and hydrodynamic stability, both of which can also be applied to gases.\",\n \"Fluid dynamics\\n\\nEquations of fluid dynamics\",\n \"Fluid dynamics\\n\\nThe foundational axioms of fluid dynamics are the conservation laws, specifically, conservation of mass, conservation of linear momentum (also known as Newton's Second Law of Motion), and conservation of energy (also known as First Law of Thermodynamics). These are based on classical mechanics and are modified in quantum mechanics and general relativity. They are expressed using the Reynolds Transport Theorem.\",\n \"Fluid dynamics\\n\\nIn addition to the above, fluids are assumed to obey the continuum assumption. Fluids are composed of molecules that collide with one another and solid objects. However, the continuum assumption considers fluids as continuous, rather than discrete. Consequently, properties such as density, pressure, temperature, and flow velocity are assumed well-defined at infinitesimally small points, and are assumed to vary continuously from one point to another. The fact that the fluid is made up of discrete molecules is ignored.\",\n \"Fluid dynamics\\n\\nFor fluids that are sufficiently dense to be a continuum, do not contain ionized species, and have flow velocities small in relation to the speed of light, the momentum equations for Newtonian fluids are the Navier–Stokes equations—which is a non-linear set of differential equations that describes the flow of a fluid whose stress depends linearly on flow velocity gradients and pressure. The unsimplified equations do not have a general closed-form solution, so they are primarily of use in Computational Fluid Dynamics. The equations can be simplified in a number of ways, all of which make them easier to solve. Some of them allow appropriate fluid dynamics problems be solved in closed form.\",\n \"Fluid dynamics\\n\\nIn addition to the mass, momentum, and energy conservation equations, a thermodynamical equation of state giving the pressure as a function of other thermodynamic variables for the fluid is required to completely specify the problem. An example of this would be the perfect gas equation of state:\",\n \"Fluid dynamics\\n\\np= \\\\frac{\\\\rho R_u T}{M}\",\n \"Fluid dynamics\\n\\nwhere p is pressure, ρ is density, Ru is the gas constant, M is molar mass and T is temperature.\\nConservation laws\",\n \"Fluid dynamics\\n\\nThree conservation laws are used to solve fluid dynamics problems, and may be written in integral or differential form. Mathematical formulations of these conservation laws may be interpreted by considering the concept of a control volume. A control volume is a specified volume in space through which air can flow in and out. Integral formulations of the conservation laws consider the change in mass, momentum, or energy within the control volume. Differential formulations of the conservation laws apply Stokes' theorem to yield an expression which may be interpreted as the integral form of the law applied to an infinitesimal volume at a point within the flow.\",\n \"Fluid dynamics\\n\\n*Mass continuity (conservation of mass): The rate of change of fluid mass inside a control volume must be equal to the net rate of fluid flow into the volume. Physically, this statement requires that mass is neither created nor destroyed in the control volume, and can be translated into the integral form of the continuity equation:\\n:{\\\\partial \\\\over \\\\partial t} \\\\iiint_V \\\\rho \\\\, dV = - \\\\, {}\",\n \"Fluid dynamics\\n\\nAbove, \\\\rho is the fluid density, u is the flow velocity vector, and t is time. The left-hand side of the above expression contains a triple integral over the control volume, whereas the right-hand side contains a surface integral over the surface of the control volume. The differential form of the continuity equation is, by the divergence theorem:\",\n \"Fluid dynamics\\n\\n:\\\\ {\\\\partial \\\\rho \\\\over \\\\partial t} + \\\\nabla \\\\cdot (\\\\rho \\\\mathbf{u}) = 0 \\n*Conservation of momentum: This equation applies Newton's second law of motion to the control volume, requiring that any change in momentum of the air within a control volume be due to the net flow of air into the volume and the action of external forces on the air within the volume. In the integral formulation of this equation, body forces here are represented by fbody, the body force per unit mass. Surface forces, such as viscous forces, are represented by \\\\mathbf{F}_\\\\text{surf}, the net force due to stresses on the control volume surface.\",\n \"Fluid dynamics\\n\\n: \\\\frac{\\\\partial}{\\\\partial t} \\\\iiint_{\\\\scriptstyle V} \\\\rho\\\\mathbf{u} \\\\, dV = -\\\\, {} (\\\\rho\\\\mathbf{u}\\\\cdot d\\\\mathbf{S}) \\\\mathbf{u} -{} \\\\displaystyle{}+ \\\\iiint_{\\\\scriptstyle V} \\\\rho \\\\mathbf{f}_\\\\text{body} \\\\, dV + \\\\mathbf{F}_\\\\text{surf}\",\n \"Fluid dynamics\\n\\nThe differential form of the momentum conservation equation is as follows. Here, both surface and body forces are accounted for in one total force, F. For example, F may be expanded into an expression for the frictional and gravitational forces acting on an internal flow.\\n:\\\\ {D \\\\mathbf{u} \\\\over D t} = \\\\mathbf{F} - {\\\\nabla p \\\\over \\\\rho}\",\n \"Fluid dynamics\\n\\nIn aerodynamics, air is assumed to be a Newtonian fluid, which posits a linear relationship between the shear stress (due to internal friction forces) and the rate of strain of the fluid. The equation above is a vector equation: in a three-dimensional flow, it can be expressed as three scalar equations. The conservation of momentum equations for the compressible, viscous flow case are called the Navier–Stokes equations. \\n*Conservation of energy: Although energy can be converted from one form to another, the total energy in a given closed system remains constant.\",\n \"Fluid dynamics\\n\\n:\\\\ \\\\rho {Dh \\\\over Dt} = {D p \\\\over D t} + \\\\nabla \\\\cdot \\\\left( k \\\\nabla T\\\\right) + \\\\Phi\",\n \"Fluid dynamics\\n\\nAbove, h is enthalpy, k is the thermal conductivity of the fluid, T is temperature, and \\\\Phi is the viscous dissipation function. The viscous dissipation function governs the rate at which mechanical energy of the flow is converted to heat. The second law of thermodynamics requires that the dissipation term is always positive: viscosity cannot create energy within the control volume. The expression on the left side is a material derivative.\",\n \"Fluid dynamics\\n\\nCompressible vs incompressible flow\",\n \"Fluid dynamics\\n\\nAll fluids are compressible to some extent, that is, changes in pressure or temperature cause changes in density. However, in many situations the changes in pressure and temperature are sufficiently small that the changes in density are negligible. In this case the flow can be modelled as an incompressible flow. Otherwise the more general compressible flow equations must be used.\",\n \"Fluid dynamics\\n\\nMathematically, incompressibility is expressed by saying that the density ρ of a fluid parcel does not change as it moves in the flow field, i.e.,\\n\\\\frac{\\\\mathrm{D} \\\\rho}{\\\\mathrm{D}t} = 0 \\\\, ,\\nwhere D/Dt is the substantial derivative, which is the sum of local and convective derivatives. This additional constraint simplifies the governing equations, especially in the case when the fluid has a uniform density.\",\n \"Fluid dynamics\\n\\nFor flow of gases, to determine whether to use compressible or incompressible fluid dynamics, the Mach number of the flow is evaluated. As a rough guide, compressible effects can be ignored at Mach numbers below approximately 0.3. For liquids, whether the incompressible assumption is valid depends on the fluid properties (specifically the critical pressure and temperature of the fluid) and the flow conditions (how close to the critical pressure the actual flow pressure becomes). Acoustic problems always require allowing compressibility, since sound waves are compression waves involving changes in pressure and density of the medium through which they propagate.\",\n \"Fluid dynamics\\n\\nInviscid vs Newtonian and non-Newtonian fluids\",\n \"Fluid dynamics\\n\\nAll fluids are viscous, meaning that they exert some resistance to deformation: neighbouring parcels of fluid moving at different velocities exert viscous forces on each other. The velocity gradient is referred to as a strain rate; it has dimensions T^{-1}. Isaac Newton showed that for many familiar fluids such as water and air, the stress due to these viscous forces is linearly related to the strain rate. Such fluids are called Newtonian fluids. The coefficient of proportionality is called the fluid's viscosity; for Newtonian fluids, it is a fluid property independent of the strain rate.\",\n \"Fluid dynamics\\n\\nNon-Newtonian fluids have a more complicated, non-linear stress-strain behaviour. The sub-discipline of rheology studies the stress-strain behaviours of these fluids, which include emulsions and slurries, some viscoelastic materials such as blood and some polymers, and sticky liquids such as latex, honey and lubricants.\",\n \"Fluid dynamics\\n\\nThe dynamic of fluid parcels is described with the help of Newton's second law. An accelerating parcel of fluid is subject to inertial effects.\",\n \"Fluid dynamics\\n\\nThe Reynolds number is a dimensionless quantity which characterises the magnitude of inertial effects compared to the magnitude of viscous effects. A low Reynolds number (Re>1) indicate that the inertial effects have more effect on the velocity field than the viscous (friction) effects. In high Reynolds number flows, the flow is often modeled as an inviscid flow, an approximation in which viscosity is completely neglected. The Navier-Stokes equations then simplify into the Euler equations. Integrating these along a streamline in an inviscid flow yields Bernoulli's equation. When in addition to being inviscid, the flow is everywhere irrotational, Bernoulli's equation can be used throughout the flow field. Such flows are called potential flows, because the velocity field may be expressed as the gradient of a potential.\",\n \"Fluid dynamics\\n\\nThis idea can work fairly well when the Reynolds number is high. However, problems such as those involving solid boundaries may require that the viscosity be included. Viscosity cannot be neglected near solid boundaries because the no-slip condition generates a thin region of large strain rate, the boundary layer, in which viscosity effects dominate and which thus generates vorticity. Therefore, to calculate net forces on bodies (such as wings), viscous flow equations must be used: inviscid flow theory fails to predict drag forces, a limitation known as the d'Alembert's paradox.\",\n \"Fluid dynamics\\n\\nA commonly used model, especially in computational fluid dynamics, is to use two flow models: the Euler equations away from the body, and boundary layer equations in a region close to the body. The two solutions can then be matched with each other, using the method of matched asymptotic expansions.\",\n \"Fluid dynamics\\n\\nSteady vs unsteady flow\",\n \"Fluid dynamics\\n\\nWhen all the time derivatives of a flow field vanish, the flow is considered steady flow. Steady-state flow refers to the condition where the fluid properties at a point in the system do not change over time. Otherwise, flow is called unsteady (also called transient ). Whether a particular flow is steady or unsteady, can depend on the chosen frame of reference. For instance, laminar flow over a sphere is steady in the frame of reference that is stationary with respect to the sphere. In a frame of reference that is stationary with respect to a background flow, the flow is unsteady.\",\n \"Fluid dynamics\\n\\nTurbulent flows are unsteady by definition. A turbulent flow can, however, be statistically stationary. According to Pope:\",\n \"Fluid dynamics\\n\\nThis roughly means that all statistical properties are constant in time. Often, the mean field is the object of interest, and this is constant too in a statistically stationary flow.\",\n \"Fluid dynamics\\n\\nSteady flows are often more tractable than otherwise similar unsteady flows. The governing equations of a steady problem have one dimension fewer (time) than the governing equations of the same problem without taking advantage of the steadiness of the flow field.\",\n \"Fluid dynamics\\n\\nLaminar vs turbulent flow\",\n \"Fluid dynamics\\n\\nTurbulence is flow characterized by recirculation, eddies, and apparent randomness. Flow in which turbulence is not exhibited is called laminar. It should be noted, however, that the presence of eddies or recirculation alone does not necessarily indicate turbulent flow—these phenomena may be present in laminar flow as well. Mathematically, turbulent flow is often represented via a Reynolds decomposition, in which the flow is broken down into the sum of an average component and a perturbation component.\",\n \"Fluid dynamics\\n\\nIt is believed that turbulent flows can be described well through the use of the Navier–Stokes equations. Direct numerical simulation (DNS), based on the Navier–Stokes equations, makes it possible to simulate turbulent flows at moderate Reynolds numbers. Restrictions depend on the power of the computer used and the efficiency of the solution algorithm. The results of DNS have been found to agree well with experimental data for some flows.\",\n \"Fluid dynamics\\n\\nMost flows of interest have Reynolds numbers much too high for DNS to be a viable option, given the state of computational power for the next few decades. Any flight vehicle large enough to carry a human (L > 3 m), moving faster than 72 km/h (20 m/s) is well beyond the limit of DNS simulation (Re = 4 million). Transport aircraft wings (such as on an Airbus A300 or Boeing 747) have Reynolds numbers of 40 million (based on the wing chord). Solving these real-life flow problems requires turbulence models for the foreseeable future. Reynolds-averaged Navier–Stokes equations (RANS) combined with turbulence modelling provides a model of the effects of the turbulent flow. Such a modelling mainly provides the additional momentum transfer by the Reynolds stresses, although the turbulence also enhances the heat and mass transfer. Another promising methodology is large eddy simulation (LES), especially in the guise of detached eddy simulation (DES)—which is a combination of RANS turbulence modelling and large eddy simulation.\",\n \"Fluid dynamics\\n\\nSubsonic vs transonic, supersonic and hypersonic flows\",\n \"Fluid dynamics\\n\\nWhile many terrestrial flows (e.g. flow of water through a pipe) occur at low mach numbers, many flows of practical interest (e.g. in aerodynamics) occur at high fractions of the Mach Number M=1 or in excess of it (supersonic flows). New phenomena occur at these Mach number regimes (e.g. shock waves for supersonic flow, transonic instability in a regime of flows with M nearly equal to 1, non-equilibrium chemical behaviour due to ionization in hypersonic flows) and it is necessary to treat each of these flow regimes separately.\",\n \"Fluid dynamics\\n\\nMagnetohydrodynamics\",\n \"Fluid dynamics\\n\\nMagnetohydrodynamics is the multi-disciplinary study of the flow of electrically conducting fluids in electromagnetic fields. Examples of such fluids include plasmas, liquid metals, and salt water. The fluid flow equations are solved simultaneously with Maxwell's equations of electromagnetism.\",\n \"Fluid dynamics\\n\\nOther approximations\",\n \"Fluid dynamics\\n\\nThere are a large number of other possible approximations to fluid dynamic problems. Some of the more commonly used are listed below.\\n* The Boussinesq approximation neglects variations in density except to calculate buoyancy forces. It is often used in free convection problems where density changes are small.\\n* Lubrication theory and Hele–Shaw flow exploits the large aspect ratio of the domain to show that certain terms in the equations are small and so can be neglected.\\n* Slender-body theory is a methodology used in Stokes flow problems to estimate the force on, or flow field around, a long slender object in a viscous fluid.\\n* The shallow-water equations can be used to describe a layer of relatively inviscid fluid with a free surface, in which surface gradients are small.\\n* The Boussinesq equations are applicable to surface waves on thicker layers of fluid and with steeper surface slopes.\\n* Darcy's law is used for flow in porous media, and works with variables averaged over several pore-widths.\\n* In rotating systems, the quasi-geostrophic equations assume an almost perfect balance between pressure gradients and the Coriolis force. It is useful in the study of atmospheric dynamics.\",\n \"Fluid dynamics\\n\\nTerminology in fluid dynamics\",\n \"Fluid dynamics\\n\\nThe concept of pressure is central to the study of both fluid statics and fluid dynamics. A pressure can be identified for every point in a body of fluid, regardless of whether the fluid is in motion or not. Pressure can be measured using an aneroid, Bourdon tube, mercury column, or various other methods.\",\n \"Fluid dynamics\\n\\nSome of the terminology that is necessary in the study of fluid dynamics is not found in other similar areas of study. In particular, some of the terminology used in fluid dynamics is not used in fluid statics.\",\n \"Fluid dynamics\\n\\nTerminology in incompressible fluid dynamics\",\n \"Fluid dynamics\\n\\nThe concepts of total pressure and dynamic pressure arise from Bernoulli's equation and are significant in the study of all fluid flows. (These two pressures are not pressures in the usual sense—they cannot be measured using an aneroid, Bourdon tube or mercury column.) To avoid potential ambiguity when referring to pressure in fluid dynamics, many authors use the term static pressure to distinguish it from total pressure and dynamic pressure. Static pressure is identical to pressure and can be identified for every point in a fluid flow field.\",\n \"Fluid dynamics\\n\\nIn Aerodynamics, L.J. Clancy writes: To distinguish it from the total and dynamic pressures, the actual pressure of the fluid, which is associated not with its motion but with its state, is often referred to as the static pressure, but where the term pressure alone is used it refers to this static pressure.\",\n \"Fluid dynamics\\n\\nA point in a fluid flow where the flow has come to rest (i.e. speed is equal to zero adjacent to some solid body immersed in the fluid flow) is of special significance. It is of such importance that it is given a special name—a stagnation point. The static pressure at the stagnation point is of special significance and is given its own name—stagnation pressure. In incompressible flows, the stagnation pressure at a stagnation point is equal to the total pressure throughout the flow field.\",\n \"Fluid dynamics\\n\\nTerminology in compressible fluid dynamics\",\n \"Fluid dynamics\\n\\nIn a compressible fluid, such as air, the temperature and density are essential when determining the state of the fluid. In addition to the concept of total pressure (also known as stagnation pressure), the concepts of total (or stagnation) temperature and total (or stagnation) density are also essential in any study of compressible fluid flows. To avoid potential ambiguity when referring to temperature and density, many authors use the terms static temperature and static density. Static temperature is identical to temperature; and static density is identical to density; and both can be identified for every point in a fluid flow field.\",\n \"Fluid dynamics\\n\\nThe temperature and density at a stagnation point are called stagnation temperature and stagnation density.\",\n \"Fluid dynamics\\n\\nA similar approach is also taken with the thermodynamic properties of compressible fluids. Many authors use the terms total (or stagnation) enthalpy and total (or stagnation) entropy. The terms static enthalpy and static entropy appear less common, but where they are used they mean enthalpy and entropy respectively, using the prefix \\\"static\\\" to avoid ambiguity with their 'total' or 'stagnation' counterparts. Because the 'total' flow conditions are defined by isentropically bringing the fluid to rest, the total (or stagnation) entropy is by definition always equal to the \\\"static\\\" entropy.\"\n]","isConversational":false}}},{"rowIdx":1796,"cells":{"id":{"kind":"string","value":"tc_2773"},"question":{"kind":"string","value":"What is described as an ionized gas with approximately equal numbers of positive and negative charges?"},"answer":{"kind":"string","value":"Plasma"},"answer_aliases":{"kind":"list like","value":["plasmas","plasma biology","plasma disambiguation","biological plasma","plasm","plasma"],"string":"[\n \"plasmas\",\n \"plasma biology\",\n \"plasma disambiguation\",\n \"biological plasma\",\n \"plasm\",\n \"plasma\"\n]","isConversational":false},"documents":{"kind":"list like","value":["Plasma (physics)\n\nPlasma (from Greek πλάσμα, \"anything formed\" ) is one of the four fundamental states of matter, the others being solid, liquid, and gas. A plasma has properties unlike those of the other states.","Plasma (physics)\n\nA plasma can be created by heating a gas or subjecting it to a strong electromagnetic field, applied with a laser or microwave generator. This decreases or increases the number of electrons, creating positive or negative charged particles called ions, and is accompanied by the dissociation of molecular bonds, if present.","Plasma (physics)\n\nThe presence of a significant number of charge carriers makes plasma electrically conductive so that it responds strongly to electromagnetic fields. Like gas, plasma does not have a definite shape or a definite volume unless enclosed in a container. Unlike gas, under the influence of a magnetic field, it may form structures such as filaments, beams and double layers.","Plasma (physics)\n\nPlasma is the most abundant form of ordinary matter in the Universe (of the forms proven to exist; the more abundant dark matter is hypothetical and may or may not be explained by ordinary matter), most of which is in the rarefied intergalactic regions, particularly the intracluster medium, and in stars, including the Sun. A common form of plasma on Earth is produced in neon signs.","Plasma (physics)\n\nMuch of the understanding of plasma has come from the pursuit of controlled nuclear fusion and fusion power, for which plasma physics provides the scientific foundation.","Plasma (physics)\n\nProperties and parameters","Plasma (physics)\n\nDefinition","Plasma (physics)\n\nPlasma is an electrically neutral medium of unbound positive and negative particles (i.e. the overall charge of a plasma is roughly zero). It is important to note that although the particles are unbound, they are not ‘free’ in the sense of not experiencing forces. When a charged particle moves, it generates an electric current with magnetic fields; in plasma, the movement of a charged particle affects and is affected by the general field created by the movement of other charges. This governs collective behavior with many degrees of variation. Three factors are listed in the definition of a plasma stream:","Plasma (physics)\n\n#The plasma approximation: Charged particles must be close enough together that each particle influences many nearby charged particles, rather than just interacting with the closest particle (these collective effects are a distinguishing feature of a plasma). The plasma approximation is valid when the number of charge carriers within the sphere of influence (called the Debye sphere whose radius is the Debye screening length) of a particular particle is higher than unity to provide collective behavior of the charged particles. The average number of particles in the Debye sphere is given by the plasma parameter, \"Λ\" (the Greek uppercase letter Lambda).\n#Bulk interactions: The Debye screening length (defined above) is short compared to the physical size of the plasma. This criterion means that interactions in the bulk of the plasma are more important than those at its edges, where boundary effects may take place. When this criterion is satisfied, the plasma is quasineutral.\n#Plasma frequency: The electron plasma frequency (measuring plasma oscillations of the electrons) is large compared to the electron-neutral collision frequency (measuring frequency of collisions between electrons and neutral particles). When this condition is valid, electrostatic interactions dominate over the processes of ordinary gas kinetics.","Plasma (physics)\n\nRanges of parameters","Plasma (physics)\n\nThe factors of a plasma stream can vary by many orders of magnitude, but the properties of plasmas with apparently disparate parameters may be very similar (see plasma scaling). The following chart considers only conventional atomic plasmas and not exotic phenomena like quark gluon plasmas:","Plasma (physics)\n\nDegree of ionization","Plasma (physics)\n\nFor plasma to exist, ionization is necessary. The term \"plasma density\" by itself usually refers to the \"electron density\", that is, the number of free electrons per unit volume. The degree of ionization of a plasma is the proportion of atoms that have lost or gained electrons, and is controlled mostly by the temperature. Even a partially ionized gas in which as little as 1% of the particles are ionized can have the characteristics of a plasma (i.e., response to magnetic fields and high electrical conductivity). The degree of ionization, \\alpha, is defined as \\alpha \\frac{n_i}{n_i + n_n}, where n_i is the number density of ions and n_n is the number density of neutral atoms. The electron density is related to this by the average charge state \\langle Z\\rangle of the ions through n_e \n \\langle Z\\rangle n_i, where n_e is the number density of electrons.","Plasma (physics)\n\nTemperatures","Plasma (physics)\n\nPlasma temperature is commonly measured in kelvins or electronvolts and is, informally, a measure of the thermal kinetic energy per particle. High temperatures are usually needed to sustain ionization, which is a defining feature of a plasma. The degree of plasma ionization is determined by the electron temperature relative to the ionization energy (and more weakly by the density), in a relationship called the Saha equation. At low temperatures, ions and electrons tend to recombine into bound states—atoms —and the plasma will eventually become a gas.","Plasma (physics)\n\nIn most cases the electrons are close enough to thermal equilibrium that their temperature is relatively well-defined, even when there is a significant deviation from a Maxwellian energy distribution function, for example, due to UV radiation, energetic particles, or strong electric fields. Because of the large difference in mass, the electrons come to thermodynamic equilibrium amongst themselves much faster than they come into equilibrium with the ions or neutral atoms. For this reason, the ion temperature may be very different from (usually lower than) the electron temperature. This is especially common in weakly ionized technological plasmas, where the ions are often near the ambient temperature.","Plasma (physics)\n\nThermal vs. nonthermal plasmas","Plasma (physics)\n\nBased on the relative temperatures of the electrons, ions and neutrals, plasmas are classified as \"thermal\" or \"non-thermal\". Thermal plasmas have electrons and the heavy particles at the same temperature, i.e. they are in thermal equilibrium with each other. Nonthermal plasmas on the other hand have the ions and neutrals at a much lower temperature (sometimes room temperature), whereas electrons are much \"hotter\" (T_e \\gg T_n).","Plasma (physics)\n\nComplete vs. incomplete ionization","Plasma (physics)\n\nA plasma is sometimes referred to as being \"hot\" if it is nearly fully ionized, or \"cold\" if only a small fraction (for example 1%) of the gas molecules are ionized, but other definitions of the terms \"hot plasma\" and \"cold plasma\" are common. Even in a \"cold\" plasma, the electron temperature is still typically several thousand degrees Celsius. Plasmas utilized in \"plasma technology\" (\"technological plasmas\") are usually cold plasmas in the sense that only a small fraction of the gas molecules are ionized.","Plasma (physics)\n\nPlasma potential","Plasma (physics)\n\nSince plasmas are very good electrical conductors, electric potentials play an important role.\nThe potential as it exists on average in the space between charged particles, independent of the question of how it can be measured, is called the \"plasma potential\", or the \"space potential\". If an electrode is inserted into a plasma, its potential will generally lie considerably below the plasma potential due to what is termed a Debye sheath. The good electrical conductivity of plasmas makes their electric fields very small. This results in the important concept of \"quasineutrality\", which says the density of negative charges is approximately equal to the density of positive charges over large volumes of the plasma (n_e = \\langle Z\\rangle n_i), but on the scale of the Debye length there can be charge imbalance. In the special case that double layers are formed, the charge separation can extend some tens of Debye lengths.","Plasma (physics)\n\nThe magnitude of the potentials and electric fields must be determined by means other than simply finding the net charge density. A common example is to assume that the electrons satisfy the Boltzmann relation:\nn_e \\propto e^{e\\Phi/k_BT_e}.","Plasma (physics)\n\nDifferentiating this relation provides a means to calculate the electric field from the density:\n\\vec{E} = (k_BT_e/e)(\\nabla n_e/n_e).","Plasma (physics)\n\nIt is possible to produce a plasma that is not quasineutral. An electron beam, for example, has only negative charges. The density of a non-neutral plasma must generally be very low, or it must be very small, otherwise it will be dissipated by the repulsive electrostatic force.","Plasma (physics)\n\nIn astrophysical plasmas, Debye screening prevents electric fields from directly affecting the plasma over large distances, i.e., greater than the Debye length. However, the existence of charged particles causes the plasma to generate, and be affected by, magnetic fields. This can and does cause extremely complex behavior, such as the generation of plasma double layers, an object that separates charge over a few tens of Debye lengths. The dynamics of plasmas interacting with external and self-generated magnetic fields are studied in the academic discipline of magnetohydrodynamics.","Plasma (physics)\n\nMagnetization","Plasma (physics)\n\nPlasma with a magnetic field strong enough to influence the motion of the charged particles is said to be magnetized. A common quantitative criterion is that a particle on average completes at least one gyration around the magnetic field before making a collision, i.e., \\omega_{\\mathrm{ce}} / v_{\\mathrm{coll}} > 1, where \\omega_{\\mathrm{ce}} is the \"electron gyrofrequency\" and v_{\\mathrm{coll}} is the \"electron collision rate\". It is often the case that the electrons are magnetized while the ions are not. Magnetized plasmas are anisotropic, meaning that their properties in the direction parallel to the magnetic field are different from those perpendicular to it. While electric fields in plasmas are usually small due to the high conductivity, the electric field associated with a plasma moving in a magnetic field is given by \\mathbf{E} = -v\\times\\mathbf{B} (where \\mathbf{E} is the electric field, \\mathbf{v} is the velocity, and \\mathbf{B} is the magnetic field), and is not affected by Debye shielding.","Plasma (physics)\n\nComparison of plasma and gas phases","Plasma (physics)\n\nPlasma is often called the fourth state of matter after solid, liquids and gases, despite plasma typically being an ionized gas. It is distinct from these and other lower-energy states of matter. Although it is closely related to the gas phase in that it also has no definite form or volume, it differs in a number of ways, including the following:","Plasma (physics)\n\nCommon plasmas","Plasma (physics)\n\nPlasmas are by far the most common phase of ordinary matter in the universe, both by mass and by volume. Essentially, all of the visible light from space comes from stars, which are plasmas with a temperature such that they radiate strongly at visible wavelengths. Most of the ordinary (or baryonic) matter in the universe, however, is found in the intergalactic medium, which is also a plasma, but much hotter, so that it radiates primarily as X-rays.","Plasma (physics)\n\nIn 1937, Hannes Alfvén argued that if plasma pervaded the universe, it could then carry electric currents capable of generating a galactic magnetic field. After winning the Nobel Prize, he emphasized that: In order to understand the phenomena in a certain plasma region, it is necessary to map not only the magnetic but also the electric field and the electric currents. Space is filled with a network of currents which transfer energy and momentum over large or very large distances. The currents often pinch to filamentary or surface currents. The latter are likely to give space, as also interstellar and intergalactic space, a cellular structure.","Plasma (physics)\n\nBy contrast the current scientific consensus is that about 96% of the total energy density in the universe is not plasma or any other form of ordinary matter, but a combination of cold dark matter and dark energy. Our Sun, and all stars, are made of plasma, much of interstellar space is filled with a plasma, albeit a very sparse one, and intergalactic space too. Even black holes, which are not directly visible, are thought to be fuelled by accreting ionising matter (i.e. plasma), and they are associated with astrophysical jets of luminous ejected plasma, such as M87's jet that extends 5,000 light-years.","Plasma (physics)\n\nIn our solar system, interplanetary space is filled with the plasma of the Solar Wind that extends from the Sun out to the heliopause. However, the density of ordinary matter is much higher than average and much higher than that of either dark matter or dark energy. The planet Jupiter accounts for most of the non-plasma within the orbit of Pluto (about 0.1% by mass, or 10−15% by volume).","Plasma (physics)\n\nDust and small grains within a plasma will also pick up a net negative charge, so that they in turn may act like a very heavy negative ion component of the plasma (see dusty plasmas).","Plasma (physics)\n\nComplex plasma phenomena","Plasma (physics)\n\nAlthough the underlying equations governing plasmas are relatively simple, plasma behavior is extraordinarily varied and subtle: the emergence of unexpected behavior from a simple model is a typical feature of a complex system. Such systems lie in some sense on the boundary between ordered and disordered behavior and cannot typically be described either by simple, smooth, mathematical functions, or by pure randomness. The spontaneous formation of interesting spatial features on a wide range of length scales is one manifestation of plasma complexity. The features are interesting, for example, because they are very sharp, spatially intermittent (the distance between features is much larger than the features themselves), or have a fractal form. Many of these features were first studied in the laboratory, and have subsequently been recognized throughout the universe. Examples of complexity and complex structures in plasmas include:","Plasma (physics)\n\nFilamentation","Plasma (physics)\n\nStriations or string-like structures, also known as birkeland currents, are seen in many plasmas, like the plasma ball, the aurora, lightning, electric arcs, solar flares, and supernova remnants. They are sometimes associated with larger current densities, and the interaction with the magnetic field can form a magnetic rope structure. High power microwave breakdown at atmospheric pressure also leads to the formation of filamentary structures. (See also Plasma pinch)","Plasma (physics)\n\nFilamentation also refers to the self-focusing of a high power laser pulse. At high powers, the nonlinear part of the index of refraction becomes important and causes a higher index of refraction in the center of the laser beam, where the laser is brighter than at the edges, causing a feedback that focuses the laser even more. The tighter focused laser has a higher peak brightness (irradiance) that forms a plasma. The plasma has an index of refraction lower than one, and causes a defocusing of the laser beam. The interplay of the focusing index of refraction, and the defocusing plasma makes the formation of a long filament of plasma that can be micrometers to kilometers in length. One interesting aspect of the filamentation generated plasma is the relatively low ion density due to defocusing effects of the ionized electrons. (See also Filament propagation)","Plasma (physics)\n\nShocks or double layers","Plasma (physics)\n\nPlasma properties change rapidly (within a few Debye lengths) across a two-dimensional sheet in the presence of a (moving) shock or (stationary) double layer. Double layers involve localized charge separation, which causes a large potential difference across the layer, but does not generate an electric field outside the layer. Double layers separate adjacent plasma regions with different physical characteristics, and are often found in current carrying plasmas. They accelerate both ions and electrons.","Plasma (physics)\n\nElectric fields and circuits","Plasma (physics)\n\nQuasineutrality of a plasma requires that plasma currents close on themselves in electric circuits. Such circuits follow Kirchhoff's circuit laws and possess a resistance and inductance. These circuits must generally be treated as a strongly coupled system, with the behavior in each plasma region dependent on the entire circuit. It is this strong coupling between system elements, together with nonlinearity, which may lead to complex behavior. Electrical circuits in plasmas store inductive (magnetic) energy, and should the circuit be disrupted, for example, by a plasma instability, the inductive energy will be released as plasma heating and acceleration. This is a common explanation for the heating that takes place in the solar corona. Electric currents, and in particular, magnetic-field-aligned electric currents (which are sometimes generically referred to as \"Birkeland currents\"), are also observed in the Earth's aurora, and in plasma filaments.","Plasma (physics)\n\nCellular structure","Plasma (physics)\n\nNarrow sheets with sharp gradients may separate regions with different properties such as magnetization, density and temperature, resulting in cell-like regions. Examples include the magnetosphere, heliosphere, and heliospheric current sheet. Hannes Alfvén wrote: \"From the cosmological point of view, the most important new space research discovery is probably the cellular structure of space. As has been seen in every region of space accessible to in situ measurements, there are a number of 'cell walls', sheets of electric currents, which divide space into compartments with different magnetization, temperature, density, etc.\"","Plasma (physics)\n\nCritical ionization velocity","Plasma (physics)\n\nThe critical ionization velocity is the relative velocity between an ionized plasma and a neutral gas, above which a runaway ionization process takes place. The critical ionization process is a quite general mechanism for the conversion of the kinetic energy of a rapidly streaming gas into ionization and plasma thermal energy. Critical phenomena in general are typical of complex systems, and may lead to sharp spatial or temporal features.","Plasma (physics)\n\nUltracold plasma","Plasma (physics)\n\nUltracold plasmas are created in a magneto-optical trap (MOT) by trapping and cooling neutral atoms, to temperatures of 1 mK or lower, and then using another laser to ionize the atoms by giving each of the outermost electrons just enough energy to escape the electrical attraction of its parent ion.","Plasma (physics)\n\nOne advantage of ultracold plasmas are their well characterized and tunable initial conditions, including their size and electron temperature. By adjusting the wavelength of the ionizing laser, the kinetic energy of the liberated electrons can be tuned as low as 0.1 K, a limit set by the frequency bandwidth of the laser pulse. The ions inherit the millikelvin temperatures of the neutral atoms, but are quickly heated through a process known as disorder induced heating (DIH). This type of non-equilibrium ultracold plasma evolves rapidly, and displays many other interesting phenomena.","Plasma (physics)\n\nOne of the metastable states of a strongly nonideal plasma is Rydberg matter, which forms upon condensation of excited atoms.","Plasma (physics)\n\nNon-neutral plasma","Plasma (physics)\n\nThe strength and range of the electric force and the good conductivity of plasmas usually ensure that the densities of positive and negative charges in any sizeable region are equal (\"quasineutrality\"). A plasma with a significant excess of charge density, or, in the extreme case, is composed of a single species, is called a non-neutral plasma. In such a plasma, electric fields play a dominant role. Examples are charged particle beams, an electron cloud in a Penning trap and positron plasmas.","Plasma (physics)\n\nDusty plasma/grain plasma","Plasma (physics)\n\nA dusty plasma contains tiny charged particles of dust (typically found in space). The dust particles acquire high charges and interact with each other. A plasma that contains larger particles is called grain plasma. Under laboratory conditions, dusty plasmas are also called complex plasmas.","Plasma (physics)\n\nImpermeable plasma","Plasma (physics)\n\nImpermeable plasma is a type of thermal plasma which acts like an impermeable solid with respect to gas or cold plasma and can be physically pushed. Interaction of cold gas and thermal plasma was briefly studied by a group led by Hannes Alfvén in 1960s and 1970s for its possible applications in insulation of fusion plasma from the reactor walls. However, later it was found that the external magnetic fields in this configuration could induce kink instabilities in the plasma and subsequently lead to an unexpectedly high heat loss to the walls. In 2013, a group of materials scientists reported that they have successfully generated stable impermeable plasma with no magnetic confinement using only an ultrahigh-pressure blanket of cold gas. While spectroscopic data on the characteristics of plasma were claimed to be difficult to obtain due to the high pressure, the passive effect of plasma on synthesis of different nanostructures clearly suggested the effective confinement.","Plasma (physics)\n\nThey also showed that upon maintaining the impermeability for a few tens of seconds, screening of ions at the plasma-gas interface could give rise to a strong secondary mode of heating (known as viscous heating) leading to different kinetics of reactions and formation of complex nanomaterials.","Plasma (physics)\n\nMathematical descriptions","Plasma (physics)\n\nTo completely describe the state of a plasma, we would need to write down all the\nparticle locations and velocities and describe the electromagnetic field in the plasma region.\nHowever, it is generally not practical or necessary to keep track of all the particles in a plasma.\nTherefore, plasma physicists commonly use less detailed descriptions, of which\nthere are two main types:","Plasma (physics)\n\nFluid model","Plasma (physics)\n\nFluid models describe plasmas in terms of smoothed quantities, like density and averaged velocity around each position (see Plasma parameters). One simple fluid model, magnetohydrodynamics, treats the plasma as a single fluid governed by a combination of Maxwell's equations and the Navier–Stokes equations. A more general description is the two-fluid plasma picture, where the ions and electrons are described separately. Fluid models are often accurate when collisionality is sufficiently high to keep the plasma velocity distribution close to a Maxwell–Boltzmann distribution. Because fluid models usually describe the plasma in terms of a single flow at a certain temperature at each spatial location, they can neither capture velocity space structures like beams or double layers, nor resolve wave-particle effects.","Plasma (physics)\n\nKinetic model","Plasma (physics)\n\nKinetic models describe the particle velocity distribution function at each point in the plasma and therefore do not need to assume a Maxwell–Boltzmann distribution. A kinetic description is often necessary for collisionless plasmas. There are two common approaches to kinetic description of a plasma. One is based on representing the smoothed distribution function on a grid in velocity and position. The other, known as the particle-in-cell (PIC) technique, includes kinetic information by following the trajectories of a large number of individual particles. Kinetic models are generally more computationally intensive than fluid models. The Vlasov equation may be used to describe the dynamics of a system of charged particles interacting with an electromagnetic field.\nIn magnetized plasmas, a gyrokinetic approach can substantially reduce the computational expense of a fully kinetic simulation.","Plasma (physics)\n\nArtificial plasmas","Plasma (physics)\n\nMost artificial plasmas are generated by the application of electric and/or magnetic fields through a gas. Plasma generated in a laboratory setting and for industrial use can be generally categorized by:\n*The type of power source used to generate the plasma—DC, RF and microwave\n*The pressure they operate at—vacuum pressure (T_e T_i \n T_{gas}), non-thermal or \"cold\" plasma (T_e \\gg T_i = T_{gas})\n*The electrode configuration used to generate the plasma\n*The magnetization of the particles within the plasma—magnetized (both ion and electrons are trapped in Larmor orbits by the magnetic field), partially magnetized (the electrons but not the ions are trapped by the magnetic field), non-magnetized (the magnetic field is too weak to trap the particles in orbits but may generate Lorentz forces)","Plasma (physics)\n\nGeneration of artificial plasma","Plasma (physics)\n\nJust like the many uses of plasma, there are several means for its generation, however, one principle is common to all of them: there must be energy input to produce and sustain it. For this case, plasma is generated when an electric current is applied across a dielectric gas or fluid (an electrically non-conducting material) as can be seen in the image to the right, which shows a discharge tube as a simple example (DC used for simplicity).","Plasma (physics)\n\nThe potential difference and subsequent electric field pull the bound electrons (negative) toward the anode (positive electrode) while the cathode (negative electrode) pulls the nucleus. As the voltage increases, the current stresses the material (by electric polarization) beyond its dielectric limit (termed strength) into a stage of electrical breakdown, marked by an electric spark, where the material transforms from being an insulator into a conductor (as it becomes increasingly ionized). The underlying process is the Townsend avalanche, where collisions between electrons and neutral gas atoms create more ions and electrons (as can be seen in the figure on the right). The first impact of an electron on an atom results in one ion and two electrons. Therefore, the number of charged particles increases rapidly (in the millions) only \"after about 20 successive sets of collisions\", mainly due to a small mean free path (average distance travelled between collisions).","Plasma (physics)\n\nElectric arc","Plasma (physics)\n\nWith ample current density and ionization, this forms a luminous electric arc (a continuous electric discharge similar to lightning) between the electrodes. Electrical resistance along the continuous electric arc creates heat, which dissociates more gas molecules and ionizes the resulting atoms (where degree of ionization is determined by temperature), and as per the sequence: solid-liquid-gas-plasma, the gas is gradually turned into a thermal plasma. A thermal plasma is in thermal equilibrium, which is to say that the temperature is relatively homogeneous throughout the heavy particles (i.e. atoms, molecules and ions) and electrons. This is so because when thermal plasmas are generated, electrical energy is given to electrons, which, due to their great mobility and large numbers, are able to disperse it rapidly and by elastic collision (without energy loss) to the heavy particles.Note that non-thermal, or non-equilibrium plasmas are not as ionized and have lower energy densities, and thus the temperature is not dispersed evenly among the particles, where some heavy ones remain ‘cold’.","Plasma (physics)\n\nExamples of industrial/commercial plasma","Plasma (physics)\n\nBecause of their sizable temperature and density ranges, plasmas find applications in many fields of research, technology and industry. For example, in: industrial and extractive metallurgy, surface treatments such as plasma spraying (coating), etching in microelectronics, metal cutting and welding; as well as in everyday vehicle exhaust cleanup and fluorescent/luminescent lamps, while even playing a part in supersonic combustion engines for aerospace engineering.","Plasma (physics)\n\nLow-pressure discharges","Plasma (physics)\n\n*Glow discharge plasmas: non-thermal plasmas generated by the application of DC or low frequency RF (2O3 to produce aluminium. *Corona discharge: this is a non-thermal discharge generated by the application of high voltage to sharp electrode tips. It is commonly used in ozone generators and particle precipitators. *Dielectric barrier discharge (DBD): this is a non-thermal discharge generated by the application of high voltages across small gaps wherein a non-conducting coating prevents the transition of the plasma discharge into an arc. It is often mislabeled 'Corona' discharge in industry and has similar application to corona discharges. It is also widely used in the web treatment of fabrics. The application of the discharge to synthetic fabrics and plastics functionalizes the surface and allows for paints, glues and similar materials to adhere. *Capacitive discharge: this is a nonthermal plasma generated by the application of RF power (e.g., 13.56 MHz) to one powered electrode, with a grounded electrode held at a small separation distance on the order of 1 cm. Such discharges are commonly stabilized using a noble gas such as helium or argon. *\"Piezoelectric direct discharge plasma:\" is a nonthermal plasma generated at the high-side of a piezoelectric transformer (PT).","Plasma (physics)\n\nThis generation variant is particularly suited for high efficient and compact devices where a separate high voltage power supply is not desired.","Plasma (physics)\n\nHistory","Plasma (physics)\n\nPlasma was first identified in a Crookes tube, and so described by Sir William Crookes in 1879 (he called it \"radiant matter\"). The nature of the Crookes tube \"cathode ray\" matter was subsequently identified by British physicist Sir J.J. Thomson in 1897. The term \"plasma\" was coined by Irving Langmuir in 1928, perhaps because the glowing discharge molds itself to the shape of the Crookes tube (Gr. πλάσμα – a thing moulded or formed). Langmuir described his observations as:","Plasma (physics)\n\nExcept near the electrodes, where there are sheaths containing very few electrons, the ionized gas contains ions and electrons in about equal numbers so that the resultant space charge is very small. We shall use the name plasma to describe this region containing balanced charges of ions and electrons.","Plasma (physics)\n\nResearch","Plasma (physics)\n\nPlasmas are the object of study of the academic field of plasma science or plasma physics, including sub-disciplines such as space plasma physics.\nThere are multiple journals devoted to the subject (see list).\nIt involves the following fields of active research (see also list of articles):","Plasma (physics)\n\n*Plasma theory\n**Plasma equilibria and stability\n**Plasma interactions with waves and beams\n**Guiding center\n**Adiabatic invariant\n**Debye sheath\n**Coulomb collision\n*Plasmas in nature\n**The Earth's ionosphere\n**Northern and southern (polar) lights\n**Space plasmas, e.g. Earth's plasmasphere (an inner portion of the magnetosphere dense with plasma)\n**Astrophysical plasma\n**Interplanetary medium\n*Industrial plasmas\n**Plasma chemistry\n**Plasma processing\n**Plasma spray\n**Plasma display\n**Plasma sources\n**Dusty plasmas\n*Plasma diagnostics\n**Thomson scattering\n**Langmuir probe\n**Ball-pen probe\n**Faraday cup\n**Spectroscopy\n**Interferometry\n**Ionospheric heating\n**Incoherent scatter radar","Plasma (physics)\n\n*Plasma applications\n**Dielectric barrier discharge\n**Enhanced oil recovery\n**Fusion power\n***Magnetic fusion energy (MFE) — tokamak, stellarator, reversed field pinch, magnetic mirror, dense plasma focus\n***Inertial fusion energy (IFE) (also Inertial confinement fusion — ICF)\n***Plasma weapon\n**Ion implantation\n**Ion thruster\n**MAGPIE (short for Mega Ampere Generator for Plasma Implosion Experiments)\n**Plasma ashing\n**Food processing (nonthermal plasma, aka \"cold plasma\")\n**Plasma arc waste disposal, convert waste into reusable material with plasma.\n**Plasma acceleration\n**Plasma medicine (e. g. Dentistry )\n**Plasma window","Plasma (physics)\n\nFile:Wispy 'Plasma Dancer' on the limb of the Sun.ogv|Solar plasma\nFile:Plasma Spraying Process.jpg|Plasma spraying","Electric charge\n\nElectric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charges: positive and negative. Like charges repel and unlike attract. An object is negatively charged if it has an excess of electrons, and is otherwise positively charged or uncharged. The SI derived unit of electric charge is the coulomb (C). In electrical engineering, it is also common to use the ampere-hour (Ah), and, in chemistry, it is common to use the elementary charge (e) as a unit. The symbol Q often denotes charge. Early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that don't require consideration of quantum effects.","Electric charge\n\nThe electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields. The interaction between a moving charge and an electromagnetic field is the source of the electromagnetic force, which is one of the four fundamental forces (See also: magnetic field).","Electric charge\n\nTwentieth-century experiments demonstrated that electric charge is quantized; that is, it comes in integer multiples of individual small units called the elementary charge, e, approximately equal to (except for particles called quarks, which have charges that are integer multiples of e/3). The proton has a charge of +e, and the electron has a charge of -e. The study of charged particles, and how their interactions are mediated by photons, is called quantum electrodynamics.","Electric charge\n\nOverview","Electric charge\n\nCharge is the fundamental property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter.\nElectric charge is a characteristic property of many subatomic particles. The charges of free-standing particles are integer multiples of the elementary charge e; we say that electric charge is quantized. Michael Faraday, in his electrolysis experiments, was the first to note the discrete nature of electric charge. Robert Millikan's oil drop experiment demonstrated this fact directly, and measured the elementary charge.","Electric charge\n\nBy convention, the charge of an electron is −1, while that of a proton is +1. Charged particles whose charges have the same sign repel one another, and particles whose charges have different signs attract. Coulomb's law quantifies the electrostatic force between two particles by asserting that the force is proportional to the product of their charges, and inversely proportional to the square of the distance between them.","Electric charge\n\nThe charge of an antiparticle equals that of the corresponding particle, but with opposite sign. Quarks have fractional charges of either − or +, but free-standing quarks have never been observed (the theoretical reason for this fact is asymptotic freedom).","Electric charge\n\nThe electric charge of a macroscopic object is the sum of the electric charges of the particles that make it up. This charge is often small, because matter is made of atoms, and atoms typically have equal numbers of protons and electrons, in which case their charges cancel out, yielding a net charge of zero, thus making the atom neutral.","Electric charge\n\nAn ion is an atom (or group of atoms) that has lost one or more electrons, giving it a net positive charge (cation), or that has gained one or more electrons, giving it a net negative charge (anion). Monatomic ions are formed from single atoms, while polyatomic ions are formed from two or more atoms that have been bonded together, in each case yielding an ion with a positive or negative net charge.","Electric charge\n\nDuring formation of macroscopic objects, constituent atoms and ions usually combine to form structures composed of neutral ionic compounds electrically bound to neutral atoms. Thus macroscopic objects tend toward being neutral overall, but macroscopic objects are rarely perfectly net neutral.","Electric charge\n\nSometimes macroscopic objects contain ions distributed throughout the material, rigidly bound in place, giving an overall net positive or negative charge to the object. Also, macroscopic objects made of conductive elements, can more or less easily (depending on the element) take on or give off electrons, and then maintain a net negative or positive charge indefinitely. When the net electric charge of an object is non-zero and motionless, the phenomenon is known as static electricity. This can easily be produced by rubbing two dissimilar materials together, such as rubbing amber with fur or glass with silk. In this way non-conductive materials can be charged to a significant degree, either positively or negatively. Charge taken from one material is moved to the other material, leaving an opposite charge of the same magnitude behind. The law of conservation of charge always applies, giving the object from which a negative charge is taken a positive charge of the same magnitude, and vice versa.","Electric charge\n\nEven when an object's net charge is zero, charge can be distributed non-uniformly in the object (e.g., due to an external electromagnetic field, or bound polar molecules). In such cases the object is said to be polarized. The charge due to polarization is known as bound charge, while charge on an object produced by electrons gained or lost from outside the object is called free charge. The motion of electrons in conductive metals in a specific direction is known as electric current.","Electric charge\n\nUnits","Electric charge\n\nThe SI unit of quantity of electric charge is the coulomb, which is equivalent to about (e is the charge of a proton). Hence, the charge of an electron is approximately . The coulomb is defined as the quantity of charge that has passed through the cross section of an electrical conductor carrying one ampere within one second. The symbol Q is often used to denote a quantity of electricity or charge. The quantity of electric charge can be directly measured with an electrometer, or indirectly measured with a ballistic galvanometer.","Electric charge\n\nAfter finding the quantized character of charge, in 1891 George Stoney proposed the unit 'electron' for this fundamental unit of electrical charge. This was before the discovery of the particle by J.J. Thomson in 1897. The unit is today treated as nameless, referred to as \"elementary charge\", \"fundamental unit of charge\", or simply as \"e\". A measure of charge should be a multiple of the elementary charge e, even if at large scales charge seems to behave as a real quantity. In some contexts it is meaningful to speak of fractions of a charge; for example in the charging of a capacitor, or in the fractional quantum Hall effect.","Electric charge\n\nIn systems of units other than SI such as cgs, electric charge is expressed as combination of only three fundamental quantities (length, mass, and time), and not four, as in SI, where electric charge is a combination of length, mass, time, and electric current.","Electric charge\n\nHistory","Electric charge\n\nAs reported by the ancient Greek mathematician Thales of Miletus around 600 BC, charge (or electricity) could be accumulated by rubbing fur on various substances, such as amber. The Greeks noted that the charged amber buttons could attract light objects such as hair. They also noted that if they rubbed the amber for long enough, they could even get an electric spark to jump. This property derives from the triboelectric effect.","Electric charge\n\nIn 1600, the English scientist William Gilbert returned to the subject in De Magnete, and coined the New Latin word electricus from (ēlektron), the Greek word for amber, which soon gave rise to the English words \"electric\" and \"electricity.\" He was followed in 1660 by Otto von Guericke, who invented what was probably the first electrostatic generator. Other European pioneers were Robert Boyle, who in 1675 stated that electric attraction and repulsion can act across a vacuum; Stephen Gray, who in 1729 classified materials as conductors and insulators; and C. F. du Fay, who proposed in 1733 that electricity comes in two varieties that cancel each other, and expressed this in terms of a two-fluid theory. When glass was rubbed with silk, du Fay said that the glass was charged with vitreous electricity, and, when amber was rubbed with fur, the amber was charged with resinous electricity. In 1839, Michael Faraday showed that the apparent division between static electricity, current electricity, and bioelectricity was incorrect, and all were a consequence of the behavior of a single kind of electricity appearing in opposite polarities. It is arbitrary which polarity is called positive and which is called negative.","Electric charge\n\nPositive charge can be defined as the charge left on a glass rod after being rubbed with silk.","Electric charge\n\nOne of the foremost experts on electricity in the 18th century was Benjamin Franklin, who argued in favour of a one-fluid theory of electricity. Franklin imagined electricity as being a type of invisible fluid present in all matter; for example, he believed that it was the glass in a Leyden jar that held the accumulated charge. He posited that rubbing insulating surfaces together caused this fluid to change location, and that a flow of this fluid constitutes an electric current. He also posited that when matter contained too little of the fluid it was \"negatively\" charged, and when it had an excess it was \"positively\" charged. For a reason that was not recorded, he identified the term \"positive\" with vitreous electricity and \"negative\" with resinous electricity. William Watson arrived at the same explanation at about the same time.","Electric charge\n\nStatic electricity and electric current","Electric charge\n\nStatic electricity and electric current are two separate phenomena. They both involve electric charge, and may occur simultaneously in the same object. Static electricity refers to the electric charge of an object and the related electrostatic discharge when two objects are brought together that are not at equilibrium. An electrostatic discharge creates a change in the charge of each of the two objects. In contrast, electric current is the flow of electric charge through an object, which produces no net loss or gain of electric charge.","Electric charge\n\nElectrification by friction","Electric charge\n\nWhen a piece of glass and a piece of resin—neither of which exhibit any electrical properties—are rubbed together and left with the rubbed surfaces in contact, they still exhibit no electrical properties. When separated, they attract each other.","Electric charge\n\nA second piece of glass rubbed with a second piece of resin, then separated and suspended near the former pieces of glass and resin causes these phenomena:\n*The two pieces of glass repel each other.\n*Each piece of glass attracts each piece of resin.\n*The two pieces of resin repel each other.","Electric charge\n\nThis attraction and repulsion is an electrical phenomena, and the bodies that exhibit them are said to be electrified, or electrically charged. Bodies may be electrified in many other ways, as well as by friction. The electrical properties of the two pieces of glass are similar to each other but opposite to those of the two pieces of resin: The glass attracts what the resin repels and repels what the resin attracts.","Electric charge\n\nIf a body electrified in any manner whatsoever behaves as the glass does, that is, if it repels the glass and attracts the resin, the body is said to be 'vitreously' electrified, and if it attracts the glass and repels the resin it is said to be 'resinously' electrified. All electrified bodies are either vitreously or resinously electrified.","Electric charge\n\nAn established convention in the scientific community defines vitreous electrification as positive, and resinous electrification as negative. The exactly opposite properties of the two kinds of electrification justify our indicating them by opposite signs, but the application of the positive sign to one rather than to the other kind must be considered as a matter of arbitrary convention—just as it is a matter of convention in mathematical diagram to reckon positive distances towards the right hand.","Electric charge\n\nNo force, either of attraction or of repulsion, can be observed between an electrified body and a body not electrified.","Electric charge\n\nActually, all bodies are electrified, but may appear not electrified because of the relatively similar charge of neighboring objects in the environment. An object further electrified + or – creates an equivalent or opposite charge by default in neighboring objects, until those charges can equalize. The effects of attraction can be observed in high-voltage experiments, while lower voltage effects are merely weaker and therefore less obvious. The attraction and repulsion forces are codified by Coulomb's law (attraction falls off at the square of the distance, which has a corollary for acceleration in a gravitational field, suggesting that gravitation may be merely electrostatic phenomenon between relatively weak charges in terms of scale). See also Casimir effect.","Electric charge\n\nIt is now known that the Franklin-Watson model was fundamentally correct. There is only one kind of electrical charge, and only one variable is required to keep track of the amount of charge. On the other hand, just knowing the charge is not a complete description of the situation. Matter is composed of several kinds of electrically charged particles, and these particles have many properties, not just charge.","Electric charge\n\nThe most common charge carriers are the positively charged proton and the negatively charged electron. The movement of any of these charged particles constitutes an electric current. In many situations, it suffices to speak of the conventional current without regard to whether it is carried by positive charges moving in the direction of the conventional current or by negative charges moving in the opposite direction. This macroscopic viewpoint is an approximation that simplifies electromagnetic concepts and calculations.","Electric charge\n\nAt the opposite extreme, if one looks at the microscopic situation, one sees there are many ways of carrying an electric current, including: a flow of electrons; a flow of electron \"holes\" that act like positive particles; and both negative and positive particles (ions or other charged particles) flowing in opposite directions in an electrolytic solution or a plasma.","Electric charge\n\nBeware that, in the common and important case of metallic wires, the direction of the conventional current is opposite to the drift velocity of the actual charge carriers, i.e., the electrons. This is a source of confusion for beginners.","Electric charge\n\nConservation of electric charge","Electric charge\n\nThe total electric charge of an isolated system remains constant regardless of changes within the system itself. This law is inherent to all processes known to physics and can be derived in a local form from gauge invariance of the wave function. The conservation of charge results in the charge-current continuity equation. More generally, the net change in charge density ρ within a volume of integration V is equal to the area integral over the current density J through the closed surface S = ∂V, which is in turn equal to the net current I:\nThus, the conservation of electric charge, as expressed by the continuity equation, gives the result:\nI = -\\frac{\\mathrm{d}Q}{\\mathrm{d}t}.","Electric charge\n\nThe charge transferred between times t_\\mathrm{i} and t_\\mathrm{f} is obtained by integrating both sides:\nQ = \\int_{t_{\\mathrm{i}}}^{t_{\\mathrm{f}}} I\\, \\mathrm{d}t \nwhere I is the net outward current through a closed surface and Q is the electric charge contained within the volume defined by the surface.","Electric charge\n\nRelativistic invariance","Electric charge\n\nAside from the properties described in articles about electromagnetism, charge is a relativistic invariant. This means that any particle that has charge Q, no matter how fast it goes, always has charge Q. This property has been experimentally verified by showing that the charge of one helium nucleus (two protons and two neutrons bound together in a nucleus and moving around at high speeds) is the same as two deuterium nuclei (one proton and one neutron bound together, but moving much more slowly than they would if they were in a helium nucleus).","Atom\n\nAn atom is the smallest constituent unit of ordinary matter that has the properties of a chemical element. Every solid, liquid, gas, and plasma is composed of neutral or ionized atoms. Atoms are very small; typical sizes are around 100 pm (a ten-billionth of a meter, in the short scale). However, atoms do not have well-defined boundaries, and there are different ways to define their size that give different but close values.","Atom\n\nAtoms are small enough that attempting to predict their behavior using classical physics - as if they were billiard balls, for example - gives noticeably incorrect predictions due to quantum effects. Through the development of physics, atomic models have incorporated quantum principles to better explain and predict the behavior.","Atom\n\nEvery atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and typically a similar number of neutrons. Protons and neutrons are called nucleons. More than 99.94% of an atom's mass is in the nucleus. The protons have a positive electric charge, the electrons have a negative electric charge, and the neutrons have no electric charge. If the number of protons and electrons are equal, that atom is electrically neutral. If an atom has more or fewer electrons than protons, then it has an overall negative or positive charge, respectively, and it is called an ion.","Atom\n\nThe electrons of an atom are attracted to the protons in an atomic nucleus by this electromagnetic force. The protons and neutrons in the nucleus are attracted to each other by a different force, the nuclear force, which is usually stronger than the electromagnetic force repelling the positively charged protons from one another. Under certain circumstances the repelling electromagnetic force becomes stronger than the nuclear force, and nucleons can be ejected from the nucleus, leaving behind a different element: nuclear decay resulting in nuclear transmutation.","Atom\n\nThe number of protons in the nucleus defines to what chemical element the atom belongs: for example, all copper atoms contain 29 protons. The number of neutrons defines the isotope of the element. The number of electrons influences the magnetic properties of an atom. Atoms can attach to one or more other atoms by chemical bonds to form chemical compounds such as molecules. The ability of atoms to associate and dissociate is responsible for most of the physical changes observed in nature, and is the subject of the discipline of chemistry.","Atom\n\nHistory of atomic theory","Atom\n\nAtoms in philosophy","Atom\n\nThe idea that matter is made up of discrete units is a very old idea, appearing in many ancient cultures such as Greece and India. The word \"atom\" was coined by ancient Greek philosophers. However, these ideas were founded in philosophical and theological reasoning rather than evidence and experimentation. As a result, their views on what atoms look like and how they behave were incorrect. They also could not convince everybody, so atomism was but one of a number of competing theories on the nature of matter. It was not until the 19th century that the idea was embraced and refined by scientists, when the blossoming science of chemistry produced discoveries that only the concept of atoms could explain.","Atom\n\nFirst evidence-based theory","Atom\n\nIn the early 1800s, John Dalton used the concept of atoms to explain why elements always react in ratios of small whole numbers (the law of multiple proportions). For instance, there are two types of tin oxide: one is 88.1% tin and 11.9% oxygen and the other is 78.7% tin and 21.3% oxygen (tin(II) oxide and tin dioxide respectively). This means that 100g of tin will combine either with 13.5g or 27g of oxygen. 13.5 and 27 form a ratio of 1:2, a ratio of small whole numbers. This common pattern in chemistry suggested to Dalton that elements react in whole number multiples of discrete units—in other words, atoms. In the case of tin oxides, one tin atom will combine with either one or two oxygen atoms.","Atom\n\nDalton also believed atomic theory could explain why water absorbs different gases in different proportions. For example, he found that water absorbs carbon dioxide far better than it absorbs nitrogen.Dalton, John. \"[http://web.lemoyne.edu/~GIUNTA/dalton52.html On the Absorption of Gases by Water and Other Liquids]\", in Memoirs of the Literary and Philosophical Society of Manchester. 1803. Retrieved on August 29, 2007. Dalton hypothesized this was due to the differences between the masses and configurations of the gases' respective particles, and carbon dioxide molecules (CO2) are heavier and larger than nitrogen molecules (N2).","Atom\n\nBrownian motion","Atom\n\nIn 1827, botanist Robert Brown used a microscope to look at dust grains floating in water and discovered that they moved about erratically, a phenomenon that became known as \"Brownian motion\". This was thought to be caused by water molecules knocking the grains about. In 1905 Albert Einstein proved the reality of these molecules and their motions by producing the first Statistical physics analysis of Brownian motion. French physicist Jean Perrin used Einstein's work to experimentally determine the mass and dimensions of atoms, thereby conclusively verifying Dalton's atomic theory.","Atom\n\nDiscovery of the electron","Atom\n\nThe physicist J. J. Thomson measured the mass of cathode rays, showing they were made of particles, but were around 1800 times lighter than the lightest atom, hydrogen. Therefore, they were not atoms, but a new particle, the first subatomic particle to be discovered, which he originally called \"corpuscle\" but was later named electron, after particles postulated by George Johnstone Stoney in 1874. He also showed they were identical to particles given off by photoelectric and radioactive materials. It was quickly recognized that they are the particles that carry electric currents in metal wires, and carry the negative electric charge within atoms. Thomson was given the 1906 Nobel Prize in Physics for this work. Thus he overturned the belief that atoms are the indivisible, ultimate particles of matter. Thomson also incorrectly postulated that the low mass, negatively charged electrons were distributed throughout the atom in a uniform sea of positive charge. This became known as the plum pudding model.","Atom\n\nDiscovery of the nucleus","Atom\n\nIn 1909, Hans Geiger and Ernest Marsden, under the direction of Ernest Rutherford, bombarded a metal foil with alpha particles to observe how they scattered. They expected all the alpha particles to pass straight through with little deflection, because Thomson's model said that the charges in the atom are so diffuse that their electric fields could not affect the alpha particles much. However, Geiger and Marsden spotted alpha particles being deflected by angles greater than 90°, which was supposed to be impossible according to Thomson's model. To explain this, Rutherford proposed that the positive charge of the atom is concentrated in a tiny nucleus at the center of the atom.","Atom\n\nDiscovery of isotopes","Atom\n\nWhile experimenting with the products of radioactive decay, in 1913 radiochemist Frederick Soddy discovered that there appeared to be more than one type of atom at each position on the periodic table. The term isotope was coined by Margaret Todd as a suitable name for different atoms that belong to the same element. J.J. Thomson created a technique for separating atom types through his work on ionized gases, which subsequently led to the discovery of stable isotopes.","Atom\n\nBohr model","Atom\n\nIn 1913 the physicist Niels Bohr proposed a model in which the electrons of an atom were assumed to orbit the nucleus but could only do so in a finite set of orbits, and could jump between these orbits only in discrete changes of energy corresponding to absorption or radiation of a photon. This quantization was used to explain why the electrons orbits are stable (given that normally, charges in acceleration, including circular motion, lose kinetic energy which is emitted as electromagnetic radiation, see synchrotron radiation) and why elements absorb and emit electromagnetic radiation in discrete spectra.","Atom\n\nLater in the same year Henry Moseley provided additional experimental evidence in favor of Niels Bohr's theory. These results refined Ernest Rutherford's and Antonius Van den Broek's model, which proposed that the atom contains in its nucleus a number of positive nuclear charges that is equal to its (atomic) number in the periodic table. Until these experiments, atomic number was not known to be a physical and experimental quantity. That it is equal to the atomic nuclear charge remains the accepted atomic model today.","Atom\n\nChemical bonding explained","Atom\n\nChemical bonds between atoms were now explained, by Gilbert Newton Lewis in 1916, as the interactions between their constituent electrons. As the chemical properties of the elements were known to largely repeat themselves according to the periodic law, in 1919 the American chemist Irving Langmuir suggested that this could be explained if the electrons in an atom were connected or clustered in some manner. Groups of electrons were thought to occupy a set of electron shells about the nucleus.","Atom\n\nFurther developments in quantum physics","Atom\n\nThe Stern–Gerlach experiment of 1922 provided further evidence of the quantum nature of the atom. When a beam of silver atoms was passed through a specially shaped magnetic field, the beam was split based on the direction of an atom's angular momentum, or spin. As this direction is random, the beam could be expected to spread into a line. Instead, the beam was split into two parts, depending on whether the atomic spin was oriented up or down.","Atom\n\nIn 1924, Louis de Broglie proposed that all particles behave to an extent like waves. In 1926, Erwin Schrödinger used this idea to develop a mathematical model of the atom that described the electrons as three-dimensional waveforms rather than point particles. A consequence of using waveforms to describe particles is that it is mathematically impossible to obtain precise values for both the position and momentum of a particle at a given point in time; this became known as the uncertainty principle, formulated by Werner Heisenberg in 1926. In this concept, for a given accuracy in measuring a position one could only obtain a range of probable values for momentum, and vice versa. \nThis model was able to explain observations of atomic behavior that previous models could not, such as certain structural and spectral patterns of atoms larger than hydrogen. Thus, the planetary model of the atom was discarded in favor of one that described atomic orbital zones around the nucleus where a given electron is most likely to be observed.","Atom\n\nDiscovery of the neutron","Atom\n\nThe development of the mass spectrometer allowed the mass of atoms to be measured with increased accuracy. The device uses a magnet to bend the trajectory of a beam of ions, and the amount of deflection is determined by the ratio of an atom's mass to its charge. The chemist Francis William Aston used this instrument to show that isotopes had different masses. The atomic mass of these isotopes varied by integer amounts, called the whole number rule. The explanation for these different isotopes awaited the discovery of the neutron, an uncharged particle with a mass similar to the proton, by the physicist James Chadwick in 1932. Isotopes were then explained as elements with the same number of protons, but different numbers of neutrons within the nucleus.","Atom\n\nFission, high-energy physics and condensed matter","Atom\n\nIn 1938, the German chemist Otto Hahn, a student of Rutherford, directed neutrons onto uranium atoms expecting to get transuranium elements. Instead, his chemical experiments showed barium as a product. A year later, Lise Meitner and her nephew Otto Frisch verified that Hahn's result were the first experimental nuclear fission. In 1944, Hahn received the Nobel prize in chemistry. Despite Hahn's efforts, the contributions of Meitner and Frisch were not recognized.","Atom\n\nIn the 1950s, the development of improved particle accelerators and particle detectors allowed scientists to study the impacts of atoms moving at high energies. Neutrons and protons were found to be hadrons, or composites of smaller particles called quarks. The standard model of particle physics was developed that so far has successfully explained the properties of the nucleus in terms of these sub-atomic particles and the forces that govern their interactions.","Atom\n\nStructure","Atom\n\nSubatomic particles","Atom\n\nThough the word atom originally denoted a particle that cannot be cut into smaller particles, in modern scientific usage the atom is composed of various subatomic particles. The constituent particles of an atom are the electron, the proton and the neutron; all three are fermions. However, the hydrogen-1 atom has no neutrons and the hydron ion has no electrons.","Atom\n\nThe electron is by far the least massive of these particles at , with a negative electrical charge and a size that is too small to be measured using available techniques. It is the lightest particle with a positive rest mass measured. Under ordinary conditions, electrons are bound to the positively charged nucleus by the attraction created from opposite electric charges. If an atom has more or fewer electrons than its atomic number, then it becomes respectively negatively or positively charged as a whole; a charged atom is called an ion. Electrons have been known since the late 19th century, mostly thanks to J.J. Thomson; see history of subatomic physics for details.","Atom\n\nProtons have a positive charge and a mass 1,836 times that of the electron, at . The number of protons in an atom is called its atomic number. Ernest Rutherford (1919) observed that nitrogen under alpha-particle bombardment ejects what appeared to be hydrogen nuclei. By 1920 he had accepted that the hydrogen nucleus is a distinct particle within the atom and named it proton.","Atom\n\nNeutrons have no electrical charge and have a free mass of 1,839 times the mass of the electron, or , the heaviest of the three constituent particles, but it can be reduced by the nuclear binding energy. Neutrons and protons (collectively known as nucleons) have comparable dimensions—on the order of —although the 'surface' of these particles is not sharply defined. The neutron was discovered in 1932 by the English physicist James Chadwick.","Atom\n\nIn the Standard Model of physics, electrons are truly elementary particles with no internal structure. However, both protons and neutrons are composite particles composed of elementary particles called quarks. There are two types of quarks in atoms, each having a fractional electric charge. Protons are composed of two up quarks (each with charge +) and one down quark (with a charge of −). Neutrons consist of one up quark and two down quarks. This distinction accounts for the difference in mass and charge between the two particles.","Atom\n\nThe quarks are held together by the strong interaction (or strong force), which is mediated by gluons. The protons and neutrons, in turn, are held to each other in the nucleus by the nuclear force, which is a residuum of the strong force that has somewhat different range-properties (see the article on the nuclear force for more). The gluon is a member of the family of gauge bosons, which are elementary particles that mediate physical forces.","Atom\n\nNucleus","Atom\n\nAll the bound protons and neutrons in an atom make up a tiny atomic nucleus, and are collectively called nucleons. The radius of a nucleus is approximately equal to 1.07 fm, where A is the total number of nucleons. This is much smaller than the radius of the atom, which is on the order of 105 fm. The nucleons are bound together by a short-ranged attractive potential called the residual strong force. At distances smaller than 2.5 fm this force is much more powerful than the electrostatic force that causes positively charged protons to repel each other.","Atom\n\nAtoms of the same element have the same number of protons, called the atomic number. Within a single element, the number of neutrons may vary, determining the isotope of that element. The total number of protons and neutrons determine the nuclide. The number of neutrons relative to the protons determines the stability of the nucleus, with certain isotopes undergoing radioactive decay.","Atom\n\nThe proton, the electron, and the neutron are classified as fermions. Fermions obey the Pauli exclusion principle which prohibits identical fermions, such as multiple protons, from occupying the same quantum state at the same time. Thus, every proton in the nucleus must occupy a quantum state different from all other protons, and the same applies to all neutrons of the nucleus and to all electrons of the electron cloud. However, a proton and a neutron are allowed to occupy the same quantum state.","Atom\n\nFor atoms with low atomic numbers, a nucleus that has more neutrons than protons tends to drop to a lower energy state through radioactive decay so that the neutron–proton ratio is closer to one. However, as the atomic number increases, a higher proportion of neutrons is required to offset the mutual repulsion of the protons. Thus, there are no stable nuclei with equal proton and neutron numbers above atomic number Z 20 (calcium) and as Z increases, the neutron–proton ratio of stable isotopes increases. The stable isotope with the highest proton–neutron ratio is lead-208 (about 1.5).","Atom\n\nThe number of protons and neutrons in the atomic nucleus can be modified, although this can require very high energies because of the strong force. Nuclear fusion occurs when multiple atomic particles join to form a heavier nucleus, such as through the energetic collision of two nuclei. For example, at the core of the Sun protons require energies of 3–10 keV to overcome their mutual repulsion—the coulomb barrier—and fuse together into a single nucleus. Nuclear fission is the opposite process, causing a nucleus to split into two smaller nuclei—usually through radioactive decay. The nucleus can also be modified through bombardment by high energy subatomic particles or photons. If this modifies the number of protons in a nucleus, the atom changes to a different chemical element.","Atom\n\nIf the mass of the nucleus following a fusion reaction is less than the sum of the masses of the separate particles, then the difference between these two values can be emitted as a type of usable energy (such as a gamma ray, or the kinetic energy of a beta particle), as described by Albert Einstein's mass–energy equivalence formula, E = mc2, where m is the mass loss and c is the speed of light. This deficit is part of the binding energy of the new nucleus, and it is the non-recoverable loss of the energy that causes the fused particles to remain together in a state that requires this energy to separate.","Atom\n\nThe fusion of two nuclei that create larger nuclei with lower atomic numbers than iron and nickel—a total nucleon number of about 60—is usually an exothermic process that releases more energy than is required to bring them together. It is this energy-releasing process that makes nuclear fusion in stars a self-sustaining reaction. For heavier nuclei, the binding energy per nucleon in the nucleus begins to decrease. That means fusion processes producing nuclei that have atomic numbers higher than about 26, and atomic masses higher than about 60, is an endothermic process. These more massive nuclei can not undergo an energy-producing fusion reaction that can sustain the hydrostatic equilibrium of a star.","Atom\n\nElectron cloud","Atom\n\nThe electrons in an atom are attracted to the protons in the nucleus by the electromagnetic force. This force binds the electrons inside an electrostatic potential well surrounding the smaller nucleus, which means that an external source of energy is needed for the electron to escape. The closer an electron is to the nucleus, the greater the attractive force. Hence electrons bound near the center of the potential well require more energy to escape than those at greater separations.","Atom\n\nElectrons, like other particles, have properties of both a particle and a wave. The electron cloud is a region inside the potential well where each electron forms a type of three-dimensional standing wave—a wave form that does not move relative to the nucleus. This behavior is defined by an atomic orbital, a mathematical function that characterises the probability that an electron appears to be at a particular location when its position is measured. Only a discrete (or quantized) set of these orbitals exist around the nucleus, as other possible wave patterns rapidly decay into a more stable form. Orbitals can have one or more ring or node structures, and differ from each other in size, shape and orientation.","Atom\n\nEach atomic orbital corresponds to a particular energy level of the electron. The electron can change its state to a higher energy level by absorbing a photon with sufficient energy to boost it into the new quantum state. Likewise, through spontaneous emission, an electron in a higher energy state can drop to a lower energy state while radiating the excess energy as a photon. These characteristic energy values, defined by the differences in the energies of the quantum states, are responsible for atomic spectral lines.","Atom\n\nThe amount of energy needed to remove or add an electron—the electron binding energy—is far less than the binding energy of nucleons. For example, it requires only 13.6 eV to strip a ground-state electron from a hydrogen atom, compared to 2.23 million eV for splitting a deuterium nucleus. Atoms are electrically neutral if they have an equal number of protons and electrons. Atoms that have either a deficit or a surplus of electrons are called ions. Electrons that are farthest from the nucleus may be transferred to other nearby atoms or shared between atoms. By this mechanism, atoms are able to bond into molecules and other types of chemical compounds like ionic and covalent network crystals.","Atom\n\nProperties","Atom\n\nNuclear properties","Atom\n\nBy definition, any two atoms with an identical number of protons in their nuclei belong to the same chemical element. Atoms with equal numbers of protons but a different number of neutrons are different isotopes of the same element. For example, all hydrogen atoms admit exactly one proton, but isotopes exist with no neutrons (hydrogen-1, by far the most common form, also called protium), one neutron (deuterium), two neutrons (tritium) and more than two neutrons. The known elements form a set of atomic numbers, from the single proton element hydrogen up to the 118-proton element ununoctium. All known isotopes of elements with atomic numbers greater than 82 are radioactive.","Atom\n\nAbout 339 nuclides occur naturally on Earth, of which 254 (about 75%) have not been observed to decay, and are referred to as \"stable isotopes\". However, only 90 of these nuclides are stable to all decay, even in theory. Another 164 (bringing the total to 254) have not been observed to decay, even though in theory it is energetically possible. These are also formally classified as \"stable\". An additional 34 radioactive nuclides have half-lives longer than 80 million years, and are long-lived enough to be present from the birth of the solar system. This collection of 288 nuclides are known as primordial nuclides. Finally, an additional 51 short-lived nuclides are known to occur naturally, as daughter products of primordial nuclide decay (such as radium from uranium), or else as products of natural energetic processes on Earth, such as cosmic ray bombardment (for example, carbon-14).For more recent updates see [http://www.nndc.bnl.gov/chart Interactive Chart of Nuclides (Brookhaven National Laboratory)].","Atom\n\nFor 80 of the chemical elements, at least one stable isotope exists. As a rule, there is only a handful of stable isotopes for each of these elements, the average being 3.2 stable isotopes per element. Twenty-six elements have only a single stable isotope, while the largest number of stable isotopes observed for any element is ten, for the element tin. Elements 43, 61, and all elements numbered 83 or higher have no stable isotopes.CRC Handbook (2002).","Atom\n\nStability of isotopes is affected by the ratio of protons to neutrons, and also by the presence of certain \"magic numbers\" of neutrons or protons that represent closed and filled quantum shells. These quantum shells correspond to a set of energy levels within the shell model of the nucleus; filled shells, such as the filled shell of 50 protons for tin, confers unusual stability on the nuclide. Of the 254 known stable nuclides, only four have both an odd number of protons and odd number of neutrons: hydrogen-2 (deuterium), lithium-6, boron-10 and nitrogen-14. Also, only four naturally occurring, radioactive odd–odd nuclides have a half-life over a billion years: potassium-40, vanadium-50, lanthanum-138 and tantalum-180m. Most odd–odd nuclei are highly unstable with respect to beta decay, because the decay products are even–even, and are therefore more strongly bound, due to nuclear pairing effects.","Atom\n\nMass","Atom\n\nThe large majority of an atom's mass comes from the protons and neutrons that make it up. The total number of these particles (called \"nucleons\") in a given atom is called the mass number. It is a positive integer and dimensionless (instead of having dimension of mass), because it expresses a count. An example of use of a mass number is \"carbon-12,\" which has 12 nucleons (six protons and six neutrons).","Atom\n\nThe actual mass of an atom at rest is often expressed using the unified atomic mass unit (u), also called dalton (Da). This unit is defined as a twelfth of the mass of a free neutral atom of carbon-12, which is approximately . Hydrogen-1 (the lightest isotope of hydrogen which is also the nuclide with the lowest mass) has an atomic weight of 1.007825 u. The value of this number is called the atomic mass. A given atom has an atomic mass approximately equal (within 1%) to its mass number times the atomic mass unit (for example the mass of a nitrogen-14 is roughly 14 u). However, this number will not be exactly an integer except in the case of carbon-12 (see below). The heaviest stable atom is lead-208, with a mass of .","Atom\n\nAs even the most massive atoms are far too light to work with directly, chemists instead use the unit of moles. One mole of atoms of any element always has the same number of atoms (about Avogadro constant|). This number was chosen so that if an element has an atomic mass of 1 u, a mole of atoms of that element has a mass close to one gram. Because of the definition of the unified atomic mass unit, each carbon-12 atom has an atomic mass of exactly 12 u, and so a mole of carbon-12 atoms weighs exactly 0.012 kg.","Atom\n\nShape and size","Atom\n\nAtoms lack a well-defined outer boundary, so their dimensions are usually described in terms of an atomic radius. This is a measure of the distance out to which the electron cloud extends from the nucleus. However, this assumes the atom to exhibit a spherical shape, which is only obeyed for atoms in vacuum or free space. Atomic radii may be derived from the distances between two nuclei when the two atoms are joined in a chemical bond. The radius varies with the location of an atom on the atomic chart, the type of chemical bond, the number of neighboring atoms (coordination number) and a quantum mechanical property known as spin. On the periodic table of the elements, atom size tends to increase when moving down columns, but decrease when moving across rows (left to right). Consequently, the smallest atom is helium with a radius of 32 pm, while one of the largest is caesium at 225 pm.","Atom\n\nWhen subjected to external forces, like electrical fields, the shape of an atom may deviate from spherical symmetry. The deformation depends on the field magnitude and the orbital type of outer shell electrons, as shown by group-theoretical considerations. Aspherical deviations might be elicited for instance in crystals, where large crystal-electrical fields may occur at low-symmetry lattice sites. Significant ellipsoidal deformations have recently been shown to occur for sulfur ions and chalcogen ions in pyrite-type compounds.","Atom\n\nAtomic dimensions are thousands of times smaller than the wavelengths of light (400–700 nm) so they cannot be viewed using an optical microscope. However, individual atoms can be observed using a scanning tunneling microscope. To visualize the minuteness of the atom, consider that a typical human hair is about 1 million carbon atoms in width. A single drop of water contains about 2 sextillion () atoms of oxygen, and twice the number of hydrogen atoms. A single carat diamond with a mass of contains about 10 sextillion (1022) atoms of carbon.A carat is 200 milligrams. By definition, carbon-12 has 0.012 kg per mole. The Avogadro constant defines atoms per mole. If an apple were magnified to the size of the Earth, then the atoms in the apple would be approximately the size of the original apple.","Atom\n\nRadioactive decay","Atom\n\nEvery element has one or more isotopes that have unstable nuclei that are subject to radioactive decay, causing the nucleus to emit particles or electromagnetic radiation. Radioactivity can occur when the radius of a nucleus is large compared with the radius of the strong force, which only acts over distances on the order of 1 fm.","Atom\n\nThe most common forms of radioactive decay are:\n* Alpha decay: this process is caused when the nucleus emits an alpha particle, which is a helium nucleus consisting of two protons and two neutrons. The result of the emission is a new element with a lower atomic number. * Beta decay (and electron capture): these processes are regulated by the weak force, and result from a transformation of a neutron into a proton, or a proton into a neutron. The neutron to proton transition is accompanied by the emission of an electron and an antineutrino, while proton to neutron transition (except in electron capture) causes the emission of a positron and a neutrino. The electron or positron emissions are called beta particles. Beta decay either increases or decreases the atomic number of the nucleus by one. Electron capture is more common than positron emission, because it requires less energy. In this type of decay, an electron is absorbed by the nucleus, rather than a positron emitted from the nucleus. A neutrino is still emitted in this process, and a proton changes to a neutron.","Atom\n\n* Gamma decay: this process results from a change in the energy level of the nucleus to a lower state, resulting in the emission of electromagnetic radiation. The excited state of a nucleus which results in gamma emission usually occurs following the emission of an alpha or a beta particle. Thus, gamma decay usually follows alpha or beta decay.","Atom\n\nOther more rare types of radioactive decay include ejection of neutrons or protons or clusters of nucleons from a nucleus, or more than one beta particle. An analog of gamma emission which allows excited nuclei to lose energy in a different way, is internal conversion— a process that produces high-speed electrons that are not beta rays, followed by production of high-energy photons that are not gamma rays. A few large nuclei explode into two or more charged fragments of varying masses plus several neutrons, in a decay called spontaneous nuclear fission.","Atom\n\nEach radioactive isotope has a characteristic decay time period—the half-life—that is determined by the amount of time needed for half of a sample to decay. This is an exponential decay process that steadily decreases the proportion of the remaining isotope by 50% every half-life. Hence after two half-lives have passed only 25% of the isotope is present, and so forth.","Atom\n\nMagnetic moment","Atom\n\nElementary particles possess an intrinsic quantum mechanical property known as spin. This is analogous to the angular momentum of an object that is spinning around its center of mass, although strictly speaking these particles are believed to be point-like and cannot be said to be rotating. Spin is measured in units of the reduced Planck constant (ħ), with electrons, protons and neutrons all having spin ½ ħ, or \"spin-½\". In an atom, electrons in motion around the nucleus possess orbital angular momentum in addition to their spin, while the nucleus itself possesses angular momentum due to its nuclear spin.","Atom\n\nThe magnetic field produced by an atom—its magnetic moment—is determined by these various forms of angular momentum, just as a rotating charged object classically produces a magnetic field. However, the most dominant contribution comes from electron spin. Due to the nature of electrons to obey the Pauli exclusion principle, in which no two electrons may be found in the same quantum state, bound electrons pair up with each other, with one member of each pair in a spin up state and the other in the opposite, spin down state. Thus these spins cancel each other out, reducing the total magnetic dipole moment to zero in some atoms with even number of electrons.","Atom\n\nIn ferromagnetic elements such as iron, cobalt and nickel, an odd number of electrons leads to an unpaired electron and a net overall magnetic moment. The orbitals of neighboring atoms overlap and a lower energy state is achieved when the spins of unpaired electrons are aligned with each other, a spontaneous process known as an exchange interaction. When the magnetic moments of ferromagnetic atoms are lined up, the material can produce a measurable macroscopic field. Paramagnetic materials have atoms with magnetic moments that line up in random directions when no magnetic field is present, but the magnetic moments of the individual atoms line up in the presence of a field.","Atom\n\nThe nucleus of an atom will have no spin when it has even numbers of both neutrons and protons, but for other cases of odd numbers, the nucleus may have a spin. Normally nuclei with spin are aligned in random directions because of thermal equilibrium. However, for certain elements (such as xenon-129) it is possible to polarize a significant proportion of the nuclear spin states so that they are aligned in the same direction—a condition called hyperpolarization. This has important applications in magnetic resonance imaging.","Atom\n\nEnergy levels","Atom\n\nThe potential energy of an electron in an atom is negative, its dependence of its position reaches the minimum (the most absolute value) inside the nucleus, and vanishes when the distance from the nucleus goes to infinity, roughly in an inverse proportion to the distance. In the quantum-mechanical model, a bound electron can only occupy a set of states centered on the nucleus, and each state corresponds to a specific energy level; see time-independent Schrödinger equation for theoretical explanation. An energy level can be measured by the amount of energy needed to unbind the electron from the atom, and is usually given in units of electronvolts (eV). The lowest energy state of a bound electron is called the ground state, i.e. stationary state, while an electron transition to a higher level results in an excited state. The electron's energy raises when n increases because the (average) distance to the nucleus increases. Dependence of the energy on azimuthal quantum number| is caused not by electrostatic potential of the nucleus, but by interaction between electrons.","Atom\n\nFor an electron to transition between two different states, e.g. grounded state to first excited level (ionization), it must absorb or emit a photon at an energy matching the difference in the potential energy of those levels, according to Niels Bohr model, what can be precisely calculated by the Schrödinger equation.\nElectrons jump between orbitals in a particle-like fashion. For example, if a single photon strikes the electrons, only a single electron changes states in response to the photon; see Electron properties.","Atom\n\nThe energy of an emitted photon is proportional to its frequency, so these specific energy levels appear as distinct bands in the electromagnetic spectrum. Each element has a characteristic spectrum that can depend on the nuclear charge, subshells filled by electrons, the electromagnetic interactions between the electrons and other factors.","Atom\n\nWhen a continuous spectrum of energy is passed through a gas or plasma, some of the photons are absorbed by atoms, causing electrons to change their energy level. Those excited electrons that remain bound to their atom spontaneously emit this energy as a photon, traveling in a random direction, and so drop back to lower energy levels. Thus the atoms behave like a filter that forms a series of dark absorption bands in the energy output. (An observer viewing the atoms from a view that does not include the continuous spectrum in the background, instead sees a series of emission lines from the photons emitted by the atoms.) Spectroscopic measurements of the strength and width of atomic spectral lines allow the composition and physical properties of a substance to be determined.","Atom\n\nClose examination of the spectral lines reveals that some display a fine structure splitting. This occurs because of spin–orbit coupling, which is an interaction between the spin and motion of the outermost electron. When an atom is in an external magnetic field, spectral lines become split into three or more components; a phenomenon called the Zeeman effect. This is caused by the interaction of the magnetic field with the magnetic moment of the atom and its electrons. Some atoms can have multiple electron configurations with the same energy level, which thus appear as a single spectral line. The interaction of the magnetic field with the atom shifts these electron configurations to slightly different energy levels, resulting in multiple spectral lines. The presence of an external electric field can cause a comparable splitting and shifting of spectral lines by modifying the electron energy levels, a phenomenon called the Stark effect.","Atom\n\nIf a bound electron is in an excited state, an interacting photon with the proper energy can cause stimulated emission of a photon with a matching energy level. For this to occur, the electron must drop to a lower energy state that has an energy difference matching the energy of the interacting photon. The emitted photon and the interacting photon then move off in parallel and with matching phases. That is, the wave patterns of the two photons are synchronized. This physical property is used to make lasers, which can emit a coherent beam of light energy in a narrow frequency band.","Atom\n\nValence and bonding behavior","Atom\n\nValency is the combining power of an element. It is equal to number of hydrogen atoms that atom can combine or displace in forming compounds. The outermost electron shell of an atom in its uncombined state is known as the valence shell, and the electrons in\nthat shell are called valence electrons. The number of valence electrons determines the bonding\nbehavior with other atoms. Atoms tend to chemically react with each other in a manner that fills (or empties) their outer valence shells. For example, a transfer of a single electron between atoms is a useful approximation for bonds that form between atoms with one-electron more than a filled shell, and others that are one-electron short of a full shell, such as occurs in the compound sodium chloride and other chemical ionic salts. However, many elements display multiple valences, or tendencies to share differing numbers of electrons in different compounds. Thus, chemical bonding between these elements takes many forms of electron-sharing that are more than simple electron transfers. Examples include the element carbon and the organic compounds.","Atom\n\nThe chemical elements are often displayed in a periodic table that is laid out to display recurring chemical properties, and elements with the same number of valence electrons form a group that is aligned in the same column of the table. (The horizontal rows correspond to the filling of a quantum shell of electrons.) The elements at the far right of the table have their outer shell completely filled with electrons, which results in chemically inert elements known as the noble gases.","Atom\n\nStates","Atom\n\nQuantities of atoms are found in different states of matter that depend on the physical conditions, such as temperature and pressure. By varying the conditions, materials can transition between solids, liquids, gases and plasmas. Within a state, a material can also exist in different allotropes. An example of this is solid carbon, which can exist as graphite or diamond. Gaseous allotropes exist as well, such as dioxygen and ozone.","Atom\n\nAt temperatures close to absolute zero, atoms can form a Bose–Einstein condensate, at which point quantum mechanical effects, which are normally only observed at the atomic scale, become apparent on a macroscopic scale. This super-cooled collection of atoms\nthen behaves as a single super atom, which may allow fundamental checks of quantum mechanical behavior.","Atom\n\nIdentification","Atom\n\nThe scanning tunneling microscope is a device for viewing surfaces at the atomic level. It uses the quantum tunneling phenomenon, which allows particles to pass through a barrier that would normally be insurmountable. Electrons tunnel through the vacuum between two planar metal electrodes, on each of which is an adsorbed atom, providing a tunneling-current density that can be measured. Scanning one atom (taken as the tip) as it moves past the other (the sample) permits plotting of tip displacement versus lateral separation for a constant current. The calculation shows the extent to which scanning-tunneling-microscope images of an individual atom are visible. It confirms that for low bias, the microscope images the space-averaged dimensions of the electron orbitals across closely packed energy levels—the Fermi level local density of states.","Atom\n\nAn atom can be ionized by removing one of its electrons. The electric charge causes the trajectory of an atom to bend when it passes through a magnetic field. The radius by which the trajectory of a moving ion is turned by the magnetic field is determined by the mass of the atom. The mass spectrometer uses this principle to measure the mass-to-charge ratio of ions. If a sample contains multiple isotopes, the mass spectrometer can determine the proportion of each isotope in the sample by measuring the intensity of the different beams of ions. Techniques to vaporize atoms include inductively coupled plasma atomic emission spectroscopy and inductively coupled plasma mass spectrometry, both of which use a plasma to vaporize samples for analysis.","Atom\n\nA more area-selective method is electron energy loss spectroscopy, which measures the energy loss of an electron beam within a transmission electron microscope when it interacts with a portion of a sample. The atom-probe tomograph has sub-nanometer resolution in 3-D and can chemically identify individual atoms using time-of-flight mass spectrometry.","Atom\n\nSpectra of excited states can be used to analyze the atomic composition of distant stars. Specific light wavelengths contained in the observed light from stars can be separated out and related to the quantized transitions in free gas atoms. These colors can be replicated using a gas-discharge lamp containing the same element. Helium was discovered in this way in the spectrum of the Sun 23 years before it was found on Earth.","Atom\n\nOrigin and current state","Atom\n\nAtoms form about 4% of the total energy density of the observable Universe, with an average density of about 0.25 atoms/m3. Within a galaxy such as the Milky Way, atoms have a much higher concentration, with the density of matter in the interstellar medium (ISM) ranging from 105 to 109 atoms/m3. The Sun is believed to be inside the Local Bubble, a region of highly ionized gas, so the density in the solar neighborhood is only about 103 atoms/m3. Stars form from dense clouds in the ISM, and the evolutionary processes of stars result in the steady enrichment of the ISM with elements more massive than hydrogen and helium. Up to 95% of the Milky Way's atoms are concentrated inside stars and the total mass of atoms forms about 10% of the mass of the galaxy. (The remainder of the mass is an unknown dark matter.)","Atom\n\nFormation","Atom\n\nElectrons are thought to exist in the Universe since early stages of the Big Bang. Atomic nuclei forms in nucleosynthesis reactions. In about three minutes Big Bang nucleosynthesis produced most of the helium, lithium, and deuterium in the Universe, and perhaps some of the beryllium and boron.","Atom\n\nUbiquitousness and stability of atoms relies on their binding energy, which means that an atom has a lower energy than an unbound system of the nucleus and electrons. Where the temperature is much higher than ionization potential, the matter exists in the form of plasma—a gas of positively charged ions (possibly, bare nuclei) and electrons. When the temperature drops below the ionization potential, atoms become statistically favorable. Atoms (complete with bound electrons) became to dominate over charged particles 380,000 years after the Big Bang—an epoch called recombination, when the expanding Universe cooled enough to allow electrons to become attached to nuclei.","Atom\n\nSince the Big Bang, which produced no carbon or heavier elements, atomic nuclei have been combined in stars through the process of nuclear fusion to produce more of the element helium, and (via the triple alpha process) the sequence of elements from carbon up to iron; see stellar nucleosynthesis for details.","Atom\n\nIsotopes such as lithium-6, as well as some beryllium and boron are generated in space through cosmic ray spallation. This occurs when a high-energy proton strikes an atomic nucleus, causing large numbers of nucleons to be ejected.","Atom\n\nElements heavier than iron were produced in supernovae through the r-process and in AGB stars through the s-process, both of which involve the capture of neutrons by atomic nuclei. Elements such as lead formed largely through the radioactive decay of heavier elements.","Atom\n\nEarth","Atom\n\nMost of the atoms that make up the Earth and its inhabitants were present in their current form in the nebula that collapsed out of a molecular cloud to form the Solar System. The rest are the result of radioactive decay, and their relative proportion can be used to determine the age of the Earth through radiometric dating. Most of the helium in the crust of the Earth (about 99% of the helium from gas wells, as shown by its lower abundance of helium-3) is a product of alpha decay.","Atom\n\nThere are a few trace atoms on Earth that were not present at the beginning (i.e., not \"primordial\"), nor are results of radioactive decay. Carbon-14 is continuously generated by cosmic rays in the atmosphere. Some atoms on Earth have been artificially generated either deliberately or as by-products of nuclear reactors or explosions. Of the transuranic elements—those with atomic numbers greater than 92—only plutonium and neptunium occur naturally on Earth. Transuranic elements have radioactive lifetimes shorter than the current age of the Earth and thus identifiable quantities of these elements have long since decayed, with the exception of traces of plutonium-244 possibly deposited by cosmic dust. Natural deposits of plutonium and neptunium are produced by neutron capture in uranium ore.","Atom\n\nThe Earth contains approximately atoms. Although small numbers of independent atoms of noble gases exist, such as argon, neon, and helium, 99% of the atmosphere is bound in the form of molecules, including carbon dioxide and diatomic oxygen and nitrogen. At the surface of the Earth, an overwhelming majority of atoms combine to form various compounds, including water, salt, silicates and oxides. Atoms can also combine to create materials that do not consist of discrete molecules, including crystals and liquid or solid metals. This atomic matter forms networked arrangements that lack the particular type of small-scale interrupted order associated with molecular matter.","Atom\n\nRare and theoretical forms","Atom\n\nSuperheavy elements","Atom\n\nWhile isotopes with atomic numbers higher than lead (82) are known to be radioactive, an \"island of stability\" has been proposed for some elements with atomic numbers above 103. These superheavy elements may have a nucleus that is relatively stable against radioactive decay. The most likely candidate for a stable superheavy atom, unbihexium, has 126 protons and 184 neutrons.","Atom\n\nExotic matter","Atom\n\nEach particle of matter has a corresponding antimatter particle with the opposite electrical charge. Thus, the positron is a positively charged antielectron and the antiproton is a negatively charged equivalent of a proton. When a matter and corresponding antimatter particle meet, they annihilate each other. Because of this, along with an imbalance between the number of matter and antimatter particles, the latter are rare in the universe. The first causes of this imbalance are not yet fully understood, although theories of baryogenesis may offer an explanation. As a result, no antimatter atoms have been discovered in nature. However, in 1996 the antimatter counterpart of the hydrogen atom (antihydrogen) was synthesized at the CERN laboratory in Geneva.","Atom\n\nOther exotic atoms have been created by replacing one of the protons, neutrons or electrons with other particles that have the same charge. For example, an electron can be replaced by a more massive muon, forming a muonic atom. These types of atoms can be used to test the fundamental predictions of physics."],"string":"[\n \"Plasma (physics)\\n\\nPlasma (from Greek πλάσμα, \\\"anything formed\\\" ) is one of the four fundamental states of matter, the others being solid, liquid, and gas. A plasma has properties unlike those of the other states.\",\n \"Plasma (physics)\\n\\nA plasma can be created by heating a gas or subjecting it to a strong electromagnetic field, applied with a laser or microwave generator. This decreases or increases the number of electrons, creating positive or negative charged particles called ions, and is accompanied by the dissociation of molecular bonds, if present.\",\n \"Plasma (physics)\\n\\nThe presence of a significant number of charge carriers makes plasma electrically conductive so that it responds strongly to electromagnetic fields. Like gas, plasma does not have a definite shape or a definite volume unless enclosed in a container. Unlike gas, under the influence of a magnetic field, it may form structures such as filaments, beams and double layers.\",\n \"Plasma (physics)\\n\\nPlasma is the most abundant form of ordinary matter in the Universe (of the forms proven to exist; the more abundant dark matter is hypothetical and may or may not be explained by ordinary matter), most of which is in the rarefied intergalactic regions, particularly the intracluster medium, and in stars, including the Sun. A common form of plasma on Earth is produced in neon signs.\",\n \"Plasma (physics)\\n\\nMuch of the understanding of plasma has come from the pursuit of controlled nuclear fusion and fusion power, for which plasma physics provides the scientific foundation.\",\n \"Plasma (physics)\\n\\nProperties and parameters\",\n \"Plasma (physics)\\n\\nDefinition\",\n \"Plasma (physics)\\n\\nPlasma is an electrically neutral medium of unbound positive and negative particles (i.e. the overall charge of a plasma is roughly zero). It is important to note that although the particles are unbound, they are not ‘free’ in the sense of not experiencing forces. When a charged particle moves, it generates an electric current with magnetic fields; in plasma, the movement of a charged particle affects and is affected by the general field created by the movement of other charges. This governs collective behavior with many degrees of variation. Three factors are listed in the definition of a plasma stream:\",\n \"Plasma (physics)\\n\\n#The plasma approximation: Charged particles must be close enough together that each particle influences many nearby charged particles, rather than just interacting with the closest particle (these collective effects are a distinguishing feature of a plasma). The plasma approximation is valid when the number of charge carriers within the sphere of influence (called the Debye sphere whose radius is the Debye screening length) of a particular particle is higher than unity to provide collective behavior of the charged particles. The average number of particles in the Debye sphere is given by the plasma parameter, \\\"Λ\\\" (the Greek uppercase letter Lambda).\\n#Bulk interactions: The Debye screening length (defined above) is short compared to the physical size of the plasma. This criterion means that interactions in the bulk of the plasma are more important than those at its edges, where boundary effects may take place. When this criterion is satisfied, the plasma is quasineutral.\\n#Plasma frequency: The electron plasma frequency (measuring plasma oscillations of the electrons) is large compared to the electron-neutral collision frequency (measuring frequency of collisions between electrons and neutral particles). When this condition is valid, electrostatic interactions dominate over the processes of ordinary gas kinetics.\",\n \"Plasma (physics)\\n\\nRanges of parameters\",\n \"Plasma (physics)\\n\\nThe factors of a plasma stream can vary by many orders of magnitude, but the properties of plasmas with apparently disparate parameters may be very similar (see plasma scaling). The following chart considers only conventional atomic plasmas and not exotic phenomena like quark gluon plasmas:\",\n \"Plasma (physics)\\n\\nDegree of ionization\",\n \"Plasma (physics)\\n\\nFor plasma to exist, ionization is necessary. The term \\\"plasma density\\\" by itself usually refers to the \\\"electron density\\\", that is, the number of free electrons per unit volume. The degree of ionization of a plasma is the proportion of atoms that have lost or gained electrons, and is controlled mostly by the temperature. Even a partially ionized gas in which as little as 1% of the particles are ionized can have the characteristics of a plasma (i.e., response to magnetic fields and high electrical conductivity). The degree of ionization, \\\\alpha, is defined as \\\\alpha \\\\frac{n_i}{n_i + n_n}, where n_i is the number density of ions and n_n is the number density of neutral atoms. The electron density is related to this by the average charge state \\\\langle Z\\\\rangle of the ions through n_e \\n \\\\langle Z\\\\rangle n_i, where n_e is the number density of electrons.\",\n \"Plasma (physics)\\n\\nTemperatures\",\n \"Plasma (physics)\\n\\nPlasma temperature is commonly measured in kelvins or electronvolts and is, informally, a measure of the thermal kinetic energy per particle. High temperatures are usually needed to sustain ionization, which is a defining feature of a plasma. The degree of plasma ionization is determined by the electron temperature relative to the ionization energy (and more weakly by the density), in a relationship called the Saha equation. At low temperatures, ions and electrons tend to recombine into bound states—atoms —and the plasma will eventually become a gas.\",\n \"Plasma (physics)\\n\\nIn most cases the electrons are close enough to thermal equilibrium that their temperature is relatively well-defined, even when there is a significant deviation from a Maxwellian energy distribution function, for example, due to UV radiation, energetic particles, or strong electric fields. Because of the large difference in mass, the electrons come to thermodynamic equilibrium amongst themselves much faster than they come into equilibrium with the ions or neutral atoms. For this reason, the ion temperature may be very different from (usually lower than) the electron temperature. This is especially common in weakly ionized technological plasmas, where the ions are often near the ambient temperature.\",\n \"Plasma (physics)\\n\\nThermal vs. nonthermal plasmas\",\n \"Plasma (physics)\\n\\nBased on the relative temperatures of the electrons, ions and neutrals, plasmas are classified as \\\"thermal\\\" or \\\"non-thermal\\\". Thermal plasmas have electrons and the heavy particles at the same temperature, i.e. they are in thermal equilibrium with each other. Nonthermal plasmas on the other hand have the ions and neutrals at a much lower temperature (sometimes room temperature), whereas electrons are much \\\"hotter\\\" (T_e \\\\gg T_n).\",\n \"Plasma (physics)\\n\\nComplete vs. incomplete ionization\",\n \"Plasma (physics)\\n\\nA plasma is sometimes referred to as being \\\"hot\\\" if it is nearly fully ionized, or \\\"cold\\\" if only a small fraction (for example 1%) of the gas molecules are ionized, but other definitions of the terms \\\"hot plasma\\\" and \\\"cold plasma\\\" are common. Even in a \\\"cold\\\" plasma, the electron temperature is still typically several thousand degrees Celsius. Plasmas utilized in \\\"plasma technology\\\" (\\\"technological plasmas\\\") are usually cold plasmas in the sense that only a small fraction of the gas molecules are ionized.\",\n \"Plasma (physics)\\n\\nPlasma potential\",\n \"Plasma (physics)\\n\\nSince plasmas are very good electrical conductors, electric potentials play an important role.\\nThe potential as it exists on average in the space between charged particles, independent of the question of how it can be measured, is called the \\\"plasma potential\\\", or the \\\"space potential\\\". If an electrode is inserted into a plasma, its potential will generally lie considerably below the plasma potential due to what is termed a Debye sheath. The good electrical conductivity of plasmas makes their electric fields very small. This results in the important concept of \\\"quasineutrality\\\", which says the density of negative charges is approximately equal to the density of positive charges over large volumes of the plasma (n_e = \\\\langle Z\\\\rangle n_i), but on the scale of the Debye length there can be charge imbalance. In the special case that double layers are formed, the charge separation can extend some tens of Debye lengths.\",\n \"Plasma (physics)\\n\\nThe magnitude of the potentials and electric fields must be determined by means other than simply finding the net charge density. A common example is to assume that the electrons satisfy the Boltzmann relation:\\nn_e \\\\propto e^{e\\\\Phi/k_BT_e}.\",\n \"Plasma (physics)\\n\\nDifferentiating this relation provides a means to calculate the electric field from the density:\\n\\\\vec{E} = (k_BT_e/e)(\\\\nabla n_e/n_e).\",\n \"Plasma (physics)\\n\\nIt is possible to produce a plasma that is not quasineutral. An electron beam, for example, has only negative charges. The density of a non-neutral plasma must generally be very low, or it must be very small, otherwise it will be dissipated by the repulsive electrostatic force.\",\n \"Plasma (physics)\\n\\nIn astrophysical plasmas, Debye screening prevents electric fields from directly affecting the plasma over large distances, i.e., greater than the Debye length. However, the existence of charged particles causes the plasma to generate, and be affected by, magnetic fields. This can and does cause extremely complex behavior, such as the generation of plasma double layers, an object that separates charge over a few tens of Debye lengths. The dynamics of plasmas interacting with external and self-generated magnetic fields are studied in the academic discipline of magnetohydrodynamics.\",\n \"Plasma (physics)\\n\\nMagnetization\",\n \"Plasma (physics)\\n\\nPlasma with a magnetic field strong enough to influence the motion of the charged particles is said to be magnetized. A common quantitative criterion is that a particle on average completes at least one gyration around the magnetic field before making a collision, i.e., \\\\omega_{\\\\mathrm{ce}} / v_{\\\\mathrm{coll}} > 1, where \\\\omega_{\\\\mathrm{ce}} is the \\\"electron gyrofrequency\\\" and v_{\\\\mathrm{coll}} is the \\\"electron collision rate\\\". It is often the case that the electrons are magnetized while the ions are not. Magnetized plasmas are anisotropic, meaning that their properties in the direction parallel to the magnetic field are different from those perpendicular to it. While electric fields in plasmas are usually small due to the high conductivity, the electric field associated with a plasma moving in a magnetic field is given by \\\\mathbf{E} = -v\\\\times\\\\mathbf{B} (where \\\\mathbf{E} is the electric field, \\\\mathbf{v} is the velocity, and \\\\mathbf{B} is the magnetic field), and is not affected by Debye shielding.\",\n \"Plasma (physics)\\n\\nComparison of plasma and gas phases\",\n \"Plasma (physics)\\n\\nPlasma is often called the fourth state of matter after solid, liquids and gases, despite plasma typically being an ionized gas. It is distinct from these and other lower-energy states of matter. Although it is closely related to the gas phase in that it also has no definite form or volume, it differs in a number of ways, including the following:\",\n \"Plasma (physics)\\n\\nCommon plasmas\",\n \"Plasma (physics)\\n\\nPlasmas are by far the most common phase of ordinary matter in the universe, both by mass and by volume. Essentially, all of the visible light from space comes from stars, which are plasmas with a temperature such that they radiate strongly at visible wavelengths. Most of the ordinary (or baryonic) matter in the universe, however, is found in the intergalactic medium, which is also a plasma, but much hotter, so that it radiates primarily as X-rays.\",\n \"Plasma (physics)\\n\\nIn 1937, Hannes Alfvén argued that if plasma pervaded the universe, it could then carry electric currents capable of generating a galactic magnetic field. After winning the Nobel Prize, he emphasized that: In order to understand the phenomena in a certain plasma region, it is necessary to map not only the magnetic but also the electric field and the electric currents. Space is filled with a network of currents which transfer energy and momentum over large or very large distances. The currents often pinch to filamentary or surface currents. The latter are likely to give space, as also interstellar and intergalactic space, a cellular structure.\",\n \"Plasma (physics)\\n\\nBy contrast the current scientific consensus is that about 96% of the total energy density in the universe is not plasma or any other form of ordinary matter, but a combination of cold dark matter and dark energy. Our Sun, and all stars, are made of plasma, much of interstellar space is filled with a plasma, albeit a very sparse one, and intergalactic space too. Even black holes, which are not directly visible, are thought to be fuelled by accreting ionising matter (i.e. plasma), and they are associated with astrophysical jets of luminous ejected plasma, such as M87's jet that extends 5,000 light-years.\",\n \"Plasma (physics)\\n\\nIn our solar system, interplanetary space is filled with the plasma of the Solar Wind that extends from the Sun out to the heliopause. However, the density of ordinary matter is much higher than average and much higher than that of either dark matter or dark energy. The planet Jupiter accounts for most of the non-plasma within the orbit of Pluto (about 0.1% by mass, or 10−15% by volume).\",\n \"Plasma (physics)\\n\\nDust and small grains within a plasma will also pick up a net negative charge, so that they in turn may act like a very heavy negative ion component of the plasma (see dusty plasmas).\",\n \"Plasma (physics)\\n\\nComplex plasma phenomena\",\n \"Plasma (physics)\\n\\nAlthough the underlying equations governing plasmas are relatively simple, plasma behavior is extraordinarily varied and subtle: the emergence of unexpected behavior from a simple model is a typical feature of a complex system. Such systems lie in some sense on the boundary between ordered and disordered behavior and cannot typically be described either by simple, smooth, mathematical functions, or by pure randomness. The spontaneous formation of interesting spatial features on a wide range of length scales is one manifestation of plasma complexity. The features are interesting, for example, because they are very sharp, spatially intermittent (the distance between features is much larger than the features themselves), or have a fractal form. Many of these features were first studied in the laboratory, and have subsequently been recognized throughout the universe. Examples of complexity and complex structures in plasmas include:\",\n \"Plasma (physics)\\n\\nFilamentation\",\n \"Plasma (physics)\\n\\nStriations or string-like structures, also known as birkeland currents, are seen in many plasmas, like the plasma ball, the aurora, lightning, electric arcs, solar flares, and supernova remnants. They are sometimes associated with larger current densities, and the interaction with the magnetic field can form a magnetic rope structure. High power microwave breakdown at atmospheric pressure also leads to the formation of filamentary structures. (See also Plasma pinch)\",\n \"Plasma (physics)\\n\\nFilamentation also refers to the self-focusing of a high power laser pulse. At high powers, the nonlinear part of the index of refraction becomes important and causes a higher index of refraction in the center of the laser beam, where the laser is brighter than at the edges, causing a feedback that focuses the laser even more. The tighter focused laser has a higher peak brightness (irradiance) that forms a plasma. The plasma has an index of refraction lower than one, and causes a defocusing of the laser beam. The interplay of the focusing index of refraction, and the defocusing plasma makes the formation of a long filament of plasma that can be micrometers to kilometers in length. One interesting aspect of the filamentation generated plasma is the relatively low ion density due to defocusing effects of the ionized electrons. (See also Filament propagation)\",\n \"Plasma (physics)\\n\\nShocks or double layers\",\n \"Plasma (physics)\\n\\nPlasma properties change rapidly (within a few Debye lengths) across a two-dimensional sheet in the presence of a (moving) shock or (stationary) double layer. Double layers involve localized charge separation, which causes a large potential difference across the layer, but does not generate an electric field outside the layer. Double layers separate adjacent plasma regions with different physical characteristics, and are often found in current carrying plasmas. They accelerate both ions and electrons.\",\n \"Plasma (physics)\\n\\nElectric fields and circuits\",\n \"Plasma (physics)\\n\\nQuasineutrality of a plasma requires that plasma currents close on themselves in electric circuits. Such circuits follow Kirchhoff's circuit laws and possess a resistance and inductance. These circuits must generally be treated as a strongly coupled system, with the behavior in each plasma region dependent on the entire circuit. It is this strong coupling between system elements, together with nonlinearity, which may lead to complex behavior. Electrical circuits in plasmas store inductive (magnetic) energy, and should the circuit be disrupted, for example, by a plasma instability, the inductive energy will be released as plasma heating and acceleration. This is a common explanation for the heating that takes place in the solar corona. Electric currents, and in particular, magnetic-field-aligned electric currents (which are sometimes generically referred to as \\\"Birkeland currents\\\"), are also observed in the Earth's aurora, and in plasma filaments.\",\n \"Plasma (physics)\\n\\nCellular structure\",\n \"Plasma (physics)\\n\\nNarrow sheets with sharp gradients may separate regions with different properties such as magnetization, density and temperature, resulting in cell-like regions. Examples include the magnetosphere, heliosphere, and heliospheric current sheet. Hannes Alfvén wrote: \\\"From the cosmological point of view, the most important new space research discovery is probably the cellular structure of space. As has been seen in every region of space accessible to in situ measurements, there are a number of 'cell walls', sheets of electric currents, which divide space into compartments with different magnetization, temperature, density, etc.\\\"\",\n \"Plasma (physics)\\n\\nCritical ionization velocity\",\n \"Plasma (physics)\\n\\nThe critical ionization velocity is the relative velocity between an ionized plasma and a neutral gas, above which a runaway ionization process takes place. The critical ionization process is a quite general mechanism for the conversion of the kinetic energy of a rapidly streaming gas into ionization and plasma thermal energy. Critical phenomena in general are typical of complex systems, and may lead to sharp spatial or temporal features.\",\n \"Plasma (physics)\\n\\nUltracold plasma\",\n \"Plasma (physics)\\n\\nUltracold plasmas are created in a magneto-optical trap (MOT) by trapping and cooling neutral atoms, to temperatures of 1 mK or lower, and then using another laser to ionize the atoms by giving each of the outermost electrons just enough energy to escape the electrical attraction of its parent ion.\",\n \"Plasma (physics)\\n\\nOne advantage of ultracold plasmas are their well characterized and tunable initial conditions, including their size and electron temperature. By adjusting the wavelength of the ionizing laser, the kinetic energy of the liberated electrons can be tuned as low as 0.1 K, a limit set by the frequency bandwidth of the laser pulse. The ions inherit the millikelvin temperatures of the neutral atoms, but are quickly heated through a process known as disorder induced heating (DIH). This type of non-equilibrium ultracold plasma evolves rapidly, and displays many other interesting phenomena.\",\n \"Plasma (physics)\\n\\nOne of the metastable states of a strongly nonideal plasma is Rydberg matter, which forms upon condensation of excited atoms.\",\n \"Plasma (physics)\\n\\nNon-neutral plasma\",\n \"Plasma (physics)\\n\\nThe strength and range of the electric force and the good conductivity of plasmas usually ensure that the densities of positive and negative charges in any sizeable region are equal (\\\"quasineutrality\\\"). A plasma with a significant excess of charge density, or, in the extreme case, is composed of a single species, is called a non-neutral plasma. In such a plasma, electric fields play a dominant role. Examples are charged particle beams, an electron cloud in a Penning trap and positron plasmas.\",\n \"Plasma (physics)\\n\\nDusty plasma/grain plasma\",\n \"Plasma (physics)\\n\\nA dusty plasma contains tiny charged particles of dust (typically found in space). The dust particles acquire high charges and interact with each other. A plasma that contains larger particles is called grain plasma. Under laboratory conditions, dusty plasmas are also called complex plasmas.\",\n \"Plasma (physics)\\n\\nImpermeable plasma\",\n \"Plasma (physics)\\n\\nImpermeable plasma is a type of thermal plasma which acts like an impermeable solid with respect to gas or cold plasma and can be physically pushed. Interaction of cold gas and thermal plasma was briefly studied by a group led by Hannes Alfvén in 1960s and 1970s for its possible applications in insulation of fusion plasma from the reactor walls. However, later it was found that the external magnetic fields in this configuration could induce kink instabilities in the plasma and subsequently lead to an unexpectedly high heat loss to the walls. In 2013, a group of materials scientists reported that they have successfully generated stable impermeable plasma with no magnetic confinement using only an ultrahigh-pressure blanket of cold gas. While spectroscopic data on the characteristics of plasma were claimed to be difficult to obtain due to the high pressure, the passive effect of plasma on synthesis of different nanostructures clearly suggested the effective confinement.\",\n \"Plasma (physics)\\n\\nThey also showed that upon maintaining the impermeability for a few tens of seconds, screening of ions at the plasma-gas interface could give rise to a strong secondary mode of heating (known as viscous heating) leading to different kinetics of reactions and formation of complex nanomaterials.\",\n \"Plasma (physics)\\n\\nMathematical descriptions\",\n \"Plasma (physics)\\n\\nTo completely describe the state of a plasma, we would need to write down all the\\nparticle locations and velocities and describe the electromagnetic field in the plasma region.\\nHowever, it is generally not practical or necessary to keep track of all the particles in a plasma.\\nTherefore, plasma physicists commonly use less detailed descriptions, of which\\nthere are two main types:\",\n \"Plasma (physics)\\n\\nFluid model\",\n \"Plasma (physics)\\n\\nFluid models describe plasmas in terms of smoothed quantities, like density and averaged velocity around each position (see Plasma parameters). One simple fluid model, magnetohydrodynamics, treats the plasma as a single fluid governed by a combination of Maxwell's equations and the Navier–Stokes equations. A more general description is the two-fluid plasma picture, where the ions and electrons are described separately. Fluid models are often accurate when collisionality is sufficiently high to keep the plasma velocity distribution close to a Maxwell–Boltzmann distribution. Because fluid models usually describe the plasma in terms of a single flow at a certain temperature at each spatial location, they can neither capture velocity space structures like beams or double layers, nor resolve wave-particle effects.\",\n \"Plasma (physics)\\n\\nKinetic model\",\n \"Plasma (physics)\\n\\nKinetic models describe the particle velocity distribution function at each point in the plasma and therefore do not need to assume a Maxwell–Boltzmann distribution. A kinetic description is often necessary for collisionless plasmas. There are two common approaches to kinetic description of a plasma. One is based on representing the smoothed distribution function on a grid in velocity and position. The other, known as the particle-in-cell (PIC) technique, includes kinetic information by following the trajectories of a large number of individual particles. Kinetic models are generally more computationally intensive than fluid models. The Vlasov equation may be used to describe the dynamics of a system of charged particles interacting with an electromagnetic field.\\nIn magnetized plasmas, a gyrokinetic approach can substantially reduce the computational expense of a fully kinetic simulation.\",\n \"Plasma (physics)\\n\\nArtificial plasmas\",\n \"Plasma (physics)\\n\\nMost artificial plasmas are generated by the application of electric and/or magnetic fields through a gas. Plasma generated in a laboratory setting and for industrial use can be generally categorized by:\\n*The type of power source used to generate the plasma—DC, RF and microwave\\n*The pressure they operate at—vacuum pressure (T_e T_i \\n T_{gas}), non-thermal or \\\"cold\\\" plasma (T_e \\\\gg T_i = T_{gas})\\n*The electrode configuration used to generate the plasma\\n*The magnetization of the particles within the plasma—magnetized (both ion and electrons are trapped in Larmor orbits by the magnetic field), partially magnetized (the electrons but not the ions are trapped by the magnetic field), non-magnetized (the magnetic field is too weak to trap the particles in orbits but may generate Lorentz forces)\",\n \"Plasma (physics)\\n\\nGeneration of artificial plasma\",\n \"Plasma (physics)\\n\\nJust like the many uses of plasma, there are several means for its generation, however, one principle is common to all of them: there must be energy input to produce and sustain it. For this case, plasma is generated when an electric current is applied across a dielectric gas or fluid (an electrically non-conducting material) as can be seen in the image to the right, which shows a discharge tube as a simple example (DC used for simplicity).\",\n \"Plasma (physics)\\n\\nThe potential difference and subsequent electric field pull the bound electrons (negative) toward the anode (positive electrode) while the cathode (negative electrode) pulls the nucleus. As the voltage increases, the current stresses the material (by electric polarization) beyond its dielectric limit (termed strength) into a stage of electrical breakdown, marked by an electric spark, where the material transforms from being an insulator into a conductor (as it becomes increasingly ionized). The underlying process is the Townsend avalanche, where collisions between electrons and neutral gas atoms create more ions and electrons (as can be seen in the figure on the right). The first impact of an electron on an atom results in one ion and two electrons. Therefore, the number of charged particles increases rapidly (in the millions) only \\\"after about 20 successive sets of collisions\\\", mainly due to a small mean free path (average distance travelled between collisions).\",\n \"Plasma (physics)\\n\\nElectric arc\",\n \"Plasma (physics)\\n\\nWith ample current density and ionization, this forms a luminous electric arc (a continuous electric discharge similar to lightning) between the electrodes. Electrical resistance along the continuous electric arc creates heat, which dissociates more gas molecules and ionizes the resulting atoms (where degree of ionization is determined by temperature), and as per the sequence: solid-liquid-gas-plasma, the gas is gradually turned into a thermal plasma. A thermal plasma is in thermal equilibrium, which is to say that the temperature is relatively homogeneous throughout the heavy particles (i.e. atoms, molecules and ions) and electrons. This is so because when thermal plasmas are generated, electrical energy is given to electrons, which, due to their great mobility and large numbers, are able to disperse it rapidly and by elastic collision (without energy loss) to the heavy particles.Note that non-thermal, or non-equilibrium plasmas are not as ionized and have lower energy densities, and thus the temperature is not dispersed evenly among the particles, where some heavy ones remain ‘cold’.\",\n \"Plasma (physics)\\n\\nExamples of industrial/commercial plasma\",\n \"Plasma (physics)\\n\\nBecause of their sizable temperature and density ranges, plasmas find applications in many fields of research, technology and industry. For example, in: industrial and extractive metallurgy, surface treatments such as plasma spraying (coating), etching in microelectronics, metal cutting and welding; as well as in everyday vehicle exhaust cleanup and fluorescent/luminescent lamps, while even playing a part in supersonic combustion engines for aerospace engineering.\",\n \"Plasma (physics)\\n\\nLow-pressure discharges\",\n \"Plasma (physics)\\n\\n*Glow discharge plasmas: non-thermal plasmas generated by the application of DC or low frequency RF (2O3 to produce aluminium. *Corona discharge: this is a non-thermal discharge generated by the application of high voltage to sharp electrode tips. It is commonly used in ozone generators and particle precipitators. *Dielectric barrier discharge (DBD): this is a non-thermal discharge generated by the application of high voltages across small gaps wherein a non-conducting coating prevents the transition of the plasma discharge into an arc. It is often mislabeled 'Corona' discharge in industry and has similar application to corona discharges. It is also widely used in the web treatment of fabrics. The application of the discharge to synthetic fabrics and plastics functionalizes the surface and allows for paints, glues and similar materials to adhere. *Capacitive discharge: this is a nonthermal plasma generated by the application of RF power (e.g., 13.56 MHz) to one powered electrode, with a grounded electrode held at a small separation distance on the order of 1 cm. Such discharges are commonly stabilized using a noble gas such as helium or argon. *\\\"Piezoelectric direct discharge plasma:\\\" is a nonthermal plasma generated at the high-side of a piezoelectric transformer (PT).\",\n \"Plasma (physics)\\n\\nThis generation variant is particularly suited for high efficient and compact devices where a separate high voltage power supply is not desired.\",\n \"Plasma (physics)\\n\\nHistory\",\n \"Plasma (physics)\\n\\nPlasma was first identified in a Crookes tube, and so described by Sir William Crookes in 1879 (he called it \\\"radiant matter\\\"). The nature of the Crookes tube \\\"cathode ray\\\" matter was subsequently identified by British physicist Sir J.J. Thomson in 1897. The term \\\"plasma\\\" was coined by Irving Langmuir in 1928, perhaps because the glowing discharge molds itself to the shape of the Crookes tube (Gr. πλάσμα – a thing moulded or formed). Langmuir described his observations as:\",\n \"Plasma (physics)\\n\\nExcept near the electrodes, where there are sheaths containing very few electrons, the ionized gas contains ions and electrons in about equal numbers so that the resultant space charge is very small. We shall use the name plasma to describe this region containing balanced charges of ions and electrons.\",\n \"Plasma (physics)\\n\\nResearch\",\n \"Plasma (physics)\\n\\nPlasmas are the object of study of the academic field of plasma science or plasma physics, including sub-disciplines such as space plasma physics.\\nThere are multiple journals devoted to the subject (see list).\\nIt involves the following fields of active research (see also list of articles):\",\n \"Plasma (physics)\\n\\n*Plasma theory\\n**Plasma equilibria and stability\\n**Plasma interactions with waves and beams\\n**Guiding center\\n**Adiabatic invariant\\n**Debye sheath\\n**Coulomb collision\\n*Plasmas in nature\\n**The Earth's ionosphere\\n**Northern and southern (polar) lights\\n**Space plasmas, e.g. Earth's plasmasphere (an inner portion of the magnetosphere dense with plasma)\\n**Astrophysical plasma\\n**Interplanetary medium\\n*Industrial plasmas\\n**Plasma chemistry\\n**Plasma processing\\n**Plasma spray\\n**Plasma display\\n**Plasma sources\\n**Dusty plasmas\\n*Plasma diagnostics\\n**Thomson scattering\\n**Langmuir probe\\n**Ball-pen probe\\n**Faraday cup\\n**Spectroscopy\\n**Interferometry\\n**Ionospheric heating\\n**Incoherent scatter radar\",\n \"Plasma (physics)\\n\\n*Plasma applications\\n**Dielectric barrier discharge\\n**Enhanced oil recovery\\n**Fusion power\\n***Magnetic fusion energy (MFE) — tokamak, stellarator, reversed field pinch, magnetic mirror, dense plasma focus\\n***Inertial fusion energy (IFE) (also Inertial confinement fusion — ICF)\\n***Plasma weapon\\n**Ion implantation\\n**Ion thruster\\n**MAGPIE (short for Mega Ampere Generator for Plasma Implosion Experiments)\\n**Plasma ashing\\n**Food processing (nonthermal plasma, aka \\\"cold plasma\\\")\\n**Plasma arc waste disposal, convert waste into reusable material with plasma.\\n**Plasma acceleration\\n**Plasma medicine (e. g. Dentistry )\\n**Plasma window\",\n \"Plasma (physics)\\n\\nFile:Wispy 'Plasma Dancer' on the limb of the Sun.ogv|Solar plasma\\nFile:Plasma Spraying Process.jpg|Plasma spraying\",\n \"Electric charge\\n\\nElectric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charges: positive and negative. Like charges repel and unlike attract. An object is negatively charged if it has an excess of electrons, and is otherwise positively charged or uncharged. The SI derived unit of electric charge is the coulomb (C). In electrical engineering, it is also common to use the ampere-hour (Ah), and, in chemistry, it is common to use the elementary charge (e) as a unit. The symbol Q often denotes charge. Early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that don't require consideration of quantum effects.\",\n \"Electric charge\\n\\nThe electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields. The interaction between a moving charge and an electromagnetic field is the source of the electromagnetic force, which is one of the four fundamental forces (See also: magnetic field).\",\n \"Electric charge\\n\\nTwentieth-century experiments demonstrated that electric charge is quantized; that is, it comes in integer multiples of individual small units called the elementary charge, e, approximately equal to (except for particles called quarks, which have charges that are integer multiples of e/3). The proton has a charge of +e, and the electron has a charge of -e. The study of charged particles, and how their interactions are mediated by photons, is called quantum electrodynamics.\",\n \"Electric charge\\n\\nOverview\",\n \"Electric charge\\n\\nCharge is the fundamental property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter.\\nElectric charge is a characteristic property of many subatomic particles. The charges of free-standing particles are integer multiples of the elementary charge e; we say that electric charge is quantized. Michael Faraday, in his electrolysis experiments, was the first to note the discrete nature of electric charge. Robert Millikan's oil drop experiment demonstrated this fact directly, and measured the elementary charge.\",\n \"Electric charge\\n\\nBy convention, the charge of an electron is −1, while that of a proton is +1. Charged particles whose charges have the same sign repel one another, and particles whose charges have different signs attract. Coulomb's law quantifies the electrostatic force between two particles by asserting that the force is proportional to the product of their charges, and inversely proportional to the square of the distance between them.\",\n \"Electric charge\\n\\nThe charge of an antiparticle equals that of the corresponding particle, but with opposite sign. Quarks have fractional charges of either − or +, but free-standing quarks have never been observed (the theoretical reason for this fact is asymptotic freedom).\",\n \"Electric charge\\n\\nThe electric charge of a macroscopic object is the sum of the electric charges of the particles that make it up. This charge is often small, because matter is made of atoms, and atoms typically have equal numbers of protons and electrons, in which case their charges cancel out, yielding a net charge of zero, thus making the atom neutral.\",\n \"Electric charge\\n\\nAn ion is an atom (or group of atoms) that has lost one or more electrons, giving it a net positive charge (cation), or that has gained one or more electrons, giving it a net negative charge (anion). Monatomic ions are formed from single atoms, while polyatomic ions are formed from two or more atoms that have been bonded together, in each case yielding an ion with a positive or negative net charge.\",\n \"Electric charge\\n\\nDuring formation of macroscopic objects, constituent atoms and ions usually combine to form structures composed of neutral ionic compounds electrically bound to neutral atoms. Thus macroscopic objects tend toward being neutral overall, but macroscopic objects are rarely perfectly net neutral.\",\n \"Electric charge\\n\\nSometimes macroscopic objects contain ions distributed throughout the material, rigidly bound in place, giving an overall net positive or negative charge to the object. Also, macroscopic objects made of conductive elements, can more or less easily (depending on the element) take on or give off electrons, and then maintain a net negative or positive charge indefinitely. When the net electric charge of an object is non-zero and motionless, the phenomenon is known as static electricity. This can easily be produced by rubbing two dissimilar materials together, such as rubbing amber with fur or glass with silk. In this way non-conductive materials can be charged to a significant degree, either positively or negatively. Charge taken from one material is moved to the other material, leaving an opposite charge of the same magnitude behind. The law of conservation of charge always applies, giving the object from which a negative charge is taken a positive charge of the same magnitude, and vice versa.\",\n \"Electric charge\\n\\nEven when an object's net charge is zero, charge can be distributed non-uniformly in the object (e.g., due to an external electromagnetic field, or bound polar molecules). In such cases the object is said to be polarized. The charge due to polarization is known as bound charge, while charge on an object produced by electrons gained or lost from outside the object is called free charge. The motion of electrons in conductive metals in a specific direction is known as electric current.\",\n \"Electric charge\\n\\nUnits\",\n \"Electric charge\\n\\nThe SI unit of quantity of electric charge is the coulomb, which is equivalent to about (e is the charge of a proton). Hence, the charge of an electron is approximately . The coulomb is defined as the quantity of charge that has passed through the cross section of an electrical conductor carrying one ampere within one second. The symbol Q is often used to denote a quantity of electricity or charge. The quantity of electric charge can be directly measured with an electrometer, or indirectly measured with a ballistic galvanometer.\",\n \"Electric charge\\n\\nAfter finding the quantized character of charge, in 1891 George Stoney proposed the unit 'electron' for this fundamental unit of electrical charge. This was before the discovery of the particle by J.J. Thomson in 1897. The unit is today treated as nameless, referred to as \\\"elementary charge\\\", \\\"fundamental unit of charge\\\", or simply as \\\"e\\\". A measure of charge should be a multiple of the elementary charge e, even if at large scales charge seems to behave as a real quantity. In some contexts it is meaningful to speak of fractions of a charge; for example in the charging of a capacitor, or in the fractional quantum Hall effect.\",\n \"Electric charge\\n\\nIn systems of units other than SI such as cgs, electric charge is expressed as combination of only three fundamental quantities (length, mass, and time), and not four, as in SI, where electric charge is a combination of length, mass, time, and electric current.\",\n \"Electric charge\\n\\nHistory\",\n \"Electric charge\\n\\nAs reported by the ancient Greek mathematician Thales of Miletus around 600 BC, charge (or electricity) could be accumulated by rubbing fur on various substances, such as amber. The Greeks noted that the charged amber buttons could attract light objects such as hair. They also noted that if they rubbed the amber for long enough, they could even get an electric spark to jump. This property derives from the triboelectric effect.\",\n \"Electric charge\\n\\nIn 1600, the English scientist William Gilbert returned to the subject in De Magnete, and coined the New Latin word electricus from (ēlektron), the Greek word for amber, which soon gave rise to the English words \\\"electric\\\" and \\\"electricity.\\\" He was followed in 1660 by Otto von Guericke, who invented what was probably the first electrostatic generator. Other European pioneers were Robert Boyle, who in 1675 stated that electric attraction and repulsion can act across a vacuum; Stephen Gray, who in 1729 classified materials as conductors and insulators; and C. F. du Fay, who proposed in 1733 that electricity comes in two varieties that cancel each other, and expressed this in terms of a two-fluid theory. When glass was rubbed with silk, du Fay said that the glass was charged with vitreous electricity, and, when amber was rubbed with fur, the amber was charged with resinous electricity. In 1839, Michael Faraday showed that the apparent division between static electricity, current electricity, and bioelectricity was incorrect, and all were a consequence of the behavior of a single kind of electricity appearing in opposite polarities. It is arbitrary which polarity is called positive and which is called negative.\",\n \"Electric charge\\n\\nPositive charge can be defined as the charge left on a glass rod after being rubbed with silk.\",\n \"Electric charge\\n\\nOne of the foremost experts on electricity in the 18th century was Benjamin Franklin, who argued in favour of a one-fluid theory of electricity. Franklin imagined electricity as being a type of invisible fluid present in all matter; for example, he believed that it was the glass in a Leyden jar that held the accumulated charge. He posited that rubbing insulating surfaces together caused this fluid to change location, and that a flow of this fluid constitutes an electric current. He also posited that when matter contained too little of the fluid it was \\\"negatively\\\" charged, and when it had an excess it was \\\"positively\\\" charged. For a reason that was not recorded, he identified the term \\\"positive\\\" with vitreous electricity and \\\"negative\\\" with resinous electricity. William Watson arrived at the same explanation at about the same time.\",\n \"Electric charge\\n\\nStatic electricity and electric current\",\n \"Electric charge\\n\\nStatic electricity and electric current are two separate phenomena. They both involve electric charge, and may occur simultaneously in the same object. Static electricity refers to the electric charge of an object and the related electrostatic discharge when two objects are brought together that are not at equilibrium. An electrostatic discharge creates a change in the charge of each of the two objects. In contrast, electric current is the flow of electric charge through an object, which produces no net loss or gain of electric charge.\",\n \"Electric charge\\n\\nElectrification by friction\",\n \"Electric charge\\n\\nWhen a piece of glass and a piece of resin—neither of which exhibit any electrical properties—are rubbed together and left with the rubbed surfaces in contact, they still exhibit no electrical properties. When separated, they attract each other.\",\n \"Electric charge\\n\\nA second piece of glass rubbed with a second piece of resin, then separated and suspended near the former pieces of glass and resin causes these phenomena:\\n*The two pieces of glass repel each other.\\n*Each piece of glass attracts each piece of resin.\\n*The two pieces of resin repel each other.\",\n \"Electric charge\\n\\nThis attraction and repulsion is an electrical phenomena, and the bodies that exhibit them are said to be electrified, or electrically charged. Bodies may be electrified in many other ways, as well as by friction. The electrical properties of the two pieces of glass are similar to each other but opposite to those of the two pieces of resin: The glass attracts what the resin repels and repels what the resin attracts.\",\n \"Electric charge\\n\\nIf a body electrified in any manner whatsoever behaves as the glass does, that is, if it repels the glass and attracts the resin, the body is said to be 'vitreously' electrified, and if it attracts the glass and repels the resin it is said to be 'resinously' electrified. All electrified bodies are either vitreously or resinously electrified.\",\n \"Electric charge\\n\\nAn established convention in the scientific community defines vitreous electrification as positive, and resinous electrification as negative. The exactly opposite properties of the two kinds of electrification justify our indicating them by opposite signs, but the application of the positive sign to one rather than to the other kind must be considered as a matter of arbitrary convention—just as it is a matter of convention in mathematical diagram to reckon positive distances towards the right hand.\",\n \"Electric charge\\n\\nNo force, either of attraction or of repulsion, can be observed between an electrified body and a body not electrified.\",\n \"Electric charge\\n\\nActually, all bodies are electrified, but may appear not electrified because of the relatively similar charge of neighboring objects in the environment. An object further electrified + or – creates an equivalent or opposite charge by default in neighboring objects, until those charges can equalize. The effects of attraction can be observed in high-voltage experiments, while lower voltage effects are merely weaker and therefore less obvious. The attraction and repulsion forces are codified by Coulomb's law (attraction falls off at the square of the distance, which has a corollary for acceleration in a gravitational field, suggesting that gravitation may be merely electrostatic phenomenon between relatively weak charges in terms of scale). See also Casimir effect.\",\n \"Electric charge\\n\\nIt is now known that the Franklin-Watson model was fundamentally correct. There is only one kind of electrical charge, and only one variable is required to keep track of the amount of charge. On the other hand, just knowing the charge is not a complete description of the situation. Matter is composed of several kinds of electrically charged particles, and these particles have many properties, not just charge.\",\n \"Electric charge\\n\\nThe most common charge carriers are the positively charged proton and the negatively charged electron. The movement of any of these charged particles constitutes an electric current. In many situations, it suffices to speak of the conventional current without regard to whether it is carried by positive charges moving in the direction of the conventional current or by negative charges moving in the opposite direction. This macroscopic viewpoint is an approximation that simplifies electromagnetic concepts and calculations.\",\n \"Electric charge\\n\\nAt the opposite extreme, if one looks at the microscopic situation, one sees there are many ways of carrying an electric current, including: a flow of electrons; a flow of electron \\\"holes\\\" that act like positive particles; and both negative and positive particles (ions or other charged particles) flowing in opposite directions in an electrolytic solution or a plasma.\",\n \"Electric charge\\n\\nBeware that, in the common and important case of metallic wires, the direction of the conventional current is opposite to the drift velocity of the actual charge carriers, i.e., the electrons. This is a source of confusion for beginners.\",\n \"Electric charge\\n\\nConservation of electric charge\",\n \"Electric charge\\n\\nThe total electric charge of an isolated system remains constant regardless of changes within the system itself. This law is inherent to all processes known to physics and can be derived in a local form from gauge invariance of the wave function. The conservation of charge results in the charge-current continuity equation. More generally, the net change in charge density ρ within a volume of integration V is equal to the area integral over the current density J through the closed surface S = ∂V, which is in turn equal to the net current I:\\nThus, the conservation of electric charge, as expressed by the continuity equation, gives the result:\\nI = -\\\\frac{\\\\mathrm{d}Q}{\\\\mathrm{d}t}.\",\n \"Electric charge\\n\\nThe charge transferred between times t_\\\\mathrm{i} and t_\\\\mathrm{f} is obtained by integrating both sides:\\nQ = \\\\int_{t_{\\\\mathrm{i}}}^{t_{\\\\mathrm{f}}} I\\\\, \\\\mathrm{d}t \\nwhere I is the net outward current through a closed surface and Q is the electric charge contained within the volume defined by the surface.\",\n \"Electric charge\\n\\nRelativistic invariance\",\n \"Electric charge\\n\\nAside from the properties described in articles about electromagnetism, charge is a relativistic invariant. This means that any particle that has charge Q, no matter how fast it goes, always has charge Q. This property has been experimentally verified by showing that the charge of one helium nucleus (two protons and two neutrons bound together in a nucleus and moving around at high speeds) is the same as two deuterium nuclei (one proton and one neutron bound together, but moving much more slowly than they would if they were in a helium nucleus).\",\n \"Atom\\n\\nAn atom is the smallest constituent unit of ordinary matter that has the properties of a chemical element. Every solid, liquid, gas, and plasma is composed of neutral or ionized atoms. Atoms are very small; typical sizes are around 100 pm (a ten-billionth of a meter, in the short scale). However, atoms do not have well-defined boundaries, and there are different ways to define their size that give different but close values.\",\n \"Atom\\n\\nAtoms are small enough that attempting to predict their behavior using classical physics - as if they were billiard balls, for example - gives noticeably incorrect predictions due to quantum effects. Through the development of physics, atomic models have incorporated quantum principles to better explain and predict the behavior.\",\n \"Atom\\n\\nEvery atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and typically a similar number of neutrons. Protons and neutrons are called nucleons. More than 99.94% of an atom's mass is in the nucleus. The protons have a positive electric charge, the electrons have a negative electric charge, and the neutrons have no electric charge. If the number of protons and electrons are equal, that atom is electrically neutral. If an atom has more or fewer electrons than protons, then it has an overall negative or positive charge, respectively, and it is called an ion.\",\n \"Atom\\n\\nThe electrons of an atom are attracted to the protons in an atomic nucleus by this electromagnetic force. The protons and neutrons in the nucleus are attracted to each other by a different force, the nuclear force, which is usually stronger than the electromagnetic force repelling the positively charged protons from one another. Under certain circumstances the repelling electromagnetic force becomes stronger than the nuclear force, and nucleons can be ejected from the nucleus, leaving behind a different element: nuclear decay resulting in nuclear transmutation.\",\n \"Atom\\n\\nThe number of protons in the nucleus defines to what chemical element the atom belongs: for example, all copper atoms contain 29 protons. The number of neutrons defines the isotope of the element. The number of electrons influences the magnetic properties of an atom. Atoms can attach to one or more other atoms by chemical bonds to form chemical compounds such as molecules. The ability of atoms to associate and dissociate is responsible for most of the physical changes observed in nature, and is the subject of the discipline of chemistry.\",\n \"Atom\\n\\nHistory of atomic theory\",\n \"Atom\\n\\nAtoms in philosophy\",\n \"Atom\\n\\nThe idea that matter is made up of discrete units is a very old idea, appearing in many ancient cultures such as Greece and India. The word \\\"atom\\\" was coined by ancient Greek philosophers. However, these ideas were founded in philosophical and theological reasoning rather than evidence and experimentation. As a result, their views on what atoms look like and how they behave were incorrect. They also could not convince everybody, so atomism was but one of a number of competing theories on the nature of matter. It was not until the 19th century that the idea was embraced and refined by scientists, when the blossoming science of chemistry produced discoveries that only the concept of atoms could explain.\",\n \"Atom\\n\\nFirst evidence-based theory\",\n \"Atom\\n\\nIn the early 1800s, John Dalton used the concept of atoms to explain why elements always react in ratios of small whole numbers (the law of multiple proportions). For instance, there are two types of tin oxide: one is 88.1% tin and 11.9% oxygen and the other is 78.7% tin and 21.3% oxygen (tin(II) oxide and tin dioxide respectively). This means that 100g of tin will combine either with 13.5g or 27g of oxygen. 13.5 and 27 form a ratio of 1:2, a ratio of small whole numbers. This common pattern in chemistry suggested to Dalton that elements react in whole number multiples of discrete units—in other words, atoms. In the case of tin oxides, one tin atom will combine with either one or two oxygen atoms.\",\n \"Atom\\n\\nDalton also believed atomic theory could explain why water absorbs different gases in different proportions. For example, he found that water absorbs carbon dioxide far better than it absorbs nitrogen.Dalton, John. \\\"[http://web.lemoyne.edu/~GIUNTA/dalton52.html On the Absorption of Gases by Water and Other Liquids]\\\", in Memoirs of the Literary and Philosophical Society of Manchester. 1803. Retrieved on August 29, 2007. Dalton hypothesized this was due to the differences between the masses and configurations of the gases' respective particles, and carbon dioxide molecules (CO2) are heavier and larger than nitrogen molecules (N2).\",\n \"Atom\\n\\nBrownian motion\",\n \"Atom\\n\\nIn 1827, botanist Robert Brown used a microscope to look at dust grains floating in water and discovered that they moved about erratically, a phenomenon that became known as \\\"Brownian motion\\\". This was thought to be caused by water molecules knocking the grains about. In 1905 Albert Einstein proved the reality of these molecules and their motions by producing the first Statistical physics analysis of Brownian motion. French physicist Jean Perrin used Einstein's work to experimentally determine the mass and dimensions of atoms, thereby conclusively verifying Dalton's atomic theory.\",\n \"Atom\\n\\nDiscovery of the electron\",\n \"Atom\\n\\nThe physicist J. J. Thomson measured the mass of cathode rays, showing they were made of particles, but were around 1800 times lighter than the lightest atom, hydrogen. Therefore, they were not atoms, but a new particle, the first subatomic particle to be discovered, which he originally called \\\"corpuscle\\\" but was later named electron, after particles postulated by George Johnstone Stoney in 1874. He also showed they were identical to particles given off by photoelectric and radioactive materials. It was quickly recognized that they are the particles that carry electric currents in metal wires, and carry the negative electric charge within atoms. Thomson was given the 1906 Nobel Prize in Physics for this work. Thus he overturned the belief that atoms are the indivisible, ultimate particles of matter. Thomson also incorrectly postulated that the low mass, negatively charged electrons were distributed throughout the atom in a uniform sea of positive charge. This became known as the plum pudding model.\",\n \"Atom\\n\\nDiscovery of the nucleus\",\n \"Atom\\n\\nIn 1909, Hans Geiger and Ernest Marsden, under the direction of Ernest Rutherford, bombarded a metal foil with alpha particles to observe how they scattered. They expected all the alpha particles to pass straight through with little deflection, because Thomson's model said that the charges in the atom are so diffuse that their electric fields could not affect the alpha particles much. However, Geiger and Marsden spotted alpha particles being deflected by angles greater than 90°, which was supposed to be impossible according to Thomson's model. To explain this, Rutherford proposed that the positive charge of the atom is concentrated in a tiny nucleus at the center of the atom.\",\n \"Atom\\n\\nDiscovery of isotopes\",\n \"Atom\\n\\nWhile experimenting with the products of radioactive decay, in 1913 radiochemist Frederick Soddy discovered that there appeared to be more than one type of atom at each position on the periodic table. The term isotope was coined by Margaret Todd as a suitable name for different atoms that belong to the same element. J.J. Thomson created a technique for separating atom types through his work on ionized gases, which subsequently led to the discovery of stable isotopes.\",\n \"Atom\\n\\nBohr model\",\n \"Atom\\n\\nIn 1913 the physicist Niels Bohr proposed a model in which the electrons of an atom were assumed to orbit the nucleus but could only do so in a finite set of orbits, and could jump between these orbits only in discrete changes of energy corresponding to absorption or radiation of a photon. This quantization was used to explain why the electrons orbits are stable (given that normally, charges in acceleration, including circular motion, lose kinetic energy which is emitted as electromagnetic radiation, see synchrotron radiation) and why elements absorb and emit electromagnetic radiation in discrete spectra.\",\n \"Atom\\n\\nLater in the same year Henry Moseley provided additional experimental evidence in favor of Niels Bohr's theory. These results refined Ernest Rutherford's and Antonius Van den Broek's model, which proposed that the atom contains in its nucleus a number of positive nuclear charges that is equal to its (atomic) number in the periodic table. Until these experiments, atomic number was not known to be a physical and experimental quantity. That it is equal to the atomic nuclear charge remains the accepted atomic model today.\",\n \"Atom\\n\\nChemical bonding explained\",\n \"Atom\\n\\nChemical bonds between atoms were now explained, by Gilbert Newton Lewis in 1916, as the interactions between their constituent electrons. As the chemical properties of the elements were known to largely repeat themselves according to the periodic law, in 1919 the American chemist Irving Langmuir suggested that this could be explained if the electrons in an atom were connected or clustered in some manner. Groups of electrons were thought to occupy a set of electron shells about the nucleus.\",\n \"Atom\\n\\nFurther developments in quantum physics\",\n \"Atom\\n\\nThe Stern–Gerlach experiment of 1922 provided further evidence of the quantum nature of the atom. When a beam of silver atoms was passed through a specially shaped magnetic field, the beam was split based on the direction of an atom's angular momentum, or spin. As this direction is random, the beam could be expected to spread into a line. Instead, the beam was split into two parts, depending on whether the atomic spin was oriented up or down.\",\n \"Atom\\n\\nIn 1924, Louis de Broglie proposed that all particles behave to an extent like waves. In 1926, Erwin Schrödinger used this idea to develop a mathematical model of the atom that described the electrons as three-dimensional waveforms rather than point particles. A consequence of using waveforms to describe particles is that it is mathematically impossible to obtain precise values for both the position and momentum of a particle at a given point in time; this became known as the uncertainty principle, formulated by Werner Heisenberg in 1926. In this concept, for a given accuracy in measuring a position one could only obtain a range of probable values for momentum, and vice versa. \\nThis model was able to explain observations of atomic behavior that previous models could not, such as certain structural and spectral patterns of atoms larger than hydrogen. Thus, the planetary model of the atom was discarded in favor of one that described atomic orbital zones around the nucleus where a given electron is most likely to be observed.\",\n \"Atom\\n\\nDiscovery of the neutron\",\n \"Atom\\n\\nThe development of the mass spectrometer allowed the mass of atoms to be measured with increased accuracy. The device uses a magnet to bend the trajectory of a beam of ions, and the amount of deflection is determined by the ratio of an atom's mass to its charge. The chemist Francis William Aston used this instrument to show that isotopes had different masses. The atomic mass of these isotopes varied by integer amounts, called the whole number rule. The explanation for these different isotopes awaited the discovery of the neutron, an uncharged particle with a mass similar to the proton, by the physicist James Chadwick in 1932. Isotopes were then explained as elements with the same number of protons, but different numbers of neutrons within the nucleus.\",\n \"Atom\\n\\nFission, high-energy physics and condensed matter\",\n \"Atom\\n\\nIn 1938, the German chemist Otto Hahn, a student of Rutherford, directed neutrons onto uranium atoms expecting to get transuranium elements. Instead, his chemical experiments showed barium as a product. A year later, Lise Meitner and her nephew Otto Frisch verified that Hahn's result were the first experimental nuclear fission. In 1944, Hahn received the Nobel prize in chemistry. Despite Hahn's efforts, the contributions of Meitner and Frisch were not recognized.\",\n \"Atom\\n\\nIn the 1950s, the development of improved particle accelerators and particle detectors allowed scientists to study the impacts of atoms moving at high energies. Neutrons and protons were found to be hadrons, or composites of smaller particles called quarks. The standard model of particle physics was developed that so far has successfully explained the properties of the nucleus in terms of these sub-atomic particles and the forces that govern their interactions.\",\n \"Atom\\n\\nStructure\",\n \"Atom\\n\\nSubatomic particles\",\n \"Atom\\n\\nThough the word atom originally denoted a particle that cannot be cut into smaller particles, in modern scientific usage the atom is composed of various subatomic particles. The constituent particles of an atom are the electron, the proton and the neutron; all three are fermions. However, the hydrogen-1 atom has no neutrons and the hydron ion has no electrons.\",\n \"Atom\\n\\nThe electron is by far the least massive of these particles at , with a negative electrical charge and a size that is too small to be measured using available techniques. It is the lightest particle with a positive rest mass measured. Under ordinary conditions, electrons are bound to the positively charged nucleus by the attraction created from opposite electric charges. If an atom has more or fewer electrons than its atomic number, then it becomes respectively negatively or positively charged as a whole; a charged atom is called an ion. Electrons have been known since the late 19th century, mostly thanks to J.J. Thomson; see history of subatomic physics for details.\",\n \"Atom\\n\\nProtons have a positive charge and a mass 1,836 times that of the electron, at . The number of protons in an atom is called its atomic number. Ernest Rutherford (1919) observed that nitrogen under alpha-particle bombardment ejects what appeared to be hydrogen nuclei. By 1920 he had accepted that the hydrogen nucleus is a distinct particle within the atom and named it proton.\",\n \"Atom\\n\\nNeutrons have no electrical charge and have a free mass of 1,839 times the mass of the electron, or , the heaviest of the three constituent particles, but it can be reduced by the nuclear binding energy. Neutrons and protons (collectively known as nucleons) have comparable dimensions—on the order of —although the 'surface' of these particles is not sharply defined. The neutron was discovered in 1932 by the English physicist James Chadwick.\",\n \"Atom\\n\\nIn the Standard Model of physics, electrons are truly elementary particles with no internal structure. However, both protons and neutrons are composite particles composed of elementary particles called quarks. There are two types of quarks in atoms, each having a fractional electric charge. Protons are composed of two up quarks (each with charge +) and one down quark (with a charge of −). Neutrons consist of one up quark and two down quarks. This distinction accounts for the difference in mass and charge between the two particles.\",\n \"Atom\\n\\nThe quarks are held together by the strong interaction (or strong force), which is mediated by gluons. The protons and neutrons, in turn, are held to each other in the nucleus by the nuclear force, which is a residuum of the strong force that has somewhat different range-properties (see the article on the nuclear force for more). The gluon is a member of the family of gauge bosons, which are elementary particles that mediate physical forces.\",\n \"Atom\\n\\nNucleus\",\n \"Atom\\n\\nAll the bound protons and neutrons in an atom make up a tiny atomic nucleus, and are collectively called nucleons. The radius of a nucleus is approximately equal to 1.07 fm, where A is the total number of nucleons. This is much smaller than the radius of the atom, which is on the order of 105 fm. The nucleons are bound together by a short-ranged attractive potential called the residual strong force. At distances smaller than 2.5 fm this force is much more powerful than the electrostatic force that causes positively charged protons to repel each other.\",\n \"Atom\\n\\nAtoms of the same element have the same number of protons, called the atomic number. Within a single element, the number of neutrons may vary, determining the isotope of that element. The total number of protons and neutrons determine the nuclide. The number of neutrons relative to the protons determines the stability of the nucleus, with certain isotopes undergoing radioactive decay.\",\n \"Atom\\n\\nThe proton, the electron, and the neutron are classified as fermions. Fermions obey the Pauli exclusion principle which prohibits identical fermions, such as multiple protons, from occupying the same quantum state at the same time. Thus, every proton in the nucleus must occupy a quantum state different from all other protons, and the same applies to all neutrons of the nucleus and to all electrons of the electron cloud. However, a proton and a neutron are allowed to occupy the same quantum state.\",\n \"Atom\\n\\nFor atoms with low atomic numbers, a nucleus that has more neutrons than protons tends to drop to a lower energy state through radioactive decay so that the neutron–proton ratio is closer to one. However, as the atomic number increases, a higher proportion of neutrons is required to offset the mutual repulsion of the protons. Thus, there are no stable nuclei with equal proton and neutron numbers above atomic number Z 20 (calcium) and as Z increases, the neutron–proton ratio of stable isotopes increases. The stable isotope with the highest proton–neutron ratio is lead-208 (about 1.5).\",\n \"Atom\\n\\nThe number of protons and neutrons in the atomic nucleus can be modified, although this can require very high energies because of the strong force. Nuclear fusion occurs when multiple atomic particles join to form a heavier nucleus, such as through the energetic collision of two nuclei. For example, at the core of the Sun protons require energies of 3–10 keV to overcome their mutual repulsion—the coulomb barrier—and fuse together into a single nucleus. Nuclear fission is the opposite process, causing a nucleus to split into two smaller nuclei—usually through radioactive decay. The nucleus can also be modified through bombardment by high energy subatomic particles or photons. If this modifies the number of protons in a nucleus, the atom changes to a different chemical element.\",\n \"Atom\\n\\nIf the mass of the nucleus following a fusion reaction is less than the sum of the masses of the separate particles, then the difference between these two values can be emitted as a type of usable energy (such as a gamma ray, or the kinetic energy of a beta particle), as described by Albert Einstein's mass–energy equivalence formula, E = mc2, where m is the mass loss and c is the speed of light. This deficit is part of the binding energy of the new nucleus, and it is the non-recoverable loss of the energy that causes the fused particles to remain together in a state that requires this energy to separate.\",\n \"Atom\\n\\nThe fusion of two nuclei that create larger nuclei with lower atomic numbers than iron and nickel—a total nucleon number of about 60—is usually an exothermic process that releases more energy than is required to bring them together. It is this energy-releasing process that makes nuclear fusion in stars a self-sustaining reaction. For heavier nuclei, the binding energy per nucleon in the nucleus begins to decrease. That means fusion processes producing nuclei that have atomic numbers higher than about 26, and atomic masses higher than about 60, is an endothermic process. These more massive nuclei can not undergo an energy-producing fusion reaction that can sustain the hydrostatic equilibrium of a star.\",\n \"Atom\\n\\nElectron cloud\",\n \"Atom\\n\\nThe electrons in an atom are attracted to the protons in the nucleus by the electromagnetic force. This force binds the electrons inside an electrostatic potential well surrounding the smaller nucleus, which means that an external source of energy is needed for the electron to escape. The closer an electron is to the nucleus, the greater the attractive force. Hence electrons bound near the center of the potential well require more energy to escape than those at greater separations.\",\n \"Atom\\n\\nElectrons, like other particles, have properties of both a particle and a wave. The electron cloud is a region inside the potential well where each electron forms a type of three-dimensional standing wave—a wave form that does not move relative to the nucleus. This behavior is defined by an atomic orbital, a mathematical function that characterises the probability that an electron appears to be at a particular location when its position is measured. Only a discrete (or quantized) set of these orbitals exist around the nucleus, as other possible wave patterns rapidly decay into a more stable form. Orbitals can have one or more ring or node structures, and differ from each other in size, shape and orientation.\",\n \"Atom\\n\\nEach atomic orbital corresponds to a particular energy level of the electron. The electron can change its state to a higher energy level by absorbing a photon with sufficient energy to boost it into the new quantum state. Likewise, through spontaneous emission, an electron in a higher energy state can drop to a lower energy state while radiating the excess energy as a photon. These characteristic energy values, defined by the differences in the energies of the quantum states, are responsible for atomic spectral lines.\",\n \"Atom\\n\\nThe amount of energy needed to remove or add an electron—the electron binding energy—is far less than the binding energy of nucleons. For example, it requires only 13.6 eV to strip a ground-state electron from a hydrogen atom, compared to 2.23 million eV for splitting a deuterium nucleus. Atoms are electrically neutral if they have an equal number of protons and electrons. Atoms that have either a deficit or a surplus of electrons are called ions. Electrons that are farthest from the nucleus may be transferred to other nearby atoms or shared between atoms. By this mechanism, atoms are able to bond into molecules and other types of chemical compounds like ionic and covalent network crystals.\",\n \"Atom\\n\\nProperties\",\n \"Atom\\n\\nNuclear properties\",\n \"Atom\\n\\nBy definition, any two atoms with an identical number of protons in their nuclei belong to the same chemical element. Atoms with equal numbers of protons but a different number of neutrons are different isotopes of the same element. For example, all hydrogen atoms admit exactly one proton, but isotopes exist with no neutrons (hydrogen-1, by far the most common form, also called protium), one neutron (deuterium), two neutrons (tritium) and more than two neutrons. The known elements form a set of atomic numbers, from the single proton element hydrogen up to the 118-proton element ununoctium. All known isotopes of elements with atomic numbers greater than 82 are radioactive.\",\n \"Atom\\n\\nAbout 339 nuclides occur naturally on Earth, of which 254 (about 75%) have not been observed to decay, and are referred to as \\\"stable isotopes\\\". However, only 90 of these nuclides are stable to all decay, even in theory. Another 164 (bringing the total to 254) have not been observed to decay, even though in theory it is energetically possible. These are also formally classified as \\\"stable\\\". An additional 34 radioactive nuclides have half-lives longer than 80 million years, and are long-lived enough to be present from the birth of the solar system. This collection of 288 nuclides are known as primordial nuclides. Finally, an additional 51 short-lived nuclides are known to occur naturally, as daughter products of primordial nuclide decay (such as radium from uranium), or else as products of natural energetic processes on Earth, such as cosmic ray bombardment (for example, carbon-14).For more recent updates see [http://www.nndc.bnl.gov/chart Interactive Chart of Nuclides (Brookhaven National Laboratory)].\",\n \"Atom\\n\\nFor 80 of the chemical elements, at least one stable isotope exists. As a rule, there is only a handful of stable isotopes for each of these elements, the average being 3.2 stable isotopes per element. Twenty-six elements have only a single stable isotope, while the largest number of stable isotopes observed for any element is ten, for the element tin. Elements 43, 61, and all elements numbered 83 or higher have no stable isotopes.CRC Handbook (2002).\",\n \"Atom\\n\\nStability of isotopes is affected by the ratio of protons to neutrons, and also by the presence of certain \\\"magic numbers\\\" of neutrons or protons that represent closed and filled quantum shells. These quantum shells correspond to a set of energy levels within the shell model of the nucleus; filled shells, such as the filled shell of 50 protons for tin, confers unusual stability on the nuclide. Of the 254 known stable nuclides, only four have both an odd number of protons and odd number of neutrons: hydrogen-2 (deuterium), lithium-6, boron-10 and nitrogen-14. Also, only four naturally occurring, radioactive odd–odd nuclides have a half-life over a billion years: potassium-40, vanadium-50, lanthanum-138 and tantalum-180m. Most odd–odd nuclei are highly unstable with respect to beta decay, because the decay products are even–even, and are therefore more strongly bound, due to nuclear pairing effects.\",\n \"Atom\\n\\nMass\",\n \"Atom\\n\\nThe large majority of an atom's mass comes from the protons and neutrons that make it up. The total number of these particles (called \\\"nucleons\\\") in a given atom is called the mass number. It is a positive integer and dimensionless (instead of having dimension of mass), because it expresses a count. An example of use of a mass number is \\\"carbon-12,\\\" which has 12 nucleons (six protons and six neutrons).\",\n \"Atom\\n\\nThe actual mass of an atom at rest is often expressed using the unified atomic mass unit (u), also called dalton (Da). This unit is defined as a twelfth of the mass of a free neutral atom of carbon-12, which is approximately . Hydrogen-1 (the lightest isotope of hydrogen which is also the nuclide with the lowest mass) has an atomic weight of 1.007825 u. The value of this number is called the atomic mass. A given atom has an atomic mass approximately equal (within 1%) to its mass number times the atomic mass unit (for example the mass of a nitrogen-14 is roughly 14 u). However, this number will not be exactly an integer except in the case of carbon-12 (see below). The heaviest stable atom is lead-208, with a mass of .\",\n \"Atom\\n\\nAs even the most massive atoms are far too light to work with directly, chemists instead use the unit of moles. One mole of atoms of any element always has the same number of atoms (about Avogadro constant|). This number was chosen so that if an element has an atomic mass of 1 u, a mole of atoms of that element has a mass close to one gram. Because of the definition of the unified atomic mass unit, each carbon-12 atom has an atomic mass of exactly 12 u, and so a mole of carbon-12 atoms weighs exactly 0.012 kg.\",\n \"Atom\\n\\nShape and size\",\n \"Atom\\n\\nAtoms lack a well-defined outer boundary, so their dimensions are usually described in terms of an atomic radius. This is a measure of the distance out to which the electron cloud extends from the nucleus. However, this assumes the atom to exhibit a spherical shape, which is only obeyed for atoms in vacuum or free space. Atomic radii may be derived from the distances between two nuclei when the two atoms are joined in a chemical bond. The radius varies with the location of an atom on the atomic chart, the type of chemical bond, the number of neighboring atoms (coordination number) and a quantum mechanical property known as spin. On the periodic table of the elements, atom size tends to increase when moving down columns, but decrease when moving across rows (left to right). Consequently, the smallest atom is helium with a radius of 32 pm, while one of the largest is caesium at 225 pm.\",\n \"Atom\\n\\nWhen subjected to external forces, like electrical fields, the shape of an atom may deviate from spherical symmetry. The deformation depends on the field magnitude and the orbital type of outer shell electrons, as shown by group-theoretical considerations. Aspherical deviations might be elicited for instance in crystals, where large crystal-electrical fields may occur at low-symmetry lattice sites. Significant ellipsoidal deformations have recently been shown to occur for sulfur ions and chalcogen ions in pyrite-type compounds.\",\n \"Atom\\n\\nAtomic dimensions are thousands of times smaller than the wavelengths of light (400–700 nm) so they cannot be viewed using an optical microscope. However, individual atoms can be observed using a scanning tunneling microscope. To visualize the minuteness of the atom, consider that a typical human hair is about 1 million carbon atoms in width. A single drop of water contains about 2 sextillion () atoms of oxygen, and twice the number of hydrogen atoms. A single carat diamond with a mass of contains about 10 sextillion (1022) atoms of carbon.A carat is 200 milligrams. By definition, carbon-12 has 0.012 kg per mole. The Avogadro constant defines atoms per mole. If an apple were magnified to the size of the Earth, then the atoms in the apple would be approximately the size of the original apple.\",\n \"Atom\\n\\nRadioactive decay\",\n \"Atom\\n\\nEvery element has one or more isotopes that have unstable nuclei that are subject to radioactive decay, causing the nucleus to emit particles or electromagnetic radiation. Radioactivity can occur when the radius of a nucleus is large compared with the radius of the strong force, which only acts over distances on the order of 1 fm.\",\n \"Atom\\n\\nThe most common forms of radioactive decay are:\\n* Alpha decay: this process is caused when the nucleus emits an alpha particle, which is a helium nucleus consisting of two protons and two neutrons. The result of the emission is a new element with a lower atomic number. * Beta decay (and electron capture): these processes are regulated by the weak force, and result from a transformation of a neutron into a proton, or a proton into a neutron. The neutron to proton transition is accompanied by the emission of an electron and an antineutrino, while proton to neutron transition (except in electron capture) causes the emission of a positron and a neutrino. The electron or positron emissions are called beta particles. Beta decay either increases or decreases the atomic number of the nucleus by one. Electron capture is more common than positron emission, because it requires less energy. In this type of decay, an electron is absorbed by the nucleus, rather than a positron emitted from the nucleus. A neutrino is still emitted in this process, and a proton changes to a neutron.\",\n \"Atom\\n\\n* Gamma decay: this process results from a change in the energy level of the nucleus to a lower state, resulting in the emission of electromagnetic radiation. The excited state of a nucleus which results in gamma emission usually occurs following the emission of an alpha or a beta particle. Thus, gamma decay usually follows alpha or beta decay.\",\n \"Atom\\n\\nOther more rare types of radioactive decay include ejection of neutrons or protons or clusters of nucleons from a nucleus, or more than one beta particle. An analog of gamma emission which allows excited nuclei to lose energy in a different way, is internal conversion— a process that produces high-speed electrons that are not beta rays, followed by production of high-energy photons that are not gamma rays. A few large nuclei explode into two or more charged fragments of varying masses plus several neutrons, in a decay called spontaneous nuclear fission.\",\n \"Atom\\n\\nEach radioactive isotope has a characteristic decay time period—the half-life—that is determined by the amount of time needed for half of a sample to decay. This is an exponential decay process that steadily decreases the proportion of the remaining isotope by 50% every half-life. Hence after two half-lives have passed only 25% of the isotope is present, and so forth.\",\n \"Atom\\n\\nMagnetic moment\",\n \"Atom\\n\\nElementary particles possess an intrinsic quantum mechanical property known as spin. This is analogous to the angular momentum of an object that is spinning around its center of mass, although strictly speaking these particles are believed to be point-like and cannot be said to be rotating. Spin is measured in units of the reduced Planck constant (ħ), with electrons, protons and neutrons all having spin ½ ħ, or \\\"spin-½\\\". In an atom, electrons in motion around the nucleus possess orbital angular momentum in addition to their spin, while the nucleus itself possesses angular momentum due to its nuclear spin.\",\n \"Atom\\n\\nThe magnetic field produced by an atom—its magnetic moment—is determined by these various forms of angular momentum, just as a rotating charged object classically produces a magnetic field. However, the most dominant contribution comes from electron spin. Due to the nature of electrons to obey the Pauli exclusion principle, in which no two electrons may be found in the same quantum state, bound electrons pair up with each other, with one member of each pair in a spin up state and the other in the opposite, spin down state. Thus these spins cancel each other out, reducing the total magnetic dipole moment to zero in some atoms with even number of electrons.\",\n \"Atom\\n\\nIn ferromagnetic elements such as iron, cobalt and nickel, an odd number of electrons leads to an unpaired electron and a net overall magnetic moment. The orbitals of neighboring atoms overlap and a lower energy state is achieved when the spins of unpaired electrons are aligned with each other, a spontaneous process known as an exchange interaction. When the magnetic moments of ferromagnetic atoms are lined up, the material can produce a measurable macroscopic field. Paramagnetic materials have atoms with magnetic moments that line up in random directions when no magnetic field is present, but the magnetic moments of the individual atoms line up in the presence of a field.\",\n \"Atom\\n\\nThe nucleus of an atom will have no spin when it has even numbers of both neutrons and protons, but for other cases of odd numbers, the nucleus may have a spin. Normally nuclei with spin are aligned in random directions because of thermal equilibrium. However, for certain elements (such as xenon-129) it is possible to polarize a significant proportion of the nuclear spin states so that they are aligned in the same direction—a condition called hyperpolarization. This has important applications in magnetic resonance imaging.\",\n \"Atom\\n\\nEnergy levels\",\n \"Atom\\n\\nThe potential energy of an electron in an atom is negative, its dependence of its position reaches the minimum (the most absolute value) inside the nucleus, and vanishes when the distance from the nucleus goes to infinity, roughly in an inverse proportion to the distance. In the quantum-mechanical model, a bound electron can only occupy a set of states centered on the nucleus, and each state corresponds to a specific energy level; see time-independent Schrödinger equation for theoretical explanation. An energy level can be measured by the amount of energy needed to unbind the electron from the atom, and is usually given in units of electronvolts (eV). The lowest energy state of a bound electron is called the ground state, i.e. stationary state, while an electron transition to a higher level results in an excited state. The electron's energy raises when n increases because the (average) distance to the nucleus increases. Dependence of the energy on azimuthal quantum number| is caused not by electrostatic potential of the nucleus, but by interaction between electrons.\",\n \"Atom\\n\\nFor an electron to transition between two different states, e.g. grounded state to first excited level (ionization), it must absorb or emit a photon at an energy matching the difference in the potential energy of those levels, according to Niels Bohr model, what can be precisely calculated by the Schrödinger equation.\\nElectrons jump between orbitals in a particle-like fashion. For example, if a single photon strikes the electrons, only a single electron changes states in response to the photon; see Electron properties.\",\n \"Atom\\n\\nThe energy of an emitted photon is proportional to its frequency, so these specific energy levels appear as distinct bands in the electromagnetic spectrum. Each element has a characteristic spectrum that can depend on the nuclear charge, subshells filled by electrons, the electromagnetic interactions between the electrons and other factors.\",\n \"Atom\\n\\nWhen a continuous spectrum of energy is passed through a gas or plasma, some of the photons are absorbed by atoms, causing electrons to change their energy level. Those excited electrons that remain bound to their atom spontaneously emit this energy as a photon, traveling in a random direction, and so drop back to lower energy levels. Thus the atoms behave like a filter that forms a series of dark absorption bands in the energy output. (An observer viewing the atoms from a view that does not include the continuous spectrum in the background, instead sees a series of emission lines from the photons emitted by the atoms.) Spectroscopic measurements of the strength and width of atomic spectral lines allow the composition and physical properties of a substance to be determined.\",\n \"Atom\\n\\nClose examination of the spectral lines reveals that some display a fine structure splitting. This occurs because of spin–orbit coupling, which is an interaction between the spin and motion of the outermost electron. When an atom is in an external magnetic field, spectral lines become split into three or more components; a phenomenon called the Zeeman effect. This is caused by the interaction of the magnetic field with the magnetic moment of the atom and its electrons. Some atoms can have multiple electron configurations with the same energy level, which thus appear as a single spectral line. The interaction of the magnetic field with the atom shifts these electron configurations to slightly different energy levels, resulting in multiple spectral lines. The presence of an external electric field can cause a comparable splitting and shifting of spectral lines by modifying the electron energy levels, a phenomenon called the Stark effect.\",\n \"Atom\\n\\nIf a bound electron is in an excited state, an interacting photon with the proper energy can cause stimulated emission of a photon with a matching energy level. For this to occur, the electron must drop to a lower energy state that has an energy difference matching the energy of the interacting photon. The emitted photon and the interacting photon then move off in parallel and with matching phases. That is, the wave patterns of the two photons are synchronized. This physical property is used to make lasers, which can emit a coherent beam of light energy in a narrow frequency band.\",\n \"Atom\\n\\nValence and bonding behavior\",\n \"Atom\\n\\nValency is the combining power of an element. It is equal to number of hydrogen atoms that atom can combine or displace in forming compounds. The outermost electron shell of an atom in its uncombined state is known as the valence shell, and the electrons in\\nthat shell are called valence electrons. The number of valence electrons determines the bonding\\nbehavior with other atoms. Atoms tend to chemically react with each other in a manner that fills (or empties) their outer valence shells. For example, a transfer of a single electron between atoms is a useful approximation for bonds that form between atoms with one-electron more than a filled shell, and others that are one-electron short of a full shell, such as occurs in the compound sodium chloride and other chemical ionic salts. However, many elements display multiple valences, or tendencies to share differing numbers of electrons in different compounds. Thus, chemical bonding between these elements takes many forms of electron-sharing that are more than simple electron transfers. Examples include the element carbon and the organic compounds.\",\n \"Atom\\n\\nThe chemical elements are often displayed in a periodic table that is laid out to display recurring chemical properties, and elements with the same number of valence electrons form a group that is aligned in the same column of the table. (The horizontal rows correspond to the filling of a quantum shell of electrons.) The elements at the far right of the table have their outer shell completely filled with electrons, which results in chemically inert elements known as the noble gases.\",\n \"Atom\\n\\nStates\",\n \"Atom\\n\\nQuantities of atoms are found in different states of matter that depend on the physical conditions, such as temperature and pressure. By varying the conditions, materials can transition between solids, liquids, gases and plasmas. Within a state, a material can also exist in different allotropes. An example of this is solid carbon, which can exist as graphite or diamond. Gaseous allotropes exist as well, such as dioxygen and ozone.\",\n \"Atom\\n\\nAt temperatures close to absolute zero, atoms can form a Bose–Einstein condensate, at which point quantum mechanical effects, which are normally only observed at the atomic scale, become apparent on a macroscopic scale. This super-cooled collection of atoms\\nthen behaves as a single super atom, which may allow fundamental checks of quantum mechanical behavior.\",\n \"Atom\\n\\nIdentification\",\n \"Atom\\n\\nThe scanning tunneling microscope is a device for viewing surfaces at the atomic level. It uses the quantum tunneling phenomenon, which allows particles to pass through a barrier that would normally be insurmountable. Electrons tunnel through the vacuum between two planar metal electrodes, on each of which is an adsorbed atom, providing a tunneling-current density that can be measured. Scanning one atom (taken as the tip) as it moves past the other (the sample) permits plotting of tip displacement versus lateral separation for a constant current. The calculation shows the extent to which scanning-tunneling-microscope images of an individual atom are visible. It confirms that for low bias, the microscope images the space-averaged dimensions of the electron orbitals across closely packed energy levels—the Fermi level local density of states.\",\n \"Atom\\n\\nAn atom can be ionized by removing one of its electrons. The electric charge causes the trajectory of an atom to bend when it passes through a magnetic field. The radius by which the trajectory of a moving ion is turned by the magnetic field is determined by the mass of the atom. The mass spectrometer uses this principle to measure the mass-to-charge ratio of ions. If a sample contains multiple isotopes, the mass spectrometer can determine the proportion of each isotope in the sample by measuring the intensity of the different beams of ions. Techniques to vaporize atoms include inductively coupled plasma atomic emission spectroscopy and inductively coupled plasma mass spectrometry, both of which use a plasma to vaporize samples for analysis.\",\n \"Atom\\n\\nA more area-selective method is electron energy loss spectroscopy, which measures the energy loss of an electron beam within a transmission electron microscope when it interacts with a portion of a sample. The atom-probe tomograph has sub-nanometer resolution in 3-D and can chemically identify individual atoms using time-of-flight mass spectrometry.\",\n \"Atom\\n\\nSpectra of excited states can be used to analyze the atomic composition of distant stars. Specific light wavelengths contained in the observed light from stars can be separated out and related to the quantized transitions in free gas atoms. These colors can be replicated using a gas-discharge lamp containing the same element. Helium was discovered in this way in the spectrum of the Sun 23 years before it was found on Earth.\",\n \"Atom\\n\\nOrigin and current state\",\n \"Atom\\n\\nAtoms form about 4% of the total energy density of the observable Universe, with an average density of about 0.25 atoms/m3. Within a galaxy such as the Milky Way, atoms have a much higher concentration, with the density of matter in the interstellar medium (ISM) ranging from 105 to 109 atoms/m3. The Sun is believed to be inside the Local Bubble, a region of highly ionized gas, so the density in the solar neighborhood is only about 103 atoms/m3. Stars form from dense clouds in the ISM, and the evolutionary processes of stars result in the steady enrichment of the ISM with elements more massive than hydrogen and helium. Up to 95% of the Milky Way's atoms are concentrated inside stars and the total mass of atoms forms about 10% of the mass of the galaxy. (The remainder of the mass is an unknown dark matter.)\",\n \"Atom\\n\\nFormation\",\n \"Atom\\n\\nElectrons are thought to exist in the Universe since early stages of the Big Bang. Atomic nuclei forms in nucleosynthesis reactions. In about three minutes Big Bang nucleosynthesis produced most of the helium, lithium, and deuterium in the Universe, and perhaps some of the beryllium and boron.\",\n \"Atom\\n\\nUbiquitousness and stability of atoms relies on their binding energy, which means that an atom has a lower energy than an unbound system of the nucleus and electrons. Where the temperature is much higher than ionization potential, the matter exists in the form of plasma—a gas of positively charged ions (possibly, bare nuclei) and electrons. When the temperature drops below the ionization potential, atoms become statistically favorable. Atoms (complete with bound electrons) became to dominate over charged particles 380,000 years after the Big Bang—an epoch called recombination, when the expanding Universe cooled enough to allow electrons to become attached to nuclei.\",\n \"Atom\\n\\nSince the Big Bang, which produced no carbon or heavier elements, atomic nuclei have been combined in stars through the process of nuclear fusion to produce more of the element helium, and (via the triple alpha process) the sequence of elements from carbon up to iron; see stellar nucleosynthesis for details.\",\n \"Atom\\n\\nIsotopes such as lithium-6, as well as some beryllium and boron are generated in space through cosmic ray spallation. This occurs when a high-energy proton strikes an atomic nucleus, causing large numbers of nucleons to be ejected.\",\n \"Atom\\n\\nElements heavier than iron were produced in supernovae through the r-process and in AGB stars through the s-process, both of which involve the capture of neutrons by atomic nuclei. Elements such as lead formed largely through the radioactive decay of heavier elements.\",\n \"Atom\\n\\nEarth\",\n \"Atom\\n\\nMost of the atoms that make up the Earth and its inhabitants were present in their current form in the nebula that collapsed out of a molecular cloud to form the Solar System. The rest are the result of radioactive decay, and their relative proportion can be used to determine the age of the Earth through radiometric dating. Most of the helium in the crust of the Earth (about 99% of the helium from gas wells, as shown by its lower abundance of helium-3) is a product of alpha decay.\",\n \"Atom\\n\\nThere are a few trace atoms on Earth that were not present at the beginning (i.e., not \\\"primordial\\\"), nor are results of radioactive decay. Carbon-14 is continuously generated by cosmic rays in the atmosphere. Some atoms on Earth have been artificially generated either deliberately or as by-products of nuclear reactors or explosions. Of the transuranic elements—those with atomic numbers greater than 92—only plutonium and neptunium occur naturally on Earth. Transuranic elements have radioactive lifetimes shorter than the current age of the Earth and thus identifiable quantities of these elements have long since decayed, with the exception of traces of plutonium-244 possibly deposited by cosmic dust. Natural deposits of plutonium and neptunium are produced by neutron capture in uranium ore.\",\n \"Atom\\n\\nThe Earth contains approximately atoms. Although small numbers of independent atoms of noble gases exist, such as argon, neon, and helium, 99% of the atmosphere is bound in the form of molecules, including carbon dioxide and diatomic oxygen and nitrogen. At the surface of the Earth, an overwhelming majority of atoms combine to form various compounds, including water, salt, silicates and oxides. Atoms can also combine to create materials that do not consist of discrete molecules, including crystals and liquid or solid metals. This atomic matter forms networked arrangements that lack the particular type of small-scale interrupted order associated with molecular matter.\",\n \"Atom\\n\\nRare and theoretical forms\",\n \"Atom\\n\\nSuperheavy elements\",\n \"Atom\\n\\nWhile isotopes with atomic numbers higher than lead (82) are known to be radioactive, an \\\"island of stability\\\" has been proposed for some elements with atomic numbers above 103. These superheavy elements may have a nucleus that is relatively stable against radioactive decay. The most likely candidate for a stable superheavy atom, unbihexium, has 126 protons and 184 neutrons.\",\n \"Atom\\n\\nExotic matter\",\n \"Atom\\n\\nEach particle of matter has a corresponding antimatter particle with the opposite electrical charge. Thus, the positron is a positively charged antielectron and the antiproton is a negatively charged equivalent of a proton. When a matter and corresponding antimatter particle meet, they annihilate each other. Because of this, along with an imbalance between the number of matter and antimatter particles, the latter are rare in the universe. The first causes of this imbalance are not yet fully understood, although theories of baryogenesis may offer an explanation. As a result, no antimatter atoms have been discovered in nature. However, in 1996 the antimatter counterpart of the hydrogen atom (antihydrogen) was synthesized at the CERN laboratory in Geneva.\",\n \"Atom\\n\\nOther exotic atoms have been created by replacing one of the protons, neutrons or electrons with other particles that have the same charge. For example, an electron can be replaced by a more massive muon, forming a muonic atom. These types of atoms can be used to test the fundamental predictions of physics.\"\n]","isConversational":false}}},{"rowIdx":1797,"cells":{"id":{"kind":"string","value":"tc_2774"},"question":{"kind":"string","value":"What name is given to the very serious chain of events which can follow the failure of the cooling system in a nuclear reactor?"},"answer":{"kind":"string","value":"Meltdown"},"answer_aliases":{"kind":"list like","value":["meltdown song","meltdown disambiguation","meltdown album","melt down","meltdown"],"string":"[\n \"meltdown song\",\n \"meltdown disambiguation\",\n \"meltdown album\",\n \"melt down\",\n \"meltdown\"\n]","isConversational":false},"documents":{"kind":"list like","value":["Nuclear reactor\n\nThis article is a subarticle of Nuclear power.","Nuclear reactor\n\nA nuclear reactor, formerly known as an atomic pile, is a device used to initiate and control a sustained nuclear chain reaction. Nuclear reactors are used at nuclear power plants for electricity generation and in propulsion of ships. Heat from nuclear fission is passed to a working fluid (water or gas), which runs through steam turbines. These either drive a ship's propellers or turn electrical generators. Nuclear generated steam in principle can be used for industrial process heat or for district heating. Some reactors are used to produce isotopes for medical and industrial use, or for production of weapons-grade plutonium. Some are run only for research. Today there are about 450 nuclear power reactors that are used to generate electricity in about 30 countries around the world.","Nuclear reactor\n\nMechanism","Nuclear reactor\n\nJust as conventional power-stations generate electricity by harnessing the thermal energy released from burning fossil fuels, nuclear reactors convert the energy released by controlled nuclear fission into thermal energy for further conversion to mechanical or electrical forms.","Nuclear reactor\n\nFission","Nuclear reactor\n\nWhen a large fissile atomic nucleus such as uranium-235 or plutonium-239 absorbs a neutron, it may undergo nuclear fission. The heavy nucleus splits into two or more lighter nuclei, (the fission products), releasing kinetic energy, gamma radiation, and free neutrons. A portion of these neutrons may later be absorbed by other fissile atoms and trigger further fission events, which release more neutrons, and so on. This is known as a nuclear chain reaction.","Nuclear reactor\n\nTo control such a nuclear chain reaction, neutron poisons and neutron moderators can change the portion of neutrons that will go on to cause more fission. Nuclear reactors generally have automatic and manual systems to shut the fission reaction down if monitoring detects unsafe conditions.","Nuclear reactor\n\nCommonly-used moderators include regular (light) water (in 74.8% of the world's reactors), solid graphite (20% of reactors) and heavy water (5% of reactors). Some experimental types of reactor have used beryllium, and hydrocarbons have been suggested as another possibility.","Nuclear reactor\n\nHeat generation","Nuclear reactor\n\nThe reactor core generates heat in a number of ways:\n* The kinetic energy of fission products is converted to thermal energy when these nuclei collide with nearby atoms.\n* The reactor absorbs some of the gamma rays produced during fission and converts their energy into heat.\n* Heat is produced by the radioactive decay of fission products and materials that have been activated by neutron absorption. This decay heat-source will remain for some time even after the reactor is shut down.","Nuclear reactor\n\nA kilogram of uranium-235 (U-235) converted via nuclear processes releases approximately three million times more energy than a kilogram of coal burned conventionally (7.2 × 1013 joules per kilogram of uranium-235 versus 2.4 × 107 joules per kilogram of coal).","Nuclear reactor\n\nCooling","Nuclear reactor\n\nA nuclear reactor coolant — usually water but sometimes a gas or a liquid metal (like liquid sodium) or molten salt — is circulated past the reactor core to absorb the heat that it generates. The heat is carried away from the reactor and is then used to generate steam. Most reactor systems employ a cooling system that is physically separated from the water that will be boiled to produce pressurized steam for the turbines, like the pressurized water reactor. However, in some reactors the water for the steam turbines is boiled directly by the reactor core; for example the boiling water reactor.","Nuclear reactor\n\nReactivity control","Nuclear reactor\n\nThe power output of the reactor is adjusted by controlling how many neutrons are able to create more fissions.","Nuclear reactor\n\nControl rods that are made of a neutron poison are used to absorb neutrons. Absorbing more neutrons in a control rod means that there are fewer neutrons available to cause fission, so pushing the control rod deeper into the reactor will reduce its power output, and extracting the control rod will increase it.","Nuclear reactor\n\nAt the first level of control in all nuclear reactors, a process of delayed neutron emission by a number of neutron-rich fission isotopes is an important physical process. These delayed neutrons account for about 0.65% of the total neutrons produced in fission, with the remainder (termed \"prompt neutrons\") released immediately upon fission. The fission products which produce delayed neutrons have half lives for their decay by neutron emission that range from milliseconds to as long as several minutes, and so considerable time is required to determine exactly when a reactor reaches the critical point. Keeping the reactor in the zone of chain-reactivity where delayed neutrons are necessary to achieve a critical mass state allows mechanical devices or human operators to control a chain reaction in \"real time\"; otherwise the time between achievement of criticality and nuclear meltdown as a result of an exponential power surge from the normal nuclear chain reaction, would be too short to allow for intervention. This last stage, where delayed neutrons are no longer required to maintain criticality, is known as the prompt critical point.","Nuclear reactor\n\nThere is a scale for describing criticality in numerical form, in which bare criticality is known as zero dollars and the prompt critical point is one dollar, and other points in the process interpolated in cents.","Nuclear reactor\n\nIn some reactors, the coolant also acts as a neutron moderator. A moderator increases the power of the reactor by causing the fast neutrons that are released from fission to lose energy and become thermal neutrons. Thermal neutrons are more likely than fast neutrons to cause fission. If the coolant is a moderator, then temperature changes can affect the density of the coolant/moderator and therefore change power output. A higher temperature coolant would be less dense, and therefore a less effective moderator.","Nuclear reactor\n\nIn other reactors the coolant acts as a poison by absorbing neutrons in the same way that the control rods do. In these reactors power output can be increased by heating the coolant, which makes it a less dense poison. Nuclear reactors generally have automatic and manual systems to scram the reactor in an emergency shut down. These systems insert large amounts of poison (often boron in the form of boric acid) into the reactor to shut the fission reaction down if unsafe conditions are detected or anticipated.","Nuclear reactor\n\nMost types of reactors are sensitive to a process variously known as xenon poisoning, or the iodine pit. The common fission product Xenon-135 produced in the fission process acts as a neutron poison that absorbs neutrons and therefore tends to shut the reactor down. Xenon-135 accumulation can be controlled by keeping power levels high enough to destroy it by neutron absorption as fast as it is produced. Fission also produces iodine-135, which in turn decays (with a half-life of 6.57 hours) to new xenon-135. When the reactor is shut down, iodine-135 continues to decay to xenon-135, making restarting the reactor more difficult for a day or two, as the xenon-135 decays into cesium-135, which is not nearly as poisonous as xenon-135, with a half-life of 9.2 hours. This temporary state is the \"iodine pit.\" If the reactor has sufficient extra reactivity capacity, it can be restarted. As the extra xenon-135 is transmuted to xenon-136, which is much less a neutron poison, within a few hours the reactor experiences a \"xenon burnoff (power) transient\". Control rods must be further inserted to replace the neutron absorption of the lost xenon-135.","Nuclear reactor\n\nFailure to properly follow such a procedure was a key step in the Chernobyl disaster.","Nuclear reactor\n\nReactors used in nuclear marine propulsion (especially nuclear submarines) often cannot be run at continuous power around the clock in the same way that land-based power reactors are normally run, and in addition often need to have a very long core life without refueling. For this reason many designs use highly enriched uranium but incorporate burnable neutron poison in the fuel rods. This allows the reactor to be constructed with an excess of fissionable material, which is nevertheless made relatively safe early in the reactor's fuel burn-cycle by the presence of the neutron-absorbing material which is later replaced by normally produced long-lived neutron poisons (far longer-lived than xenon-135) which gradually accumulate over the fuel load's operating life.","Nuclear reactor\n\nElectrical power generation","Nuclear reactor\n\nThe energy released in the fission process generates heat, some of which can be converted into usable energy. A common method of harnessing this thermal energy is to use it to boil water to produce pressurized steam which will then drive a steam turbine that turns an alternator and generates electricity.","Nuclear reactor\n\nEarly reactors","Nuclear reactor\n\nThe neutron was discovered in 1932. The concept of a nuclear chain reaction brought about by nuclear reactions mediated by neutrons was first realized shortly thereafter, by Hungarian scientist Leó Szilárd, in 1933. He filed a patent for his idea of a simple reactor the following year while working at the Admiralty in London. However, Szilárd's idea did not incorporate the idea of nuclear fission as a neutron source, since that process was not yet discovered. Szilárd's ideas for nuclear reactors using neutron-mediated nuclear chain reactions in light elements proved unworkable.","Nuclear reactor\n\nInspiration for a new type of reactor using uranium came from the discovery by Lise Meitner, Fritz Strassmann and Otto Hahn in 1938 that bombardment of uranium with neutrons (provided by an alpha-on-beryllium fusion reaction, a \"neutron howitzer\") produced a barium residue, which they reasoned was created by the fissioning of the uranium nuclei. Subsequent studies in early 1939 (one of them by Szilárd and Fermi) revealed that several neutrons were also released during the fissioning, making available the opportunity for the nuclear chain reaction that Szilárd had envisioned six years previously.","Nuclear reactor\n\nOn 2 August 1939 Albert Einstein signed a letter to President Franklin D. Roosevelt (written by Szilárd) suggesting that the discovery of uranium's fission could lead to the development of \"extremely powerful bombs of a new type\", giving impetus to the study of reactors and fission. Szilárd and Einstein knew each other well and had worked together years previously, but Einstein had never thought about this possibility for nuclear energy until Szilard reported it to him, at the beginning of his quest to produce the Einstein-Szilárd letter to alert the U.S. government.","Nuclear reactor\n\nShortly after, Hitler's Germany invaded Poland in 1939, starting World War II in Europe. The U.S. was not yet officially at war, but in October, when the Einstein-Szilárd letter was delivered to him, Roosevelt commented that the purpose of doing the research was to make sure \"the Nazis don't blow us up.\" The U.S. nuclear project followed, although with some delay as there remained skepticism (some of it from Fermi) and also little action from the small number of officials in the government who were initially charged with moving the project forward.","Nuclear reactor\n\nThe following year the U.S. Government received the Frisch–Peierls memorandum from the UK, which stated that the amount of uranium needed for a chain reaction was far lower than had previously been thought. The memorandum was a product of the MAUD Committee, which was working on the UK atomic bomb project, known as Tube Alloys, later to be subsumed within the Manhattan Project.","Nuclear reactor\n\nEventually, the first artificial nuclear reactor, Chicago Pile-1, was constructed at the University of Chicago, by a team led by Enrico Fermi, in late 1942. By this time, the program had been pressured for a year by U.S. entry into the war. The Chicago Pile achieved criticality on 2 December 1942 at 3:25 PM. The reactor support structure was made of wood, which supported a pile (hence the name) of graphite blocks, embedded in which was natural uranium-oxide 'pseudospheres' or 'briquettes'.","Nuclear reactor\n\nSoon after the Chicago Pile, the U.S. military developed a number of nuclear reactors for the Manhattan Project starting in 1943. The primary purpose for the largest reactors (located at the Hanford Site in Washington state), was the mass production of plutonium for nuclear weapons. Fermi and Szilard applied for a patent on reactors on 19 December 1944. Its issuance was delayed for 10 years because of wartime secrecy.","Nuclear reactor\n\n\"World's first nuclear power plant\" is the claim made by signs at the site of the EBR-I, which is now a museum near Arco, Idaho. Originally called \"Chicago Pile-4\", it was carried out under the direction of Walter Zinn for Argonne National Laboratory. This experimental LMFBR operated by the U.S. Atomic Energy Commission produced 0.8 kW in a test on 20 December 1951 and 100 kW (electrical) the following day, having a design output of 200 kW (electrical).","Nuclear reactor\n\nBesides the military uses of nuclear reactors, there were political reasons to pursue civilian use of atomic energy. U.S. President Dwight Eisenhower made his famous Atoms for Peace speech to the UN General Assembly on 8 December 1953. This diplomacy led to the dissemination of reactor technology to U.S. institutions and worldwide.","Nuclear reactor\n\nThe first nuclear power plant built for civil purposes was the AM-1 Obninsk Nuclear Power Plant, launched on 27 June 1954 in the Soviet Union. It produced around 5 MW (electrical).","Nuclear reactor\n\nAfter World War II, the U.S. military sought other uses for nuclear reactor technology. Research by the Army and the Air Force never came to fruition; however, the U.S. Navy succeeded when they steamed the USS Nautilus (SSN-571) on nuclear power 17 January 1955.","Nuclear reactor\n\nThe first commercial nuclear power station, Calder Hall in Sellafield, England was opened in 1956 with an initial capacity of 50 MW (later 200 MW).","Nuclear reactor\n\nThe first portable nuclear reactor \"Alco PM-2A\" used to generate electrical power (2 MW) for Camp Century from 1960.","Nuclear reactor\n\nComponents","Nuclear reactor\n\nThe key components common to most types of nuclear power plants are:\n* Nuclear fuel\n* Nuclear reactor core\n* Neutron moderator\n* Neutron poison\n* Neutron howitzer (provides steady source of neutrons to re-initiate reaction following shutdown)\n* Coolant (often the Neutron Moderator and the Coolant are the same, usually both purified water)\n* Control rods\n* Reactor vessel\n* Boiler feedwater pump\n* Steam generators (not in BWRs)\n* Steam turbine\n* Electrical generator\n* Condenser\n* Cooling tower (not always required)\n* Radwaste System (a section of the plant handling radioactive waste)\n* Refueling Floor\n* Spent fuel pool\n* Nuclear safety systems\n** Reactor Protective System (RPS)\n** Emergency Diesel Generators\n** Emergency Core Cooling Systems (ECCS)\n** Standby Liquid Control System (emergency boron injection, in BWRs only)\n* Essential service water system (ESWS)\n* Containment building\n* Control room\n* Emergency Operations Facility\n* Nuclear training facility (usually contains a Control Room simulator)","Nuclear reactor\n\nReactor types","Nuclear reactor\n\nClassifications","Nuclear reactor\n\nNuclear Reactors are classified by several methods; a brief outline of these classification methods is provided.","Nuclear reactor\n\nClassification by type of nuclear reaction","Nuclear reactor\n\nNuclear fission","Nuclear reactor\n\nAll commercial power reactors are based on nuclear fission. They generally use uranium and its product plutonium as nuclear fuel, though a thorium fuel cycle is also possible. Fission reactors can be divided roughly into two classes, depending on the energy of the neutrons that sustain the fission chain reaction:\n* Thermal reactors (the most common type of nuclear reactor) use slowed or thermal neutrons to keep up the fission of their fuel. Almost all current reactors are of this type. These contain neutron moderator materials that slow neutrons until their neutron temperature is thermalized, that is, until their kinetic energy approaches the average kinetic energy of the surrounding particles. Thermal neutrons have a far higher cross-section (probability) of fissioning the fissile nuclei uranium-235, plutonium-239, and plutonium-241, and a relatively lower probability of neutron capture by uranium-238 (U-238) compared to the faster neutrons that originally result from fission, allowing use of low-enriched uranium or even natural uranium fuel. The moderator is often also the coolant, usually water under high pressure to increase the boiling point. These are surrounded by a reactor vessel, instrumentation to monitor and control the reactor, radiation shielding, and a containment building.","Nuclear reactor\n\n* Fast neutron reactors use fast neutrons to cause fission in their fuel. They do not have a neutron moderator, and use less-moderating coolants. Maintaining a chain reaction requires the fuel to be more highly enriched in fissile material (about 20% or more) due to the relatively lower probability of fission versus capture by U-238. Fast reactors have the potential to produce less transuranic waste because all actinides are fissionable with fast neutrons, but they are more difficult to build and more expensive to operate. Overall, fast reactors are less common than thermal reactors in most applications. Some early power stations were fast reactors, as are some Russian naval propulsion units. Construction of prototypes is continuing (see fast breeder or generation IV reactors).","Nuclear reactor\n\nNuclear fusion","Nuclear reactor\n\nFusion power is an experimental technology, generally with hydrogen as fuel. While not suitable for power production, Farnsworth-Hirsch fusors are used to produce neutron radiation.","Nuclear reactor\n\nClassification by moderator material","Nuclear reactor\n\nUsed by thermal reactors:\n* Graphite-moderated reactors\n* Water moderated reactors\n** Heavy-water reactors (Used in Canada, India, Argentina, China, Pakistan, Romania and South Korea). )\n** Light-water-moderated reactors (LWRs). Light-water reactors (the most common type of thermal reactor) use ordinary water to moderate and cool the reactors. When at operating temperature, if the temperature of the water increases, its density drops, and fewer neutrons passing through it are slowed enough to trigger further reactions. That negative feedback stabilizes the reaction rate. Graphite and heavy-water reactors tend to be more thoroughly thermalized than light water reactors. Due to the extra thermalization, these types can use natural uranium/unenriched fuel.\n* Light-element-moderated reactors.\n** Molten salt reactors (MSRs) are moderated by light elements such as lithium or beryllium, which are constituents of the coolant/fuel matrix salts LiF and BeF2.\n** Liquid metal cooled reactors, such as those whose coolant is a mixture of lead and bismuth, may use BeO as a moderator.\n* Organically moderated reactors (OMR) use biphenyl and terphenyl as moderator and coolant.","Nuclear reactor\n\nClassification by coolant","Nuclear reactor\n\n* Water cooled reactor. There are 104 operating reactors in the United States. Of these, 69 are pressurized water reactors (PWR), and 35 are boiling water reactors (BWR). ** Pressurized water reactor (PWR) Pressurized water reactors constitute the large majority of all Western nuclear power plants. *** A primary characteristic of PWRs is a pressurizer, a specialized pressure vessel. Most commercial PWRs and naval reactors use pressurizers. During normal operation, a pressurizer is partially filled with water, and a steam bubble is maintained above it by heating the water with submerged heaters. During normal operation, the pressurizer is connected to the primary reactor pressure vessel (RPV) and the pressurizer \"bubble\" provides an expansion space for changes in water volume in the reactor. This arrangement also provides a means of pressure control for the reactor by increasing or decreasing the steam pressure in the pressurizer using the pressurizer heaters. *** Pressurised heavy water reactors are a subset of pressurized water reactors, sharing the use of a pressurized, isolated heat transport loop, but using heavy water as coolant and moderator for the greater neutron economies it offers.","Nuclear reactor\n\n** Boiling water reactor (BWR)\n*** BWRs are characterized by boiling water around the fuel rods in the lower portion of a primary reactor pressure vessel. A boiling water reactor uses 235U, enriched as uranium dioxide, as its fuel. The fuel is assembled into rods housed in a steel vessel that is submerged in water. The nuclear fission causes the water to boil, generating steam. This steam flows through pipes into turbines. The turbines are driven by the steam, and this process generates electricity. During normal operation, pressure is controlled by the amount of steam flowing from the reactor pressure vessel to the turbine. ** Pool-type reactor\n* Liquid metal cooled reactor. Since water is a moderator, it cannot be used as a coolant in a fast reactor. Liquid metal coolants have included sodium, NaK, lead, lead-bismuth eutectic, and in early reactors, mercury. ** Sodium-cooled fast reactor\n** Lead-cooled fast reactor\n* Gas cooled reactors are cooled by a circulating inert gas, often helium in high-temperature designs, while carbon dioxide has been used in past British and French nuclear power plants. Nitrogen has also been used. Utilization of the heat varies, depending on the reactor.","Nuclear reactor\n\nSome reactors run hot enough that the gas can directly power a gas turbine. Older designs usually run the gas through a heat exchanger to make steam for a steam turbine. * Molten salt reactors (MSRs) are cooled by circulating a molten salt, typically a eutectic mixture of fluoride salts, such as FLiBe. In a typical MSR, the coolant is also used as a matrix in which the fissile material is dissolved.","Nuclear reactor\n\nClassification by generation","Nuclear reactor\n\n* Generation I reactor (early prototypes, research reactors, non-commercial power producing reactors)\n* Generation II reactor (most current nuclear power plants 1965–1996)\n* Generation III reactor (evolutionary improvements of existing designs 1996-now)\n* Generation IV reactor (technologies still under development unknown start date, possibly 2030)","Nuclear reactor\n\nIn 2003, the French Commissariat à l'Énergie Atomique (CEA) was the first to refer to \"Gen II\" types in Nucleonics Week.","Nuclear reactor\n\nThe first mentioning of \"Gen III\" was in 2000, in conjunction with the launch of the Generation IV International Forum (GIF) plans.","Nuclear reactor\n\n\"Gen IV\" was named in 2000, by the United States Department of Energy (DOE) for developing new plant types.","Nuclear reactor\n\nClassification by phase of fuel","Nuclear reactor\n\n* Solid fueled\n* Fluid fueled\n** Aqueous homogeneous reactor\n** Molten salt reactor\n* Gas fueled (theoretical)","Nuclear reactor\n\nClassification by use","Nuclear reactor\n\n* Electricity\n** Nuclear power plants including small modular reactors\n* Propulsion, see nuclear propulsion\n** Nuclear marine propulsion\n** Various proposed forms of rocket propulsion\n* Other uses of heat\n** Desalination\n** Heat for domestic and industrial heating\n** Hydrogen production for use in a hydrogen economy\n* Production reactors for transmutation of elements\n** Breeder reactors are capable of producing more fissile material than they consume during the fission chain reaction (by converting fertile U-238 to Pu-239, or Th-232 to U-233). Thus, a uranium breeder reactor, once running, can be re-fueled with natural or even depleted uranium, and a thorium breeder reactor can be re-fueled with thorium; however, an initial stock of fissile material is required. ** Creating various radioactive isotopes, such as americium for use in smoke detectors, and cobalt-60, molybdenum-99 and others, used for imaging and medical treatment. ** Production of materials for nuclear weapons such as weapons-grade plutonium\n* Providing a source of neutron radiation (for example with the pulsed Godiva device) and positron radiation (e.g.","Nuclear reactor\n\nneutron activation analysis and potassium-argon dating)\n* Research reactor: Typically reactors used for research and training, materials testing, or the production of radioisotopes for medicine and industry. These are much smaller than power reactors or those propelling ships, and many are on university campuses. There are about 280 such reactors operating, in 56 countries. Some operate with high-enriched uranium fuel, and international efforts are underway to substitute low-enriched fuel.","Nuclear reactor\n\nCurrent technologies","Nuclear reactor\n\n;; Pressurized water reactors (PWR)\n: These reactors use a pressure vessel to contain the nuclear fuel, control rods, moderator, and coolant. They are cooled and moderated by high-pressure liquid water. The hot radioactive water that leaves the pressure vessel is looped through a steam generator, which in turn heats a secondary (non-radioactive) loop of water to steam that can run turbines. They are the majority of current reactors. This is a thermal neutron reactor design, the newest of which are the VVER-1200, Advanced Pressurized Water Reactor and the European Pressurized Reactor. United States Naval reactors are of this type. ;; Boiling water reactors (BWR)\n: A BWR is like a PWR without the steam generator. A boiling water reactor is cooled and moderated by water like a PWR, but at a lower pressure, which allows the water to boil inside the pressure vessel producing the steam that runs the turbines. Unlike a PWR, there is no primary and secondary loop. The thermal efficiency of these reactors can be higher, and they can be simpler, and even potentially more stable and safe.","Nuclear reactor\n\nThis is a thermal neutron reactor design, the newest of which are the Advanced Boiling Water Reactor and the Economic Simplified Boiling Water Reactor.","Nuclear reactor\n\n;; Pressurized Heavy Water Reactor (PHWR)\n: A Canadian design (known as CANDU), these reactors are heavy-water-cooled and -moderated pressurized-water reactors. Instead of using a single large pressure vessel as in a PWR, the fuel is contained in hundreds of pressure tubes. These reactors are fueled with natural uranium and are thermal neutron reactor designs. PHWRs can be refueled while at full power, which makes them very efficient in their use of uranium (it allows for precise flux control in the core). CANDU PHWRs have been built in Canada, Argentina, China, India, Pakistan, Romania, and South Korea. India also operates a number of PHWRs, often termed 'CANDU-derivatives', built after the Government of Canada halted nuclear dealings with India following the 1974 Smiling Buddha nuclear weapon test. ;; Reaktor Bolshoy Moschnosti Kanalniy (High Power Channel Reactor) (RBMK)\n: A Soviet design, built to produce plutonium as well as power. RBMKs are water cooled with a graphite moderator. RBMKs are in some respects similar to CANDU in that they are refuelable during power operation and employ a pressure tube design instead of a PWR-style pressure vessel. However, unlike CANDU they are very unstable and large, making containment buildings for them expensive.","Nuclear reactor\n\nA series of critical safety flaws have also been identified with the RBMK design, though some of these were corrected following the Chernobyl disaster. Their main attraction is their use of light water and un-enriched uranium. As of 2010, 11 remain open, mostly due to safety improvements and help from international safety agencies such as the DOE. Despite these safety improvements, RBMK reactors are still considered one of the most dangerous reactor designs in use. RBMK reactors were deployed only in the former Soviet Union.","Nuclear reactor\n\n;; Gas-cooled reactor (GCR) and advanced gas-cooled reactor (AGR)\n: These are generally graphite moderated and CO2 cooled. They can have a high thermal efficiency compared with PWRs due to higher operating temperatures. There are a number of operating reactors of this design, mostly in the United Kingdom, where the concept was developed. Older designs (i.e. Magnox stations) are either shut down or will be in the near future. However, the AGCRs have an anticipated life of a further 10 to 20 years. This is a thermal neutron reactor design. Decommissioning costs can be high due to large volume of reactor core. ;; Liquid-metal fast-breeder reactor (LMFBR)\n: This is a reactor design that is cooled by liquid metal, totally unmoderated, and produces more fuel than it consumes. They are said to \"breed\" fuel, because they produce fissionable fuel during operation because of neutron capture. These reactors can function much like a PWR in terms of efficiency, and do not require much high-pressure containment, as the liquid metal does not need to be kept at high pressure, even at very high temperatures.","Nuclear reactor\n\nBN-350 and BN-600 in USSR and Superphénix in France were a reactor of this type, as was Fermi-I in the United States. The Monju reactor in Japan suffered a sodium leak in 1995 and was restarted in May 2010. All of them use/used liquid sodium. These reactors are fast neutron, not thermal neutron designs. These reactors come in two types:","Nuclear reactor\n\n:: Lead-cooled\n::: Using lead as the liquid metal provides excellent radiation shielding, and allows for operation at very high temperatures. Also, lead is (mostly) transparent to neutrons, so fewer neutrons are lost in the coolant, and the coolant does not become radioactive. Unlike sodium, lead is mostly inert, so there is less risk of explosion or accident, but such large quantities of lead may be problematic from toxicology and disposal points of view. Often a reactor of this type would use a lead-bismuth eutectic mixture. In this case, the bismuth would present some minor radiation problems, as it is not quite as transparent to neutrons, and can be transmuted to a radioactive isotope more readily than lead. The Russian Alfa class submarine uses a lead-bismuth-cooled fast reactor as its main power plant. :: Sodium-cooled\n::: Most LMFBRs are of this type. The sodium is relatively easy to obtain and work with, and it also manages to actually prevent corrosion on the various reactor parts immersed in it.","Nuclear reactor\n\nHowever, sodium explodes violently when exposed to water, so care must be taken, but such explosions would not be vastly more violent than (for example) a leak of superheated fluid from a SCWR or PWR. EBR-I, the first reactor to have a core meltdown, was of this type. ;; Pebble-bed reactors (PBR)\n: These use fuel molded into ceramic balls, and then circulate gas through the balls. The result is an efficient, low-maintenance, very safe reactor with inexpensive, standardized fuel. The prototype was the AVR. ;; Molten salt reactors\n:These dissolve the fuels in fluoride salts, or use fluoride salts for coolant. These have many safety features, high efficiency and a high power density suitable for vehicles. Notably, they have no high pressures or flammable components in the core. The prototype was the MSRE, which also used the Thorium fuel cycle. As a breeder reactor type, it reprocesses the spent fuel, extracting both Uranium and transuranics, leaving only 0.1% of transuranic waste compared to conventional once-through uranium-fueled light water reactors currently in use. A separate issue are the radioactive fission products, which are not reprocessable and need to be disposed of as with conventional reactors.","Nuclear reactor\n\n;; Aqueous Homogeneous Reactor (AHR)\n: These reactors use soluble nuclear salts dissolved in water and mixed with a coolant and a neutron moderator.","Nuclear reactor\n\nFuture and developing technologies","Nuclear reactor\n\nAdvanced reactors","Nuclear reactor\n\nMore than a dozen advanced reactor designs are in various stages of development. Some are evolutionary from the PWR, BWR and PHWR designs above, some are more radical departures. The former include the advanced boiling water reactor (ABWR), two of which are now operating with others under construction, and the planned passively safe Economic Simplified Boiling Water Reactor (ESBWR) and AP1000 units (see Nuclear Power 2010 Program). * The Integral Fast Reactor (IFR) was built, tested and evaluated during the 1980s and then retired under the Clinton administration in the 1990s due to nuclear non-proliferation policies of the administration. Recycling spent fuel is the core of its design and it therefore produces only a fraction of the waste of current reactors. * The pebble-bed reactor, a high-temperature gas-cooled reactor (HTGCR), is designed so high temperatures reduce power output by Doppler broadening of the fuel's neutron cross-section. It uses ceramic fuels so its safe operating temperatures exceed the power-reduction temperature range. Most designs are cooled by inert helium. Helium is not subject to steam explosions, resists neutron absorption leading to radioactivity, and does not dissolve contaminants that can become radioactive.","Nuclear reactor\n\nTypical designs have more layers (up to 7) of passive containment than light water reactors (usually 3). A unique feature that may aid safety is that the fuel-balls actually form the core's mechanism, and are replaced one-by-one as they age. The design of the fuel makes fuel reprocessing expensive. * The Small, sealed, transportable, autonomous reactor (SSTAR) is being primarily researched and developed in the US, intended as a fast breeder reactor that is passively safe and could be remotely shut down in case the suspicion arises that it is being tampered with. * The Clean And Environmentally Safe Advanced Reactor (CAESAR) is a nuclear reactor concept that uses steam as a moderator – this design is still in development. * The Reduced moderation water reactor builds upon the Advanced boiling water reactor(ABWR) that is presently in use, it is not a complete fast reactor instead using mostly epithermal neutrons, which are between thermal and fast neutrons in speed. * The hydrogen-moderated self-regulating nuclear power module (HPM) is a reactor design emanating from the Los Alamos National Laboratory that uses uranium hydride as fuel.","Nuclear reactor\n\n* Subcritical reactors are designed to be safer and more stable, but pose a number of engineering and economic difficulties. One example is the Energy amplifier. * Thorium-based reactors. It is possible to convert Thorium-232 into U-233 in reactors specially designed for the purpose. In this way, thorium, which is four times more abundant than uranium, can be used to breed U-233 nuclear fuel. U-233 is also believed to have favourable nuclear properties as compared to traditionally used U-235, including better neutron economy and lower production of long lived transuranic waste. ** Advanced heavy-water reactor (AHWR)— A proposed heavy water moderated nuclear power reactor that will be the next generation design of the PHWR type. Under development in the Bhabha Atomic Research Centre (BARC), India. ** KAMINI — A unique reactor using Uranium-233 isotope for fuel. Built in India by BARC and Indira Gandhi Center for Atomic Research (IGCAR). ** India is also planning to build fast breeder reactors using the thorium – Uranium-233 fuel cycle. The FBTR (Fast Breeder Test Reactor) in operation at Kalpakkam (India) uses Plutonium as a fuel and liquid sodium as a coolant.","Nuclear reactor\n\nGeneration IV reactors","Nuclear reactor\n\nGeneration IV reactors are a set of theoretical nuclear reactor designs currently being researched. These designs are generally not expected to be available for commercial construction before 2030. Current reactors in operation around the world are generally considered second- or third-generation systems, with the first-generation systems having been retired some time ago. Research into these reactor types was officially started by the Generation IV International Forum (GIF) based on eight technology goals. The primary goals being to improve nuclear safety, improve proliferation resistance, minimize waste and natural resource utilization, and to decrease the cost to build and run such plants. \n* Gas-cooled fast reactor\n* Lead-cooled fast reactor\n* Molten salt reactor\n* Sodium-cooled fast reactor\n* Supercritical water reactor\n* Very-high-temperature reactor","Nuclear reactor\n\nGeneration V+ reactors","Nuclear reactor\n\nGeneration V reactors are designs which are theoretically possible, but which are not being actively considered or researched at present. Though such reactors could be built with current or near term technology, they trigger little interest for reasons of economics, practicality, or safety. * Liquid-core reactor. A closed loop liquid-core nuclear reactor, where the fissile material is molten uranium or uranium solution cooled by a working gas pumped in through holes in the base of the containment vessel. * Gas-core reactor. A closed loop version of the nuclear lightbulb rocket, where the fissile material is gaseous uranium-hexafluoride contained in a fused silica vessel. A working gas (such as hydrogen) would flow around this vessel and absorb the UV light produced by the reaction. This reactor design could also function as a rocket engine, as featured in Harry Harrison's 1976 science-fiction novel 'Skyfall'. In theory, using UF6 as a working fuel directly (rather than as a stage to one, as is done now) would mean lower processing costs, and very small reactors.","Nuclear reactor\n\nIn practice, running a reactor at such high power densities would probably produce unmanageable neutron flux, weakening most reactor materials, and therefore as the flux would be similar to that expected in fusion reactors, it would require similar materials to those selected by the International Fusion Materials Irradiation Facility. ** Gas core EM reactor. As in the gas core reactor, but with photovoltaic arrays converting the UV light directly to electricity. * Fission fragment reactor\n* Hybrid nuclear fusion. Would use the neutrons emitted by fusion to fission a blanket of fertile material, like U-238 or Th-232 and transmutate other reactor's spent nuclear fuel/nuclear waste into relatively more benign isotopes.","Nuclear reactor\n\nFusion reactors","Nuclear reactor\n\nControlled nuclear fusion could in principle be used in fusion power plants to produce power without the complexities of handling actinides, but significant scientific and technical obstacles remain. Several fusion reactors have been built, but only recently reactors have been able to release more energy than the amount of energy used in the process. Despite research having started in the 1950s, no commercial fusion reactor is expected before 2050. The ITER project is currently leading the effort to harness fusion power.","Nuclear reactor\n\nNuclear fuel cycle","Nuclear reactor\n\nThermal reactors generally depend on refined and enriched uranium. Some nuclear reactors can operate with a mixture of plutonium and uranium (see MOX). The process by which uranium ore is mined, processed, enriched, used, possibly reprocessed and disposed of is known as the nuclear fuel cycle.","Nuclear reactor\n\nUnder 1% of the uranium found in nature is the easily fissionable U-235 isotope and as a result most reactor designs require enriched fuel.\nEnrichment involves increasing the percentage of U-235 and is usually done by means of gaseous diffusion or gas centrifuge. The enriched result is then converted into uranium dioxide powder, which is pressed and fired into pellet form. These pellets are stacked into tubes which are then sealed and called fuel rods. Many of these fuel rods are used in each nuclear reactor.","Nuclear reactor\n\nMost BWR and PWR commercial reactors use uranium enriched to about 4% U-235, and some commercial reactors with a high neutron economy do not require the fuel to be enriched at all (that is, they can use natural uranium). According to the International Atomic Energy Agency there are at least 100 research reactors in the world fueled by highly enriched (weapons-grade/90% enrichment uranium). Theft risk of this fuel (potentially used in the production of a nuclear weapon) has led to campaigns advocating conversion of this type of reactor to low-enrichment uranium (which poses less threat of proliferation).","Nuclear reactor\n\nFissile U-235 and non-fissile but fissionable and fertile U-238 are both used in the fission process. U-235 is fissionable by thermal (i.e. slow-moving) neutrons. A thermal neutron is one which is moving about the same speed as the atoms around it. Since all atoms vibrate proportionally to their absolute temperature, a thermal neutron has the best opportunity to fission U-235 when it is moving at this same vibrational speed. On the other hand, U-238 is more likely to capture a neutron when the neutron is moving very fast. This U-239 atom will soon decay into plutonium-239, which is another fuel. Pu-239 is a viable fuel and must be accounted for even when a highly enriched uranium fuel is used. Plutonium fissions will dominate the U-235 fissions in some reactors, especially after the initial loading of U-235 is spent. Plutonium is fissionable with both fast and thermal neutrons, which make it ideal for either nuclear reactors or nuclear bombs.","Nuclear reactor\n\nMost reactor designs in existence are thermal reactors and typically use water as a neutron moderator (moderator means that it slows down the neutron to a thermal speed) and as a coolant. But in a fast breeder reactor, some other kind of coolant is used which will not moderate or slow the neutrons down much. This enables fast neutrons to dominate, which can effectively be used to constantly replenish the fuel supply. By merely placing cheap unenriched uranium into such a core, the non-fissionable U-238 will be turned into Pu-239, \"breeding\" fuel.","Nuclear reactor\n\nIn thorium fuel cycle thorium-232 absorbs a neutron in either a fast or thermal reactor. The thorium-233 beta decays to protactinium-233 and then to uranium-233, which in turn is used as fuel. Hence, like uranium-238, thorium-232 is a fertile material.","Nuclear reactor\n\nFueling of nuclear reactors","Nuclear reactor\n\nThe amount of energy in the reservoir of nuclear fuel is frequently expressed in terms of \"full-power days,\" which is the number of 24-hour periods (days) a reactor is scheduled for operation at full power output for the generation of heat energy. The number of full-power days in a reactor's operating cycle (between refueling outage times) is related to the amount of fissile uranium-235 (U-235) contained in the fuel assemblies at the beginning of the cycle. A higher percentage of U-235 in the core at the beginning of a cycle will permit the reactor to be run for a greater number of full-power days.","Nuclear reactor\n\nAt the end of the operating cycle, the fuel in some of the assemblies is \"spent\" and is discharged and replaced with new (fresh) fuel assemblies, although in practice it is the buildup of reaction poisons in nuclear fuel that determines the lifetime of nuclear fuel in a reactor. Long before all possible fission has taken place, the buildup of long-lived neutron absorbing fission byproducts impedes the chain reaction. The fraction of the reactor's fuel core replaced during refueling is typically one-fourth for a boiling-water reactor and one-third for a pressurized-water reactor. The disposition and storage of this spent fuel is one of the most challenging aspects of the operation of a commercial nuclear power plant. This nuclear waste is highly radioactive and its toxicity presents a danger for thousands of years.","Nuclear reactor\n\nNot all reactors need to be shut down for refueling; for example, pebble bed reactors, RBMK reactors, molten salt reactors, Magnox, AGR and CANDU reactors allow fuel to be shifted through the reactor while it is running. In a CANDU reactor, this also allows individual fuel elements to be situated within the reactor core that are best suited to the amount of U-235 in the fuel element.","Nuclear reactor\n\nThe amount of energy extracted from nuclear fuel is called its burnup, which is expressed in terms of the heat energy produced per initial unit of fuel weight. Burn up is commonly expressed as megawatt days thermal per metric ton of initial heavy metal.","Nuclear reactor\n\nSafety","Nuclear reactor\n\nNuclear safety covers the actions taken to prevent nuclear and radiation accidents or to limit their consequences. The nuclear power industry has improved the safety and performance of reactors, and has proposed new safer (but generally untested) reactor designs but there is no guarantee that the reactors will be designed, built and operated correctly. Mistakes do occur and the designers of reactors at Fukushima in Japan did not anticipate that a tsunami generated by an earthquake would disable the backup systems that were supposed to stabilize the reactor after the earthquake, despite multiple warnings by the NRG and the Japanese nuclear safety administration. According to UBS AG, the Fukushima I nuclear accidents have cast doubt on whether even an advanced economy like Japan can master nuclear safety. Catastrophic scenarios involving terrorist attacks are also conceivable. An interdisciplinary team from MIT has estimated that given the expected growth of nuclear power from 2005–2055, at least four serious nuclear accidents would be expected in that period.","Nuclear reactor\n\nAccidents","Nuclear reactor\n\nSome serious nuclear and radiation accidents have occurred. Nuclear power plant accidents include the SL-1 accident (1961), the Three Mile Island accident (1979), Chernobyl disaster (1986), and the Fukushima Daiichi nuclear disaster (2011). Nuclear-powered submarine mishaps include the K-19 reactor accident (1961),[http://www.iaea.org/Publications/Magazines/Bulletin/Bull413/article1.pdf Strengthening the Safety of Radiation Sources] p. 14. the K-27 reactor accident (1968), and the K-431 reactor accident (1985).[http://www.time.com/time/photogallery/0,29307,1887705,00.html The Worst Nuclear Disasters]. Time.","Nuclear reactor\n\nNuclear reactors have been launched into Earth orbit at least 34 times. A number of incidents connected with the unmanned nuclear-reactor-powered Soviet RORSAT radar satellite program resulted in spent nuclear fuel re-entering the Earth's atmosphere from orbit.","Nuclear reactor\n\nNatural nuclear reactors","Nuclear reactor\n\nAlthough nuclear fission reactors are often thought of as being solely a product of modern technology, the first nuclear fission reactors were in fact naturally occurring. A natural nuclear fission reactor can occur under certain circumstances that mimic the conditions in a constructed reactor. Fifteen natural fission reactors have so far been found in three separate ore deposits at the Oklo uranium mine in Gabon, West Africa. First discovered in 1972 by French physicist Francis Perrin, they are collectively known as the Oklo Fossil Reactors. Self-sustaining nuclear fission reactions took place in these reactors approximately 1.5 billion years ago, and ran for a few hundred thousand years, averaging 100 kW of power output during that time. The concept of a natural nuclear reactor was theorized as early as 1956 by Paul Kuroda at the University of Arkansas.","Nuclear reactor\n\nSuch reactors can no longer form on Earth: radioactive decay over this immense time span has reduced the proportion of U-235 in naturally occurring uranium to below the amount required to sustain a chain reaction.","Nuclear reactor\n\nThe natural nuclear reactors formed when a uranium-rich mineral deposit became inundated with groundwater that acted as a neutron moderator, and a strong chain reaction took place. The water moderator would boil away as the reaction increased, slowing it back down again and preventing a meltdown. The fission reaction was sustained for hundreds of thousands of years.","Nuclear reactor\n\nThese natural reactors are extensively studied by scientists interested in geologic radioactive waste disposal. They offer a case study of how radioactive isotopes migrate through the Earth's crust. This is a significant area of controversy as opponents of geologic waste disposal fear that isotopes from stored waste could end up in water supplies or be carried into the environment."],"string":"[\n \"Nuclear reactor\\n\\nThis article is a subarticle of Nuclear power.\",\n \"Nuclear reactor\\n\\nA nuclear reactor, formerly known as an atomic pile, is a device used to initiate and control a sustained nuclear chain reaction. Nuclear reactors are used at nuclear power plants for electricity generation and in propulsion of ships. Heat from nuclear fission is passed to a working fluid (water or gas), which runs through steam turbines. These either drive a ship's propellers or turn electrical generators. Nuclear generated steam in principle can be used for industrial process heat or for district heating. Some reactors are used to produce isotopes for medical and industrial use, or for production of weapons-grade plutonium. Some are run only for research. Today there are about 450 nuclear power reactors that are used to generate electricity in about 30 countries around the world.\",\n \"Nuclear reactor\\n\\nMechanism\",\n \"Nuclear reactor\\n\\nJust as conventional power-stations generate electricity by harnessing the thermal energy released from burning fossil fuels, nuclear reactors convert the energy released by controlled nuclear fission into thermal energy for further conversion to mechanical or electrical forms.\",\n \"Nuclear reactor\\n\\nFission\",\n \"Nuclear reactor\\n\\nWhen a large fissile atomic nucleus such as uranium-235 or plutonium-239 absorbs a neutron, it may undergo nuclear fission. The heavy nucleus splits into two or more lighter nuclei, (the fission products), releasing kinetic energy, gamma radiation, and free neutrons. A portion of these neutrons may later be absorbed by other fissile atoms and trigger further fission events, which release more neutrons, and so on. This is known as a nuclear chain reaction.\",\n \"Nuclear reactor\\n\\nTo control such a nuclear chain reaction, neutron poisons and neutron moderators can change the portion of neutrons that will go on to cause more fission. Nuclear reactors generally have automatic and manual systems to shut the fission reaction down if monitoring detects unsafe conditions.\",\n \"Nuclear reactor\\n\\nCommonly-used moderators include regular (light) water (in 74.8% of the world's reactors), solid graphite (20% of reactors) and heavy water (5% of reactors). Some experimental types of reactor have used beryllium, and hydrocarbons have been suggested as another possibility.\",\n \"Nuclear reactor\\n\\nHeat generation\",\n \"Nuclear reactor\\n\\nThe reactor core generates heat in a number of ways:\\n* The kinetic energy of fission products is converted to thermal energy when these nuclei collide with nearby atoms.\\n* The reactor absorbs some of the gamma rays produced during fission and converts their energy into heat.\\n* Heat is produced by the radioactive decay of fission products and materials that have been activated by neutron absorption. This decay heat-source will remain for some time even after the reactor is shut down.\",\n \"Nuclear reactor\\n\\nA kilogram of uranium-235 (U-235) converted via nuclear processes releases approximately three million times more energy than a kilogram of coal burned conventionally (7.2 × 1013 joules per kilogram of uranium-235 versus 2.4 × 107 joules per kilogram of coal).\",\n \"Nuclear reactor\\n\\nCooling\",\n \"Nuclear reactor\\n\\nA nuclear reactor coolant — usually water but sometimes a gas or a liquid metal (like liquid sodium) or molten salt — is circulated past the reactor core to absorb the heat that it generates. The heat is carried away from the reactor and is then used to generate steam. Most reactor systems employ a cooling system that is physically separated from the water that will be boiled to produce pressurized steam for the turbines, like the pressurized water reactor. However, in some reactors the water for the steam turbines is boiled directly by the reactor core; for example the boiling water reactor.\",\n \"Nuclear reactor\\n\\nReactivity control\",\n \"Nuclear reactor\\n\\nThe power output of the reactor is adjusted by controlling how many neutrons are able to create more fissions.\",\n \"Nuclear reactor\\n\\nControl rods that are made of a neutron poison are used to absorb neutrons. Absorbing more neutrons in a control rod means that there are fewer neutrons available to cause fission, so pushing the control rod deeper into the reactor will reduce its power output, and extracting the control rod will increase it.\",\n \"Nuclear reactor\\n\\nAt the first level of control in all nuclear reactors, a process of delayed neutron emission by a number of neutron-rich fission isotopes is an important physical process. These delayed neutrons account for about 0.65% of the total neutrons produced in fission, with the remainder (termed \\\"prompt neutrons\\\") released immediately upon fission. The fission products which produce delayed neutrons have half lives for their decay by neutron emission that range from milliseconds to as long as several minutes, and so considerable time is required to determine exactly when a reactor reaches the critical point. Keeping the reactor in the zone of chain-reactivity where delayed neutrons are necessary to achieve a critical mass state allows mechanical devices or human operators to control a chain reaction in \\\"real time\\\"; otherwise the time between achievement of criticality and nuclear meltdown as a result of an exponential power surge from the normal nuclear chain reaction, would be too short to allow for intervention. This last stage, where delayed neutrons are no longer required to maintain criticality, is known as the prompt critical point.\",\n \"Nuclear reactor\\n\\nThere is a scale for describing criticality in numerical form, in which bare criticality is known as zero dollars and the prompt critical point is one dollar, and other points in the process interpolated in cents.\",\n \"Nuclear reactor\\n\\nIn some reactors, the coolant also acts as a neutron moderator. A moderator increases the power of the reactor by causing the fast neutrons that are released from fission to lose energy and become thermal neutrons. Thermal neutrons are more likely than fast neutrons to cause fission. If the coolant is a moderator, then temperature changes can affect the density of the coolant/moderator and therefore change power output. A higher temperature coolant would be less dense, and therefore a less effective moderator.\",\n \"Nuclear reactor\\n\\nIn other reactors the coolant acts as a poison by absorbing neutrons in the same way that the control rods do. In these reactors power output can be increased by heating the coolant, which makes it a less dense poison. Nuclear reactors generally have automatic and manual systems to scram the reactor in an emergency shut down. These systems insert large amounts of poison (often boron in the form of boric acid) into the reactor to shut the fission reaction down if unsafe conditions are detected or anticipated.\",\n \"Nuclear reactor\\n\\nMost types of reactors are sensitive to a process variously known as xenon poisoning, or the iodine pit. The common fission product Xenon-135 produced in the fission process acts as a neutron poison that absorbs neutrons and therefore tends to shut the reactor down. Xenon-135 accumulation can be controlled by keeping power levels high enough to destroy it by neutron absorption as fast as it is produced. Fission also produces iodine-135, which in turn decays (with a half-life of 6.57 hours) to new xenon-135. When the reactor is shut down, iodine-135 continues to decay to xenon-135, making restarting the reactor more difficult for a day or two, as the xenon-135 decays into cesium-135, which is not nearly as poisonous as xenon-135, with a half-life of 9.2 hours. This temporary state is the \\\"iodine pit.\\\" If the reactor has sufficient extra reactivity capacity, it can be restarted. As the extra xenon-135 is transmuted to xenon-136, which is much less a neutron poison, within a few hours the reactor experiences a \\\"xenon burnoff (power) transient\\\". Control rods must be further inserted to replace the neutron absorption of the lost xenon-135.\",\n \"Nuclear reactor\\n\\nFailure to properly follow such a procedure was a key step in the Chernobyl disaster.\",\n \"Nuclear reactor\\n\\nReactors used in nuclear marine propulsion (especially nuclear submarines) often cannot be run at continuous power around the clock in the same way that land-based power reactors are normally run, and in addition often need to have a very long core life without refueling. For this reason many designs use highly enriched uranium but incorporate burnable neutron poison in the fuel rods. This allows the reactor to be constructed with an excess of fissionable material, which is nevertheless made relatively safe early in the reactor's fuel burn-cycle by the presence of the neutron-absorbing material which is later replaced by normally produced long-lived neutron poisons (far longer-lived than xenon-135) which gradually accumulate over the fuel load's operating life.\",\n \"Nuclear reactor\\n\\nElectrical power generation\",\n \"Nuclear reactor\\n\\nThe energy released in the fission process generates heat, some of which can be converted into usable energy. A common method of harnessing this thermal energy is to use it to boil water to produce pressurized steam which will then drive a steam turbine that turns an alternator and generates electricity.\",\n \"Nuclear reactor\\n\\nEarly reactors\",\n \"Nuclear reactor\\n\\nThe neutron was discovered in 1932. The concept of a nuclear chain reaction brought about by nuclear reactions mediated by neutrons was first realized shortly thereafter, by Hungarian scientist Leó Szilárd, in 1933. He filed a patent for his idea of a simple reactor the following year while working at the Admiralty in London. However, Szilárd's idea did not incorporate the idea of nuclear fission as a neutron source, since that process was not yet discovered. Szilárd's ideas for nuclear reactors using neutron-mediated nuclear chain reactions in light elements proved unworkable.\",\n \"Nuclear reactor\\n\\nInspiration for a new type of reactor using uranium came from the discovery by Lise Meitner, Fritz Strassmann and Otto Hahn in 1938 that bombardment of uranium with neutrons (provided by an alpha-on-beryllium fusion reaction, a \\\"neutron howitzer\\\") produced a barium residue, which they reasoned was created by the fissioning of the uranium nuclei. Subsequent studies in early 1939 (one of them by Szilárd and Fermi) revealed that several neutrons were also released during the fissioning, making available the opportunity for the nuclear chain reaction that Szilárd had envisioned six years previously.\",\n \"Nuclear reactor\\n\\nOn 2 August 1939 Albert Einstein signed a letter to President Franklin D. Roosevelt (written by Szilárd) suggesting that the discovery of uranium's fission could lead to the development of \\\"extremely powerful bombs of a new type\\\", giving impetus to the study of reactors and fission. Szilárd and Einstein knew each other well and had worked together years previously, but Einstein had never thought about this possibility for nuclear energy until Szilard reported it to him, at the beginning of his quest to produce the Einstein-Szilárd letter to alert the U.S. government.\",\n \"Nuclear reactor\\n\\nShortly after, Hitler's Germany invaded Poland in 1939, starting World War II in Europe. The U.S. was not yet officially at war, but in October, when the Einstein-Szilárd letter was delivered to him, Roosevelt commented that the purpose of doing the research was to make sure \\\"the Nazis don't blow us up.\\\" The U.S. nuclear project followed, although with some delay as there remained skepticism (some of it from Fermi) and also little action from the small number of officials in the government who were initially charged with moving the project forward.\",\n \"Nuclear reactor\\n\\nThe following year the U.S. Government received the Frisch–Peierls memorandum from the UK, which stated that the amount of uranium needed for a chain reaction was far lower than had previously been thought. The memorandum was a product of the MAUD Committee, which was working on the UK atomic bomb project, known as Tube Alloys, later to be subsumed within the Manhattan Project.\",\n \"Nuclear reactor\\n\\nEventually, the first artificial nuclear reactor, Chicago Pile-1, was constructed at the University of Chicago, by a team led by Enrico Fermi, in late 1942. By this time, the program had been pressured for a year by U.S. entry into the war. The Chicago Pile achieved criticality on 2 December 1942 at 3:25 PM. The reactor support structure was made of wood, which supported a pile (hence the name) of graphite blocks, embedded in which was natural uranium-oxide 'pseudospheres' or 'briquettes'.\",\n \"Nuclear reactor\\n\\nSoon after the Chicago Pile, the U.S. military developed a number of nuclear reactors for the Manhattan Project starting in 1943. The primary purpose for the largest reactors (located at the Hanford Site in Washington state), was the mass production of plutonium for nuclear weapons. Fermi and Szilard applied for a patent on reactors on 19 December 1944. Its issuance was delayed for 10 years because of wartime secrecy.\",\n \"Nuclear reactor\\n\\n\\\"World's first nuclear power plant\\\" is the claim made by signs at the site of the EBR-I, which is now a museum near Arco, Idaho. Originally called \\\"Chicago Pile-4\\\", it was carried out under the direction of Walter Zinn for Argonne National Laboratory. This experimental LMFBR operated by the U.S. Atomic Energy Commission produced 0.8 kW in a test on 20 December 1951 and 100 kW (electrical) the following day, having a design output of 200 kW (electrical).\",\n \"Nuclear reactor\\n\\nBesides the military uses of nuclear reactors, there were political reasons to pursue civilian use of atomic energy. U.S. President Dwight Eisenhower made his famous Atoms for Peace speech to the UN General Assembly on 8 December 1953. This diplomacy led to the dissemination of reactor technology to U.S. institutions and worldwide.\",\n \"Nuclear reactor\\n\\nThe first nuclear power plant built for civil purposes was the AM-1 Obninsk Nuclear Power Plant, launched on 27 June 1954 in the Soviet Union. It produced around 5 MW (electrical).\",\n \"Nuclear reactor\\n\\nAfter World War II, the U.S. military sought other uses for nuclear reactor technology. Research by the Army and the Air Force never came to fruition; however, the U.S. Navy succeeded when they steamed the USS Nautilus (SSN-571) on nuclear power 17 January 1955.\",\n \"Nuclear reactor\\n\\nThe first commercial nuclear power station, Calder Hall in Sellafield, England was opened in 1956 with an initial capacity of 50 MW (later 200 MW).\",\n \"Nuclear reactor\\n\\nThe first portable nuclear reactor \\\"Alco PM-2A\\\" used to generate electrical power (2 MW) for Camp Century from 1960.\",\n \"Nuclear reactor\\n\\nComponents\",\n \"Nuclear reactor\\n\\nThe key components common to most types of nuclear power plants are:\\n* Nuclear fuel\\n* Nuclear reactor core\\n* Neutron moderator\\n* Neutron poison\\n* Neutron howitzer (provides steady source of neutrons to re-initiate reaction following shutdown)\\n* Coolant (often the Neutron Moderator and the Coolant are the same, usually both purified water)\\n* Control rods\\n* Reactor vessel\\n* Boiler feedwater pump\\n* Steam generators (not in BWRs)\\n* Steam turbine\\n* Electrical generator\\n* Condenser\\n* Cooling tower (not always required)\\n* Radwaste System (a section of the plant handling radioactive waste)\\n* Refueling Floor\\n* Spent fuel pool\\n* Nuclear safety systems\\n** Reactor Protective System (RPS)\\n** Emergency Diesel Generators\\n** Emergency Core Cooling Systems (ECCS)\\n** Standby Liquid Control System (emergency boron injection, in BWRs only)\\n* Essential service water system (ESWS)\\n* Containment building\\n* Control room\\n* Emergency Operations Facility\\n* Nuclear training facility (usually contains a Control Room simulator)\",\n \"Nuclear reactor\\n\\nReactor types\",\n \"Nuclear reactor\\n\\nClassifications\",\n \"Nuclear reactor\\n\\nNuclear Reactors are classified by several methods; a brief outline of these classification methods is provided.\",\n \"Nuclear reactor\\n\\nClassification by type of nuclear reaction\",\n \"Nuclear reactor\\n\\nNuclear fission\",\n \"Nuclear reactor\\n\\nAll commercial power reactors are based on nuclear fission. They generally use uranium and its product plutonium as nuclear fuel, though a thorium fuel cycle is also possible. Fission reactors can be divided roughly into two classes, depending on the energy of the neutrons that sustain the fission chain reaction:\\n* Thermal reactors (the most common type of nuclear reactor) use slowed or thermal neutrons to keep up the fission of their fuel. Almost all current reactors are of this type. These contain neutron moderator materials that slow neutrons until their neutron temperature is thermalized, that is, until their kinetic energy approaches the average kinetic energy of the surrounding particles. Thermal neutrons have a far higher cross-section (probability) of fissioning the fissile nuclei uranium-235, plutonium-239, and plutonium-241, and a relatively lower probability of neutron capture by uranium-238 (U-238) compared to the faster neutrons that originally result from fission, allowing use of low-enriched uranium or even natural uranium fuel. The moderator is often also the coolant, usually water under high pressure to increase the boiling point. These are surrounded by a reactor vessel, instrumentation to monitor and control the reactor, radiation shielding, and a containment building.\",\n \"Nuclear reactor\\n\\n* Fast neutron reactors use fast neutrons to cause fission in their fuel. They do not have a neutron moderator, and use less-moderating coolants. Maintaining a chain reaction requires the fuel to be more highly enriched in fissile material (about 20% or more) due to the relatively lower probability of fission versus capture by U-238. Fast reactors have the potential to produce less transuranic waste because all actinides are fissionable with fast neutrons, but they are more difficult to build and more expensive to operate. Overall, fast reactors are less common than thermal reactors in most applications. Some early power stations were fast reactors, as are some Russian naval propulsion units. Construction of prototypes is continuing (see fast breeder or generation IV reactors).\",\n \"Nuclear reactor\\n\\nNuclear fusion\",\n \"Nuclear reactor\\n\\nFusion power is an experimental technology, generally with hydrogen as fuel. While not suitable for power production, Farnsworth-Hirsch fusors are used to produce neutron radiation.\",\n \"Nuclear reactor\\n\\nClassification by moderator material\",\n \"Nuclear reactor\\n\\nUsed by thermal reactors:\\n* Graphite-moderated reactors\\n* Water moderated reactors\\n** Heavy-water reactors (Used in Canada, India, Argentina, China, Pakistan, Romania and South Korea). )\\n** Light-water-moderated reactors (LWRs). Light-water reactors (the most common type of thermal reactor) use ordinary water to moderate and cool the reactors. When at operating temperature, if the temperature of the water increases, its density drops, and fewer neutrons passing through it are slowed enough to trigger further reactions. That negative feedback stabilizes the reaction rate. Graphite and heavy-water reactors tend to be more thoroughly thermalized than light water reactors. Due to the extra thermalization, these types can use natural uranium/unenriched fuel.\\n* Light-element-moderated reactors.\\n** Molten salt reactors (MSRs) are moderated by light elements such as lithium or beryllium, which are constituents of the coolant/fuel matrix salts LiF and BeF2.\\n** Liquid metal cooled reactors, such as those whose coolant is a mixture of lead and bismuth, may use BeO as a moderator.\\n* Organically moderated reactors (OMR) use biphenyl and terphenyl as moderator and coolant.\",\n \"Nuclear reactor\\n\\nClassification by coolant\",\n \"Nuclear reactor\\n\\n* Water cooled reactor. There are 104 operating reactors in the United States. Of these, 69 are pressurized water reactors (PWR), and 35 are boiling water reactors (BWR). ** Pressurized water reactor (PWR) Pressurized water reactors constitute the large majority of all Western nuclear power plants. *** A primary characteristic of PWRs is a pressurizer, a specialized pressure vessel. Most commercial PWRs and naval reactors use pressurizers. During normal operation, a pressurizer is partially filled with water, and a steam bubble is maintained above it by heating the water with submerged heaters. During normal operation, the pressurizer is connected to the primary reactor pressure vessel (RPV) and the pressurizer \\\"bubble\\\" provides an expansion space for changes in water volume in the reactor. This arrangement also provides a means of pressure control for the reactor by increasing or decreasing the steam pressure in the pressurizer using the pressurizer heaters. *** Pressurised heavy water reactors are a subset of pressurized water reactors, sharing the use of a pressurized, isolated heat transport loop, but using heavy water as coolant and moderator for the greater neutron economies it offers.\",\n \"Nuclear reactor\\n\\n** Boiling water reactor (BWR)\\n*** BWRs are characterized by boiling water around the fuel rods in the lower portion of a primary reactor pressure vessel. A boiling water reactor uses 235U, enriched as uranium dioxide, as its fuel. The fuel is assembled into rods housed in a steel vessel that is submerged in water. The nuclear fission causes the water to boil, generating steam. This steam flows through pipes into turbines. The turbines are driven by the steam, and this process generates electricity. During normal operation, pressure is controlled by the amount of steam flowing from the reactor pressure vessel to the turbine. ** Pool-type reactor\\n* Liquid metal cooled reactor. Since water is a moderator, it cannot be used as a coolant in a fast reactor. Liquid metal coolants have included sodium, NaK, lead, lead-bismuth eutectic, and in early reactors, mercury. ** Sodium-cooled fast reactor\\n** Lead-cooled fast reactor\\n* Gas cooled reactors are cooled by a circulating inert gas, often helium in high-temperature designs, while carbon dioxide has been used in past British and French nuclear power plants. Nitrogen has also been used. Utilization of the heat varies, depending on the reactor.\",\n \"Nuclear reactor\\n\\nSome reactors run hot enough that the gas can directly power a gas turbine. Older designs usually run the gas through a heat exchanger to make steam for a steam turbine. * Molten salt reactors (MSRs) are cooled by circulating a molten salt, typically a eutectic mixture of fluoride salts, such as FLiBe. In a typical MSR, the coolant is also used as a matrix in which the fissile material is dissolved.\",\n \"Nuclear reactor\\n\\nClassification by generation\",\n \"Nuclear reactor\\n\\n* Generation I reactor (early prototypes, research reactors, non-commercial power producing reactors)\\n* Generation II reactor (most current nuclear power plants 1965–1996)\\n* Generation III reactor (evolutionary improvements of existing designs 1996-now)\\n* Generation IV reactor (technologies still under development unknown start date, possibly 2030)\",\n \"Nuclear reactor\\n\\nIn 2003, the French Commissariat à l'Énergie Atomique (CEA) was the first to refer to \\\"Gen II\\\" types in Nucleonics Week.\",\n \"Nuclear reactor\\n\\nThe first mentioning of \\\"Gen III\\\" was in 2000, in conjunction with the launch of the Generation IV International Forum (GIF) plans.\",\n \"Nuclear reactor\\n\\n\\\"Gen IV\\\" was named in 2000, by the United States Department of Energy (DOE) for developing new plant types.\",\n \"Nuclear reactor\\n\\nClassification by phase of fuel\",\n \"Nuclear reactor\\n\\n* Solid fueled\\n* Fluid fueled\\n** Aqueous homogeneous reactor\\n** Molten salt reactor\\n* Gas fueled (theoretical)\",\n \"Nuclear reactor\\n\\nClassification by use\",\n \"Nuclear reactor\\n\\n* Electricity\\n** Nuclear power plants including small modular reactors\\n* Propulsion, see nuclear propulsion\\n** Nuclear marine propulsion\\n** Various proposed forms of rocket propulsion\\n* Other uses of heat\\n** Desalination\\n** Heat for domestic and industrial heating\\n** Hydrogen production for use in a hydrogen economy\\n* Production reactors for transmutation of elements\\n** Breeder reactors are capable of producing more fissile material than they consume during the fission chain reaction (by converting fertile U-238 to Pu-239, or Th-232 to U-233). Thus, a uranium breeder reactor, once running, can be re-fueled with natural or even depleted uranium, and a thorium breeder reactor can be re-fueled with thorium; however, an initial stock of fissile material is required. ** Creating various radioactive isotopes, such as americium for use in smoke detectors, and cobalt-60, molybdenum-99 and others, used for imaging and medical treatment. ** Production of materials for nuclear weapons such as weapons-grade plutonium\\n* Providing a source of neutron radiation (for example with the pulsed Godiva device) and positron radiation (e.g.\",\n \"Nuclear reactor\\n\\nneutron activation analysis and potassium-argon dating)\\n* Research reactor: Typically reactors used for research and training, materials testing, or the production of radioisotopes for medicine and industry. These are much smaller than power reactors or those propelling ships, and many are on university campuses. There are about 280 such reactors operating, in 56 countries. Some operate with high-enriched uranium fuel, and international efforts are underway to substitute low-enriched fuel.\",\n \"Nuclear reactor\\n\\nCurrent technologies\",\n \"Nuclear reactor\\n\\n;; Pressurized water reactors (PWR)\\n: These reactors use a pressure vessel to contain the nuclear fuel, control rods, moderator, and coolant. They are cooled and moderated by high-pressure liquid water. The hot radioactive water that leaves the pressure vessel is looped through a steam generator, which in turn heats a secondary (non-radioactive) loop of water to steam that can run turbines. They are the majority of current reactors. This is a thermal neutron reactor design, the newest of which are the VVER-1200, Advanced Pressurized Water Reactor and the European Pressurized Reactor. United States Naval reactors are of this type. ;; Boiling water reactors (BWR)\\n: A BWR is like a PWR without the steam generator. A boiling water reactor is cooled and moderated by water like a PWR, but at a lower pressure, which allows the water to boil inside the pressure vessel producing the steam that runs the turbines. Unlike a PWR, there is no primary and secondary loop. The thermal efficiency of these reactors can be higher, and they can be simpler, and even potentially more stable and safe.\",\n \"Nuclear reactor\\n\\nThis is a thermal neutron reactor design, the newest of which are the Advanced Boiling Water Reactor and the Economic Simplified Boiling Water Reactor.\",\n \"Nuclear reactor\\n\\n;; Pressurized Heavy Water Reactor (PHWR)\\n: A Canadian design (known as CANDU), these reactors are heavy-water-cooled and -moderated pressurized-water reactors. Instead of using a single large pressure vessel as in a PWR, the fuel is contained in hundreds of pressure tubes. These reactors are fueled with natural uranium and are thermal neutron reactor designs. PHWRs can be refueled while at full power, which makes them very efficient in their use of uranium (it allows for precise flux control in the core). CANDU PHWRs have been built in Canada, Argentina, China, India, Pakistan, Romania, and South Korea. India also operates a number of PHWRs, often termed 'CANDU-derivatives', built after the Government of Canada halted nuclear dealings with India following the 1974 Smiling Buddha nuclear weapon test. ;; Reaktor Bolshoy Moschnosti Kanalniy (High Power Channel Reactor) (RBMK)\\n: A Soviet design, built to produce plutonium as well as power. RBMKs are water cooled with a graphite moderator. RBMKs are in some respects similar to CANDU in that they are refuelable during power operation and employ a pressure tube design instead of a PWR-style pressure vessel. However, unlike CANDU they are very unstable and large, making containment buildings for them expensive.\",\n \"Nuclear reactor\\n\\nA series of critical safety flaws have also been identified with the RBMK design, though some of these were corrected following the Chernobyl disaster. Their main attraction is their use of light water and un-enriched uranium. As of 2010, 11 remain open, mostly due to safety improvements and help from international safety agencies such as the DOE. Despite these safety improvements, RBMK reactors are still considered one of the most dangerous reactor designs in use. RBMK reactors were deployed only in the former Soviet Union.\",\n \"Nuclear reactor\\n\\n;; Gas-cooled reactor (GCR) and advanced gas-cooled reactor (AGR)\\n: These are generally graphite moderated and CO2 cooled. They can have a high thermal efficiency compared with PWRs due to higher operating temperatures. There are a number of operating reactors of this design, mostly in the United Kingdom, where the concept was developed. Older designs (i.e. Magnox stations) are either shut down or will be in the near future. However, the AGCRs have an anticipated life of a further 10 to 20 years. This is a thermal neutron reactor design. Decommissioning costs can be high due to large volume of reactor core. ;; Liquid-metal fast-breeder reactor (LMFBR)\\n: This is a reactor design that is cooled by liquid metal, totally unmoderated, and produces more fuel than it consumes. They are said to \\\"breed\\\" fuel, because they produce fissionable fuel during operation because of neutron capture. These reactors can function much like a PWR in terms of efficiency, and do not require much high-pressure containment, as the liquid metal does not need to be kept at high pressure, even at very high temperatures.\",\n \"Nuclear reactor\\n\\nBN-350 and BN-600 in USSR and Superphénix in France were a reactor of this type, as was Fermi-I in the United States. The Monju reactor in Japan suffered a sodium leak in 1995 and was restarted in May 2010. All of them use/used liquid sodium. These reactors are fast neutron, not thermal neutron designs. These reactors come in two types:\",\n \"Nuclear reactor\\n\\n:: Lead-cooled\\n::: Using lead as the liquid metal provides excellent radiation shielding, and allows for operation at very high temperatures. Also, lead is (mostly) transparent to neutrons, so fewer neutrons are lost in the coolant, and the coolant does not become radioactive. Unlike sodium, lead is mostly inert, so there is less risk of explosion or accident, but such large quantities of lead may be problematic from toxicology and disposal points of view. Often a reactor of this type would use a lead-bismuth eutectic mixture. In this case, the bismuth would present some minor radiation problems, as it is not quite as transparent to neutrons, and can be transmuted to a radioactive isotope more readily than lead. The Russian Alfa class submarine uses a lead-bismuth-cooled fast reactor as its main power plant. :: Sodium-cooled\\n::: Most LMFBRs are of this type. The sodium is relatively easy to obtain and work with, and it also manages to actually prevent corrosion on the various reactor parts immersed in it.\",\n \"Nuclear reactor\\n\\nHowever, sodium explodes violently when exposed to water, so care must be taken, but such explosions would not be vastly more violent than (for example) a leak of superheated fluid from a SCWR or PWR. EBR-I, the first reactor to have a core meltdown, was of this type. ;; Pebble-bed reactors (PBR)\\n: These use fuel molded into ceramic balls, and then circulate gas through the balls. The result is an efficient, low-maintenance, very safe reactor with inexpensive, standardized fuel. The prototype was the AVR. ;; Molten salt reactors\\n:These dissolve the fuels in fluoride salts, or use fluoride salts for coolant. These have many safety features, high efficiency and a high power density suitable for vehicles. Notably, they have no high pressures or flammable components in the core. The prototype was the MSRE, which also used the Thorium fuel cycle. As a breeder reactor type, it reprocesses the spent fuel, extracting both Uranium and transuranics, leaving only 0.1% of transuranic waste compared to conventional once-through uranium-fueled light water reactors currently in use. A separate issue are the radioactive fission products, which are not reprocessable and need to be disposed of as with conventional reactors.\",\n \"Nuclear reactor\\n\\n;; Aqueous Homogeneous Reactor (AHR)\\n: These reactors use soluble nuclear salts dissolved in water and mixed with a coolant and a neutron moderator.\",\n \"Nuclear reactor\\n\\nFuture and developing technologies\",\n \"Nuclear reactor\\n\\nAdvanced reactors\",\n \"Nuclear reactor\\n\\nMore than a dozen advanced reactor designs are in various stages of development. Some are evolutionary from the PWR, BWR and PHWR designs above, some are more radical departures. The former include the advanced boiling water reactor (ABWR), two of which are now operating with others under construction, and the planned passively safe Economic Simplified Boiling Water Reactor (ESBWR) and AP1000 units (see Nuclear Power 2010 Program). * The Integral Fast Reactor (IFR) was built, tested and evaluated during the 1980s and then retired under the Clinton administration in the 1990s due to nuclear non-proliferation policies of the administration. Recycling spent fuel is the core of its design and it therefore produces only a fraction of the waste of current reactors. * The pebble-bed reactor, a high-temperature gas-cooled reactor (HTGCR), is designed so high temperatures reduce power output by Doppler broadening of the fuel's neutron cross-section. It uses ceramic fuels so its safe operating temperatures exceed the power-reduction temperature range. Most designs are cooled by inert helium. Helium is not subject to steam explosions, resists neutron absorption leading to radioactivity, and does not dissolve contaminants that can become radioactive.\",\n \"Nuclear reactor\\n\\nTypical designs have more layers (up to 7) of passive containment than light water reactors (usually 3). A unique feature that may aid safety is that the fuel-balls actually form the core's mechanism, and are replaced one-by-one as they age. The design of the fuel makes fuel reprocessing expensive. * The Small, sealed, transportable, autonomous reactor (SSTAR) is being primarily researched and developed in the US, intended as a fast breeder reactor that is passively safe and could be remotely shut down in case the suspicion arises that it is being tampered with. * The Clean And Environmentally Safe Advanced Reactor (CAESAR) is a nuclear reactor concept that uses steam as a moderator – this design is still in development. * The Reduced moderation water reactor builds upon the Advanced boiling water reactor(ABWR) that is presently in use, it is not a complete fast reactor instead using mostly epithermal neutrons, which are between thermal and fast neutrons in speed. * The hydrogen-moderated self-regulating nuclear power module (HPM) is a reactor design emanating from the Los Alamos National Laboratory that uses uranium hydride as fuel.\",\n \"Nuclear reactor\\n\\n* Subcritical reactors are designed to be safer and more stable, but pose a number of engineering and economic difficulties. One example is the Energy amplifier. * Thorium-based reactors. It is possible to convert Thorium-232 into U-233 in reactors specially designed for the purpose. In this way, thorium, which is four times more abundant than uranium, can be used to breed U-233 nuclear fuel. U-233 is also believed to have favourable nuclear properties as compared to traditionally used U-235, including better neutron economy and lower production of long lived transuranic waste. ** Advanced heavy-water reactor (AHWR)— A proposed heavy water moderated nuclear power reactor that will be the next generation design of the PHWR type. Under development in the Bhabha Atomic Research Centre (BARC), India. ** KAMINI — A unique reactor using Uranium-233 isotope for fuel. Built in India by BARC and Indira Gandhi Center for Atomic Research (IGCAR). ** India is also planning to build fast breeder reactors using the thorium – Uranium-233 fuel cycle. The FBTR (Fast Breeder Test Reactor) in operation at Kalpakkam (India) uses Plutonium as a fuel and liquid sodium as a coolant.\",\n \"Nuclear reactor\\n\\nGeneration IV reactors\",\n \"Nuclear reactor\\n\\nGeneration IV reactors are a set of theoretical nuclear reactor designs currently being researched. These designs are generally not expected to be available for commercial construction before 2030. Current reactors in operation around the world are generally considered second- or third-generation systems, with the first-generation systems having been retired some time ago. Research into these reactor types was officially started by the Generation IV International Forum (GIF) based on eight technology goals. The primary goals being to improve nuclear safety, improve proliferation resistance, minimize waste and natural resource utilization, and to decrease the cost to build and run such plants. \\n* Gas-cooled fast reactor\\n* Lead-cooled fast reactor\\n* Molten salt reactor\\n* Sodium-cooled fast reactor\\n* Supercritical water reactor\\n* Very-high-temperature reactor\",\n \"Nuclear reactor\\n\\nGeneration V+ reactors\",\n \"Nuclear reactor\\n\\nGeneration V reactors are designs which are theoretically possible, but which are not being actively considered or researched at present. Though such reactors could be built with current or near term technology, they trigger little interest for reasons of economics, practicality, or safety. * Liquid-core reactor. A closed loop liquid-core nuclear reactor, where the fissile material is molten uranium or uranium solution cooled by a working gas pumped in through holes in the base of the containment vessel. * Gas-core reactor. A closed loop version of the nuclear lightbulb rocket, where the fissile material is gaseous uranium-hexafluoride contained in a fused silica vessel. A working gas (such as hydrogen) would flow around this vessel and absorb the UV light produced by the reaction. This reactor design could also function as a rocket engine, as featured in Harry Harrison's 1976 science-fiction novel 'Skyfall'. In theory, using UF6 as a working fuel directly (rather than as a stage to one, as is done now) would mean lower processing costs, and very small reactors.\",\n \"Nuclear reactor\\n\\nIn practice, running a reactor at such high power densities would probably produce unmanageable neutron flux, weakening most reactor materials, and therefore as the flux would be similar to that expected in fusion reactors, it would require similar materials to those selected by the International Fusion Materials Irradiation Facility. ** Gas core EM reactor. As in the gas core reactor, but with photovoltaic arrays converting the UV light directly to electricity. * Fission fragment reactor\\n* Hybrid nuclear fusion. Would use the neutrons emitted by fusion to fission a blanket of fertile material, like U-238 or Th-232 and transmutate other reactor's spent nuclear fuel/nuclear waste into relatively more benign isotopes.\",\n \"Nuclear reactor\\n\\nFusion reactors\",\n \"Nuclear reactor\\n\\nControlled nuclear fusion could in principle be used in fusion power plants to produce power without the complexities of handling actinides, but significant scientific and technical obstacles remain. Several fusion reactors have been built, but only recently reactors have been able to release more energy than the amount of energy used in the process. Despite research having started in the 1950s, no commercial fusion reactor is expected before 2050. The ITER project is currently leading the effort to harness fusion power.\",\n \"Nuclear reactor\\n\\nNuclear fuel cycle\",\n \"Nuclear reactor\\n\\nThermal reactors generally depend on refined and enriched uranium. Some nuclear reactors can operate with a mixture of plutonium and uranium (see MOX). The process by which uranium ore is mined, processed, enriched, used, possibly reprocessed and disposed of is known as the nuclear fuel cycle.\",\n \"Nuclear reactor\\n\\nUnder 1% of the uranium found in nature is the easily fissionable U-235 isotope and as a result most reactor designs require enriched fuel.\\nEnrichment involves increasing the percentage of U-235 and is usually done by means of gaseous diffusion or gas centrifuge. The enriched result is then converted into uranium dioxide powder, which is pressed and fired into pellet form. These pellets are stacked into tubes which are then sealed and called fuel rods. Many of these fuel rods are used in each nuclear reactor.\",\n \"Nuclear reactor\\n\\nMost BWR and PWR commercial reactors use uranium enriched to about 4% U-235, and some commercial reactors with a high neutron economy do not require the fuel to be enriched at all (that is, they can use natural uranium). According to the International Atomic Energy Agency there are at least 100 research reactors in the world fueled by highly enriched (weapons-grade/90% enrichment uranium). Theft risk of this fuel (potentially used in the production of a nuclear weapon) has led to campaigns advocating conversion of this type of reactor to low-enrichment uranium (which poses less threat of proliferation).\",\n \"Nuclear reactor\\n\\nFissile U-235 and non-fissile but fissionable and fertile U-238 are both used in the fission process. U-235 is fissionable by thermal (i.e. slow-moving) neutrons. A thermal neutron is one which is moving about the same speed as the atoms around it. Since all atoms vibrate proportionally to their absolute temperature, a thermal neutron has the best opportunity to fission U-235 when it is moving at this same vibrational speed. On the other hand, U-238 is more likely to capture a neutron when the neutron is moving very fast. This U-239 atom will soon decay into plutonium-239, which is another fuel. Pu-239 is a viable fuel and must be accounted for even when a highly enriched uranium fuel is used. Plutonium fissions will dominate the U-235 fissions in some reactors, especially after the initial loading of U-235 is spent. Plutonium is fissionable with both fast and thermal neutrons, which make it ideal for either nuclear reactors or nuclear bombs.\",\n \"Nuclear reactor\\n\\nMost reactor designs in existence are thermal reactors and typically use water as a neutron moderator (moderator means that it slows down the neutron to a thermal speed) and as a coolant. But in a fast breeder reactor, some other kind of coolant is used which will not moderate or slow the neutrons down much. This enables fast neutrons to dominate, which can effectively be used to constantly replenish the fuel supply. By merely placing cheap unenriched uranium into such a core, the non-fissionable U-238 will be turned into Pu-239, \\\"breeding\\\" fuel.\",\n \"Nuclear reactor\\n\\nIn thorium fuel cycle thorium-232 absorbs a neutron in either a fast or thermal reactor. The thorium-233 beta decays to protactinium-233 and then to uranium-233, which in turn is used as fuel. Hence, like uranium-238, thorium-232 is a fertile material.\",\n \"Nuclear reactor\\n\\nFueling of nuclear reactors\",\n \"Nuclear reactor\\n\\nThe amount of energy in the reservoir of nuclear fuel is frequently expressed in terms of \\\"full-power days,\\\" which is the number of 24-hour periods (days) a reactor is scheduled for operation at full power output for the generation of heat energy. The number of full-power days in a reactor's operating cycle (between refueling outage times) is related to the amount of fissile uranium-235 (U-235) contained in the fuel assemblies at the beginning of the cycle. A higher percentage of U-235 in the core at the beginning of a cycle will permit the reactor to be run for a greater number of full-power days.\",\n \"Nuclear reactor\\n\\nAt the end of the operating cycle, the fuel in some of the assemblies is \\\"spent\\\" and is discharged and replaced with new (fresh) fuel assemblies, although in practice it is the buildup of reaction poisons in nuclear fuel that determines the lifetime of nuclear fuel in a reactor. Long before all possible fission has taken place, the buildup of long-lived neutron absorbing fission byproducts impedes the chain reaction. The fraction of the reactor's fuel core replaced during refueling is typically one-fourth for a boiling-water reactor and one-third for a pressurized-water reactor. The disposition and storage of this spent fuel is one of the most challenging aspects of the operation of a commercial nuclear power plant. This nuclear waste is highly radioactive and its toxicity presents a danger for thousands of years.\",\n \"Nuclear reactor\\n\\nNot all reactors need to be shut down for refueling; for example, pebble bed reactors, RBMK reactors, molten salt reactors, Magnox, AGR and CANDU reactors allow fuel to be shifted through the reactor while it is running. In a CANDU reactor, this also allows individual fuel elements to be situated within the reactor core that are best suited to the amount of U-235 in the fuel element.\",\n \"Nuclear reactor\\n\\nThe amount of energy extracted from nuclear fuel is called its burnup, which is expressed in terms of the heat energy produced per initial unit of fuel weight. Burn up is commonly expressed as megawatt days thermal per metric ton of initial heavy metal.\",\n \"Nuclear reactor\\n\\nSafety\",\n \"Nuclear reactor\\n\\nNuclear safety covers the actions taken to prevent nuclear and radiation accidents or to limit their consequences. The nuclear power industry has improved the safety and performance of reactors, and has proposed new safer (but generally untested) reactor designs but there is no guarantee that the reactors will be designed, built and operated correctly. Mistakes do occur and the designers of reactors at Fukushima in Japan did not anticipate that a tsunami generated by an earthquake would disable the backup systems that were supposed to stabilize the reactor after the earthquake, despite multiple warnings by the NRG and the Japanese nuclear safety administration. According to UBS AG, the Fukushima I nuclear accidents have cast doubt on whether even an advanced economy like Japan can master nuclear safety. Catastrophic scenarios involving terrorist attacks are also conceivable. An interdisciplinary team from MIT has estimated that given the expected growth of nuclear power from 2005–2055, at least four serious nuclear accidents would be expected in that period.\",\n \"Nuclear reactor\\n\\nAccidents\",\n \"Nuclear reactor\\n\\nSome serious nuclear and radiation accidents have occurred. Nuclear power plant accidents include the SL-1 accident (1961), the Three Mile Island accident (1979), Chernobyl disaster (1986), and the Fukushima Daiichi nuclear disaster (2011). Nuclear-powered submarine mishaps include the K-19 reactor accident (1961),[http://www.iaea.org/Publications/Magazines/Bulletin/Bull413/article1.pdf Strengthening the Safety of Radiation Sources] p. 14. the K-27 reactor accident (1968), and the K-431 reactor accident (1985).[http://www.time.com/time/photogallery/0,29307,1887705,00.html The Worst Nuclear Disasters]. Time.\",\n \"Nuclear reactor\\n\\nNuclear reactors have been launched into Earth orbit at least 34 times. A number of incidents connected with the unmanned nuclear-reactor-powered Soviet RORSAT radar satellite program resulted in spent nuclear fuel re-entering the Earth's atmosphere from orbit.\",\n \"Nuclear reactor\\n\\nNatural nuclear reactors\",\n \"Nuclear reactor\\n\\nAlthough nuclear fission reactors are often thought of as being solely a product of modern technology, the first nuclear fission reactors were in fact naturally occurring. A natural nuclear fission reactor can occur under certain circumstances that mimic the conditions in a constructed reactor. Fifteen natural fission reactors have so far been found in three separate ore deposits at the Oklo uranium mine in Gabon, West Africa. First discovered in 1972 by French physicist Francis Perrin, they are collectively known as the Oklo Fossil Reactors. Self-sustaining nuclear fission reactions took place in these reactors approximately 1.5 billion years ago, and ran for a few hundred thousand years, averaging 100 kW of power output during that time. The concept of a natural nuclear reactor was theorized as early as 1956 by Paul Kuroda at the University of Arkansas.\",\n \"Nuclear reactor\\n\\nSuch reactors can no longer form on Earth: radioactive decay over this immense time span has reduced the proportion of U-235 in naturally occurring uranium to below the amount required to sustain a chain reaction.\",\n \"Nuclear reactor\\n\\nThe natural nuclear reactors formed when a uranium-rich mineral deposit became inundated with groundwater that acted as a neutron moderator, and a strong chain reaction took place. The water moderator would boil away as the reaction increased, slowing it back down again and preventing a meltdown. The fission reaction was sustained for hundreds of thousands of years.\",\n \"Nuclear reactor\\n\\nThese natural reactors are extensively studied by scientists interested in geologic radioactive waste disposal. They offer a case study of how radioactive isotopes migrate through the Earth's crust. This is a significant area of controversy as opponents of geologic waste disposal fear that isotopes from stored waste could end up in water supplies or be carried into the environment.\"\n]","isConversational":false}}},{"rowIdx":1798,"cells":{"id":{"kind":"string","value":"tc_2775"},"question":{"kind":"string","value":"Which electronic device magnifies the strength of a signal?"},"answer":{"kind":"string","value":"Amplifier"},"answer_aliases":{"kind":"list like","value":["common plate","class c amplifier","power amplifier","penguat peralatan","electronic amplifier","class b amplifier","class ab","amplifier stage","piezo audio amplifier","common cathode","single stage amplifier","class amplifier","class ab amplifier","common grid","piezoelectric audio amplifier","class ab amplifiers","class e amplifier","cathode follower","amplifier class","current amplifier","amplifiers","amplifier","voltage amplifier"],"string":"[\n \"common plate\",\n \"class c amplifier\",\n \"power amplifier\",\n \"penguat peralatan\",\n \"electronic amplifier\",\n \"class b amplifier\",\n \"class ab\",\n \"amplifier stage\",\n \"piezo audio amplifier\",\n \"common cathode\",\n \"single stage amplifier\",\n \"class amplifier\",\n \"class ab amplifier\",\n \"common grid\",\n \"piezoelectric audio amplifier\",\n \"class ab amplifiers\",\n \"class e amplifier\",\n \"cathode follower\",\n \"amplifier class\",\n \"current amplifier\",\n \"amplifiers\",\n \"amplifier\",\n \"voltage amplifier\"\n]","isConversational":false},"documents":{"kind":"list like","value":["Electronics\n\nElectronics is the science of how to control electric energy, energy in which the electrons have a fundamental role. Electronics deals with electrical circuits that involve active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive electrical components and interconnection technologies. Commonly, electronic devices contain circuitry consisting primarily or exclusively of active semiconductors supplemented with passive elements; such a circuit is described as an electronic circuit.","Electronics\n\nThe nonlinear behaviour of active components and their ability to control electron flows makes amplification of weak signals possible, and electronics is widely used in information processing, telecommunication, and signal processing. The ability of electronic devices to act as switches makes digital information processing possible. Interconnection technologies such as circuit boards, electronics packaging technology, and other varied forms of communication infrastructure complete circuit functionality and transform the mixed components into a regular working system.","Electronics\n\nElectronics is distinct from electrical and electro-mechanical science and technology, which deal with the generation, distribution, switching, storage, and conversion of electrical energy to and from other energy forms using wires, motors, generators, batteries, switches, relays, transformers, resistors, and other passive components. This distinction started around 1906 with the invention by Lee De Forest of the triode, which made electrical amplification of weak radio signals and audio signals possible with a non-mechanical device. Until 1950 this field was called \"radio technology\" because its principal application was the design and theory of radio transmitters, receivers, and vacuum tubes.","Electronics\n\nToday, most electronic devices use semiconductor components to perform electron control. The study of semiconductor devices and related technology is considered a branch of solid-state physics, whereas the design and construction of electronic circuits to solve practical problems come under electronics engineering. This article focuses on engineering aspects of electronics.","Electronics\n\nBranches of electronics","Electronics\n\nElectronics has branches as follows:","Electronics\n\n#Digital electronics\n#Analogue electronics\n#Microelectronics\n#Circuit design\n#Integrated circuits\n#Optoelectronics\n#Semiconductor devices\n#Embedded systems","Electronics\n\nElectronic devices and components","Electronics\n\nAn electronic component is any physical entity in an electronic system used to affect the electrons or their associated fields in a manner consistent with the intended function of the electronic system. Components are generally intended to be connected together, usually by being soldered to a printed circuit board (PCB), to create an electronic circuit with a particular function (for example an amplifier, radio receiver, or oscillator). Components may be packaged singly, or in more complex groups as integrated circuits. Some common electronic components are capacitors, inductors, resistors, diodes, transistors, etc. Components are often categorized as active (e.g. transistors and thyristors) or passive (e.g. resistors, diodes, inductors and capacitors).","Electronics\n\nHistory of electronic components","Electronics\n\nVacuum tubes (Thermionic valves) were one of the earliest electronic components. They were almost solely responsible for the electronics revolution of the first half of the Twentieth Century. They took electronics from parlor tricks and gave us radio, television, phonographs, radar, long distance telephony and much more. They played a leading role in the field of microwave and high power transmission as well as television receivers until the middle of the 1980s. Since that time, solid state devices have all but completely taken over. Vacuum tubes are still used in some specialist applications such as high power RF amplifiers, cathode ray tubes, specialist audio equipment, guitar amplifiers and some microwave devices.","Electronics\n\nIn April 1955 the IBM 608 was the first IBM product to use transistor circuits without any vacuum tubes and is believed to be the world's first all-transistorized calculator to be manufactured for the commercial market. The 608 contained more than 3,000 germanium transistors. Thomas J. Watson Jr. ordered all future IBM products to use transistors in their design. From that time on transistors were almost exclusively used for computer logic and peripherals.","Electronics\n\nTypes of circuits","Electronics\n\nCircuits and components can be divided into two groups: analog and digital. A particular device may consist of circuitry that has one or the other or a mix of the two types.","Electronics\n\nAnalog circuits","Electronics\n\nMost analog electronic appliances, such as radio receivers, are constructed from combinations of a few types of basic circuits. Analog circuits use a continuous range of voltage or current as opposed to discrete levels as in digital circuits.","Electronics\n\nThe number of different analog circuits so far devised is huge, especially because a 'circuit' can be defined as anything from a single component, to systems containing thousands of components.","Electronics\n\nAnalog circuits are sometimes called linear circuits although many non-linear effects are used in analog circuits such as mixers, modulators, etc. Good examples of analog circuits include vacuum tube and transistor amplifiers, operational amplifiers and oscillators.","Electronics\n\nOne rarely finds modern circuits that are entirely analog. These days analog circuitry may use digital or even microprocessor techniques to improve performance. This type of circuit is usually called \"mixed signal\" rather than analog or digital.","Electronics\n\nSometimes it may be difficult to differentiate between analog and digital circuits as they have elements of both linear and non-linear operation. An example is the comparator which takes in a continuous range of voltage but only outputs one of two levels as in a digital circuit. Similarly, an overdriven transistor amplifier can take on the characteristics of a controlled switch having essentially two levels of output. In fact, many digital circuits are actually implemented as variations of analog circuits similar to this example—after all, all aspects of the real physical world are essentially analog, so digital effects are only realized by constraining analog behavior.","Electronics\n\nDigital circuits","Electronics\n\nDigital circuits are electric circuits based on a number of discrete voltage levels. Digital circuits are the most common physical representation of Boolean algebra, and are the basis of all digital computers. To most engineers, the terms \"digital circuit\", \"digital system\" and \"logic\" are interchangeable in the context of digital circuits.\nMost digital circuits use a binary system with two voltage levels labeled \"0\" and \"1\". Often logic \"0\" will be a lower voltage and referred to as \"Low\" while logic \"1\" is referred to as \"High\". However, some systems use the reverse definition (\"0\" is \"High\") or are current based. Quite often the logic designer may reverse these definitions from one circuit to the next as he sees fit to facilitate his design. The definition of the levels as \"0\" or \"1\" is arbitrary.","Electronics\n\nTernary (with three states) logic has been studied, and some prototype computers made.","Electronics\n\nComputers, electronic clocks, and programmable logic controllers (used to control industrial processes) are constructed of digital circuits. Digital signal processors are another example.","Electronics\n\nBuilding blocks:\n* Logic gates\n* Adders\n* Flip-flops\n* Counters\n* Registers\n* Multiplexers\n* Schmitt triggers","Electronics\n\nHighly integrated devices:\n* Microprocessors\n* Microcontrollers\n* Application-specific integrated circuit (ASIC)\n* Digital signal processor (DSP)\n* Field-programmable gate array (FPGA)","Electronics\n\nHeat dissipation and thermal management","Electronics\n\nHeat generated by electronic circuitry must be dissipated to prevent immediate failure and improve long term reliability. Heat dissipation is mostly achieved by passive conduction/convection. Means to achieve greater dissipation include heat sinks and fans for air cooling, and other forms of computer cooling such as water cooling. These techniques use convection, conduction, and radiation of heat energy.","Electronics\n\nNoise","Electronics\n\nElectronic noise is defined as unwanted disturbances superposed on a useful signal that tend to obscure its information content. Noise is not the same as signal distortion caused by a circuit. Noise is associated with all electronic circuits. Noise may be electromagnetically or thermally generated, which can be decreased by lowering the operating temperature of the circuit. Other types of noise, such as shot noise cannot be removed as they are due to limitations in physical properties.","Electronics\n\nElectronics theory","Electronics\n\nMathematical methods are integral to the study of electronics. To become proficient in electronics it is also necessary to become proficient in the mathematics of circuit analysis.","Electronics\n\nCircuit analysis is the study of methods of solving generally linear systems for unknown variables such as the voltage at a certain node or the current through a certain branch of a network. A common analytical tool for this is the SPICE circuit simulator.","Electronics\n\nAlso important to electronics is the study and understanding of electromagnetic field theory.","Electronics\n\nElectronics lab","Electronics\n\nDue to the complex nature of electronics theory, laboratory experimentation is an important part of the development of electronic devices. These experiments are used to test or verify the engineer’s design and detect errors. Historically, electronics labs have consisted of electronics devices and equipment located in a physical space, although in more recent years the trend has been towards electronics lab simulation software, such as CircuitLogix, Multisim, and PSpice.","Electronics\n\nComputer aided design (CAD)","Electronics\n\nToday's electronics engineers have the ability to design circuits using premanufactured building blocks such as power supplies, semiconductors (i.e. semiconductor devices, such as transistors), and integrated circuits. Electronic design automation software programs include schematic capture programs and printed circuit board design programs. Popular names in the EDA software world are NI Multisim, Cadence (ORCAD), EAGLE PCB and Schematic, Mentor (PADS PCB and LOGIC Schematic), Altium (Protel), LabCentre Electronics (Proteus), gEDA, KiCad and many others.","Electronics\n\nConstruction methods","Electronics\n\nMany different methods of connecting components have been used over the years. For instance, early electronics often used point to point wiring with components attached to wooden breadboards to construct circuits. Cordwood construction and wire wrap were other methods used. Most modern day electronics now use printed circuit boards made of materials such as FR4, or the cheaper (and less hard-wearing) Synthetic Resin Bonded Paper (SRBP, also known as Paxoline/Paxolin (trade marks) and FR2) - characterised by its brown colour. Health and environmental concerns associated with electronics assembly have gained increased attention in recent years, especially for products destined to the European Union, with its Restriction of Hazardous Substances Directive (RoHS) and Waste Electrical and Electronic Equipment Directive (WEEE), which went into force in July 2006.","Electronics\n\nDegradation","Electronics\n\nRasberry crazy ants have been known to consume the insides of electrical wiring, and nest inside of electronics; they prefer DC to AC currents. This behavior is not well understood by scientists."],"string":"[\n \"Electronics\\n\\nElectronics is the science of how to control electric energy, energy in which the electrons have a fundamental role. Electronics deals with electrical circuits that involve active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive electrical components and interconnection technologies. Commonly, electronic devices contain circuitry consisting primarily or exclusively of active semiconductors supplemented with passive elements; such a circuit is described as an electronic circuit.\",\n \"Electronics\\n\\nThe nonlinear behaviour of active components and their ability to control electron flows makes amplification of weak signals possible, and electronics is widely used in information processing, telecommunication, and signal processing. The ability of electronic devices to act as switches makes digital information processing possible. Interconnection technologies such as circuit boards, electronics packaging technology, and other varied forms of communication infrastructure complete circuit functionality and transform the mixed components into a regular working system.\",\n \"Electronics\\n\\nElectronics is distinct from electrical and electro-mechanical science and technology, which deal with the generation, distribution, switching, storage, and conversion of electrical energy to and from other energy forms using wires, motors, generators, batteries, switches, relays, transformers, resistors, and other passive components. This distinction started around 1906 with the invention by Lee De Forest of the triode, which made electrical amplification of weak radio signals and audio signals possible with a non-mechanical device. Until 1950 this field was called \\\"radio technology\\\" because its principal application was the design and theory of radio transmitters, receivers, and vacuum tubes.\",\n \"Electronics\\n\\nToday, most electronic devices use semiconductor components to perform electron control. The study of semiconductor devices and related technology is considered a branch of solid-state physics, whereas the design and construction of electronic circuits to solve practical problems come under electronics engineering. This article focuses on engineering aspects of electronics.\",\n \"Electronics\\n\\nBranches of electronics\",\n \"Electronics\\n\\nElectronics has branches as follows:\",\n \"Electronics\\n\\n#Digital electronics\\n#Analogue electronics\\n#Microelectronics\\n#Circuit design\\n#Integrated circuits\\n#Optoelectronics\\n#Semiconductor devices\\n#Embedded systems\",\n \"Electronics\\n\\nElectronic devices and components\",\n \"Electronics\\n\\nAn electronic component is any physical entity in an electronic system used to affect the electrons or their associated fields in a manner consistent with the intended function of the electronic system. Components are generally intended to be connected together, usually by being soldered to a printed circuit board (PCB), to create an electronic circuit with a particular function (for example an amplifier, radio receiver, or oscillator). Components may be packaged singly, or in more complex groups as integrated circuits. Some common electronic components are capacitors, inductors, resistors, diodes, transistors, etc. Components are often categorized as active (e.g. transistors and thyristors) or passive (e.g. resistors, diodes, inductors and capacitors).\",\n \"Electronics\\n\\nHistory of electronic components\",\n \"Electronics\\n\\nVacuum tubes (Thermionic valves) were one of the earliest electronic components. They were almost solely responsible for the electronics revolution of the first half of the Twentieth Century. They took electronics from parlor tricks and gave us radio, television, phonographs, radar, long distance telephony and much more. They played a leading role in the field of microwave and high power transmission as well as television receivers until the middle of the 1980s. Since that time, solid state devices have all but completely taken over. Vacuum tubes are still used in some specialist applications such as high power RF amplifiers, cathode ray tubes, specialist audio equipment, guitar amplifiers and some microwave devices.\",\n \"Electronics\\n\\nIn April 1955 the IBM 608 was the first IBM product to use transistor circuits without any vacuum tubes and is believed to be the world's first all-transistorized calculator to be manufactured for the commercial market. The 608 contained more than 3,000 germanium transistors. Thomas J. Watson Jr. ordered all future IBM products to use transistors in their design. From that time on transistors were almost exclusively used for computer logic and peripherals.\",\n \"Electronics\\n\\nTypes of circuits\",\n \"Electronics\\n\\nCircuits and components can be divided into two groups: analog and digital. A particular device may consist of circuitry that has one or the other or a mix of the two types.\",\n \"Electronics\\n\\nAnalog circuits\",\n \"Electronics\\n\\nMost analog electronic appliances, such as radio receivers, are constructed from combinations of a few types of basic circuits. Analog circuits use a continuous range of voltage or current as opposed to discrete levels as in digital circuits.\",\n \"Electronics\\n\\nThe number of different analog circuits so far devised is huge, especially because a 'circuit' can be defined as anything from a single component, to systems containing thousands of components.\",\n \"Electronics\\n\\nAnalog circuits are sometimes called linear circuits although many non-linear effects are used in analog circuits such as mixers, modulators, etc. Good examples of analog circuits include vacuum tube and transistor amplifiers, operational amplifiers and oscillators.\",\n \"Electronics\\n\\nOne rarely finds modern circuits that are entirely analog. These days analog circuitry may use digital or even microprocessor techniques to improve performance. This type of circuit is usually called \\\"mixed signal\\\" rather than analog or digital.\",\n \"Electronics\\n\\nSometimes it may be difficult to differentiate between analog and digital circuits as they have elements of both linear and non-linear operation. An example is the comparator which takes in a continuous range of voltage but only outputs one of two levels as in a digital circuit. Similarly, an overdriven transistor amplifier can take on the characteristics of a controlled switch having essentially two levels of output. In fact, many digital circuits are actually implemented as variations of analog circuits similar to this example—after all, all aspects of the real physical world are essentially analog, so digital effects are only realized by constraining analog behavior.\",\n \"Electronics\\n\\nDigital circuits\",\n \"Electronics\\n\\nDigital circuits are electric circuits based on a number of discrete voltage levels. Digital circuits are the most common physical representation of Boolean algebra, and are the basis of all digital computers. To most engineers, the terms \\\"digital circuit\\\", \\\"digital system\\\" and \\\"logic\\\" are interchangeable in the context of digital circuits.\\nMost digital circuits use a binary system with two voltage levels labeled \\\"0\\\" and \\\"1\\\". Often logic \\\"0\\\" will be a lower voltage and referred to as \\\"Low\\\" while logic \\\"1\\\" is referred to as \\\"High\\\". However, some systems use the reverse definition (\\\"0\\\" is \\\"High\\\") or are current based. Quite often the logic designer may reverse these definitions from one circuit to the next as he sees fit to facilitate his design. The definition of the levels as \\\"0\\\" or \\\"1\\\" is arbitrary.\",\n \"Electronics\\n\\nTernary (with three states) logic has been studied, and some prototype computers made.\",\n \"Electronics\\n\\nComputers, electronic clocks, and programmable logic controllers (used to control industrial processes) are constructed of digital circuits. Digital signal processors are another example.\",\n \"Electronics\\n\\nBuilding blocks:\\n* Logic gates\\n* Adders\\n* Flip-flops\\n* Counters\\n* Registers\\n* Multiplexers\\n* Schmitt triggers\",\n \"Electronics\\n\\nHighly integrated devices:\\n* Microprocessors\\n* Microcontrollers\\n* Application-specific integrated circuit (ASIC)\\n* Digital signal processor (DSP)\\n* Field-programmable gate array (FPGA)\",\n \"Electronics\\n\\nHeat dissipation and thermal management\",\n \"Electronics\\n\\nHeat generated by electronic circuitry must be dissipated to prevent immediate failure and improve long term reliability. Heat dissipation is mostly achieved by passive conduction/convection. Means to achieve greater dissipation include heat sinks and fans for air cooling, and other forms of computer cooling such as water cooling. These techniques use convection, conduction, and radiation of heat energy.\",\n \"Electronics\\n\\nNoise\",\n \"Electronics\\n\\nElectronic noise is defined as unwanted disturbances superposed on a useful signal that tend to obscure its information content. Noise is not the same as signal distortion caused by a circuit. Noise is associated with all electronic circuits. Noise may be electromagnetically or thermally generated, which can be decreased by lowering the operating temperature of the circuit. Other types of noise, such as shot noise cannot be removed as they are due to limitations in physical properties.\",\n \"Electronics\\n\\nElectronics theory\",\n \"Electronics\\n\\nMathematical methods are integral to the study of electronics. To become proficient in electronics it is also necessary to become proficient in the mathematics of circuit analysis.\",\n \"Electronics\\n\\nCircuit analysis is the study of methods of solving generally linear systems for unknown variables such as the voltage at a certain node or the current through a certain branch of a network. A common analytical tool for this is the SPICE circuit simulator.\",\n \"Electronics\\n\\nAlso important to electronics is the study and understanding of electromagnetic field theory.\",\n \"Electronics\\n\\nElectronics lab\",\n \"Electronics\\n\\nDue to the complex nature of electronics theory, laboratory experimentation is an important part of the development of electronic devices. These experiments are used to test or verify the engineer’s design and detect errors. Historically, electronics labs have consisted of electronics devices and equipment located in a physical space, although in more recent years the trend has been towards electronics lab simulation software, such as CircuitLogix, Multisim, and PSpice.\",\n \"Electronics\\n\\nComputer aided design (CAD)\",\n \"Electronics\\n\\nToday's electronics engineers have the ability to design circuits using premanufactured building blocks such as power supplies, semiconductors (i.e. semiconductor devices, such as transistors), and integrated circuits. Electronic design automation software programs include schematic capture programs and printed circuit board design programs. Popular names in the EDA software world are NI Multisim, Cadence (ORCAD), EAGLE PCB and Schematic, Mentor (PADS PCB and LOGIC Schematic), Altium (Protel), LabCentre Electronics (Proteus), gEDA, KiCad and many others.\",\n \"Electronics\\n\\nConstruction methods\",\n \"Electronics\\n\\nMany different methods of connecting components have been used over the years. For instance, early electronics often used point to point wiring with components attached to wooden breadboards to construct circuits. Cordwood construction and wire wrap were other methods used. Most modern day electronics now use printed circuit boards made of materials such as FR4, or the cheaper (and less hard-wearing) Synthetic Resin Bonded Paper (SRBP, also known as Paxoline/Paxolin (trade marks) and FR2) - characterised by its brown colour. Health and environmental concerns associated with electronics assembly have gained increased attention in recent years, especially for products destined to the European Union, with its Restriction of Hazardous Substances Directive (RoHS) and Waste Electrical and Electronic Equipment Directive (WEEE), which went into force in July 2006.\",\n \"Electronics\\n\\nDegradation\",\n \"Electronics\\n\\nRasberry crazy ants have been known to consume the insides of electrical wiring, and nest inside of electronics; they prefer DC to AC currents. This behavior is not well understood by scientists.\"\n]","isConversational":false}}},{"rowIdx":1799,"cells":{"id":{"kind":"string","value":"tc_2776"},"question":{"kind":"string","value":"What was the name of the unit of heat now replaced by the joule?"},"answer":{"kind":"string","value":"Calorie"},"answer_aliases":{"kind":"list like","value":["㎉","kcals","nutritional calories","calorific","large calorie","nutritional calorie","small calorie","thermochemical calorie","callories","calories","gigacalorie","calory","calorie nutrition","㎈","kilogram calorie","kilocalorie","gram calorie","kilocalories","thermodynamic calorie","calorie counter","callory","callorie","calorie unit","calorie","kcal","calorie per hour"],"string":"[\n \"㎉\",\n \"kcals\",\n \"nutritional calories\",\n \"calorific\",\n \"large calorie\",\n \"nutritional calorie\",\n \"small calorie\",\n \"thermochemical calorie\",\n \"callories\",\n \"calories\",\n \"gigacalorie\",\n \"calory\",\n \"calorie nutrition\",\n \"㎈\",\n \"kilogram calorie\",\n \"kilocalorie\",\n \"gram calorie\",\n \"kilocalories\",\n \"thermodynamic calorie\",\n \"calorie counter\",\n \"callory\",\n \"callorie\",\n \"calorie unit\",\n \"calorie\",\n \"kcal\",\n \"calorie per hour\"\n]","isConversational":false},"documents":{"kind":"list like","value":["Joule\n\nThe joule, symbol J, is a derived unit of energy in the International System of Units. It is equal to the energy transferred (or work done) to an object when a force of one newton acts on that object in the direction of its motion through a distance of one metre (1 newton metre or N·m). It is also the energy dissipated as heat when an electric current of one ampere passes through a resistance of one ohm for one second. It is named after the English physicist James Prescott Joule (1818–1889).","Joule\n\nIn terms firstly of base SI units and then in terms of other SI units:\n\\rm J {}\\rm \\frac{kg \\cdot m^2}{s^2} \n N \\cdot m \\rm Pa \\cdot m^3\n{}\\rm W \\cdot s = C \\cdot V","Joule\n\nwhere kg is the kilogram, m is the metre, s is the second, N is the newton, Pa is the pascal, W is the watt, C is the coulomb, and V is the volt.","Joule\n\nOne joule can also be defined as:\n* The work required to move an electric charge of one coulomb through an electrical potential difference of one volt, or one '\"coulomb volt\" (C·V). This relationship can be used to define the volt.\n* The work required to produce one watt of power for one second, or one \"watt second\" (W·s) (compare kilowatt hour - 3.6 megajoules). This relationship can be used to define the watt.","Joule\n\nUsage","Joule\n\nConfusion with newton-metre","Joule\n\nIn angular mechanics, torque is analogous to the linear Newtonian mechanics parameter of force, moment of inertia to mass, and angle to distance. Energy is the same in both systems. Thus, although the joule has the same dimensions as the newton-metre (1 J 1 N·m \n 1 kg·m2·s−2), these units are not interchangeable: the CGPM has given the unit of energy the name \"joule\", but has not given the unit of torque any special name, hence the unit of torque is known as the newton-metre (N·m) - a compound name derived from its constituent parts. Torque and energy are related to each other using the equation\nE= \\tau \\theta\\ \nwhere E is the energy, τ is the torque, and θ is the angle moved (in radians). Since radians are dimensionless, it follows that torque and energy have the same dimensions.","Joule\n\nThe use of newton-metres for torque and joules for energy is useful in helping avoid misunderstandings and miscommunications.","Joule\n\nAn additional solution is to realize that joules are scalars – they are the dot product of a vector force and a vector displacement whereas torque is a vector. Torque is the cross product of a distance vector and a force vector. Drawing a traditional vector arrow over \"newton-metre\" in a torque resolves the ambiguity.","Joule\n\nPractical examples","Joule\n\nOne joule in everyday life represents approximately:\n* The energy required to lift a medium-size tomato (100 g) 1 meter vertically from the surface of the Earth. \n* The energy released when that same tomato falls back down to the ground.\n* The energy required to accelerate a 1 kg mass at 1 m·s−2 through a 1 m distance in space.\n* The heat required to raise the temperature of 1 g of water by 0.24 K. \n* The typical energy released as heat by a person at rest every 1/60 second (approximately 17 ms). \n* The kinetic energy of a 50 kg human moving very slowly ().\n* The kinetic energy of a 56 g tennis ball moving at 6 m/s. \n* The kinetic energy of an object with mass 1 kg moving at √2 ≈ 1.4 m/s.\n* The amount of electricity required to light a 1 watt LED for 1 s.","Joule\n\nSince the joule is also a watt-second and the common unit for electricity sales to homes is the kW·h (kilowatt-hour), a kW·h is thus 1000 (kilo) watt × 3600 seconds = 3.6 megajoules (MJ).","Joule\n\nMultiples","Joule\n\nFor additional examples, see: Orders of magnitude (energy)","Joule\n\nZeptojoule","Joule\n\nThe zeptojoule (zJ) is equal to one sextillionth (10−21) of one joule. 160 zeptojoules is equivalent to one electronvolt.","Joule\n\nNanojoule","Joule\n\nThe nanojoule (nJ) is equal to one billionth (10−9) of one joule. One nanojoule is about 1/160 of the kinetic energy of a flying mosquito.","Joule\n\nMicrojoule","Joule\n\nThe microjoule (μJ) is equal to one millionth (10−6) of one joule. The Large Hadron Collider (LHC) produces collisions of the microjoule order (7 TeV) per particle.","Joule\n\nMillijoule","Joule\n\nThe millijoule (mJ) is equal to one thousandth (10−3) of a joule.","Joule\n\nKilojoule","Joule\n\nThe kilojoule (kJ) is equal to one thousand (103) joules. Nutritional food labels in some countries express energy in kilojoules (kJ).","Joule\n\nOne square metre of the Earth receives about 1.4 kilojoules of solar radiation every second in full daylight.","Joule\n\nMegajoule","Joule\n\nThe megajoule (MJ) is equal to one million (106) joules, or approximately the kinetic energy of a one megagram (tonne) vehicle moving at 160 km/h.","Joule\n\nOne kilowatt hour of electricity is 3.6 megajoules.","Joule\n\nGigajoule","Joule\n\nThe gigajoule (GJ) is equal to one billion (109) joules. 6 GJ is about the amount of potential chemical energy in 160 L (approximately one US standard barrel) of oil, when combusted.","Joule\n\nTerajoule","Joule\n\nThe terajoule (TJ) is equal to one trillion (1012) joules. About 63 TJ of energy was released by the atomic bomb that exploded over Hiroshima. The International Space Station, with a mass of approximately 450 megagrams and orbital velocity of 7.7 km/s, has a kinetic energy of roughly 13 TJ.","Joule\n\nPetajoule","Joule\n\nThe petajoule (PJ) is equal to one quadrillion (1015) joules. 210 PJ is equivalent to about 50 megatons of TNT. This is the amount of energy released by the Tsar Bomba, the largest man-made nuclear explosion ever.","Joule\n\nExajoule","Joule\n\nThe exajoule (EJ) is equal to one quintillion (1018) joules. The 2011 Tōhoku earthquake and tsunami in Japan had 1.41 EJ of energy according to its 9.0 on the moment magnitude scale. Energy in the United States used per year is roughly 94 EJ.","Joule\n\nZettajoule","Joule\n\nThe zettajoule (ZJ) is equal to one sextillion (1021) joules. The human annual global energy consumption is approximately 0.5 ZJ.","Joule\n\nYottajoule","Joule\n\nThe yottajoule (YJ) is equal to one septillion (1024) joules. This is approximately the amount of energy required to heat all the water on Earth by 1 °C. The thermal output of the Sun is approximately 400 YJ per second.","Joule\n\nConversions","Joule\n\n1 joule is equal to:\n* (exactly) \n* \n* (gram calories)\n* (food calories)\n* \n* \n* (foot-poundal)\n* \n* \n* (litre-atmosphere)\n* (by way of mass-energy equivalence)\n* (exactly)","Joule\n\nUnits defined exactly in terms of the joule include:\n* 1 thermochemical calorie 4.184 J[http://www.fao.org/docrep/meeting/009/ae906e/ae906e17.htm The adoption of joules as units of energy], FAO/WHO Ad Hoc Committee of Experts on Energy and Protein, 1971. A report on the changeover from calories to joules in nutrition.\n* 1 International Table calorie = 4.1868 J \n* 1 watt hour = 3600 J (or 3.6 kJ)\n* 1 kilowatt hour = (or 3.6 MJ)\n* 1 watt second = \n* 1 ton TNT ="],"string":"[\n \"Joule\\n\\nThe joule, symbol J, is a derived unit of energy in the International System of Units. It is equal to the energy transferred (or work done) to an object when a force of one newton acts on that object in the direction of its motion through a distance of one metre (1 newton metre or N·m). It is also the energy dissipated as heat when an electric current of one ampere passes through a resistance of one ohm for one second. It is named after the English physicist James Prescott Joule (1818–1889).\",\n \"Joule\\n\\nIn terms firstly of base SI units and then in terms of other SI units:\\n\\\\rm J {}\\\\rm \\\\frac{kg \\\\cdot m^2}{s^2} \\n N \\\\cdot m \\\\rm Pa \\\\cdot m^3\\n{}\\\\rm W \\\\cdot s = C \\\\cdot V\",\n \"Joule\\n\\nwhere kg is the kilogram, m is the metre, s is the second, N is the newton, Pa is the pascal, W is the watt, C is the coulomb, and V is the volt.\",\n \"Joule\\n\\nOne joule can also be defined as:\\n* The work required to move an electric charge of one coulomb through an electrical potential difference of one volt, or one '\\\"coulomb volt\\\" (C·V). This relationship can be used to define the volt.\\n* The work required to produce one watt of power for one second, or one \\\"watt second\\\" (W·s) (compare kilowatt hour - 3.6 megajoules). This relationship can be used to define the watt.\",\n \"Joule\\n\\nUsage\",\n \"Joule\\n\\nConfusion with newton-metre\",\n \"Joule\\n\\nIn angular mechanics, torque is analogous to the linear Newtonian mechanics parameter of force, moment of inertia to mass, and angle to distance. Energy is the same in both systems. Thus, although the joule has the same dimensions as the newton-metre (1 J 1 N·m \\n 1 kg·m2·s−2), these units are not interchangeable: the CGPM has given the unit of energy the name \\\"joule\\\", but has not given the unit of torque any special name, hence the unit of torque is known as the newton-metre (N·m) - a compound name derived from its constituent parts. Torque and energy are related to each other using the equation\\nE= \\\\tau \\\\theta\\\\ \\nwhere E is the energy, τ is the torque, and θ is the angle moved (in radians). Since radians are dimensionless, it follows that torque and energy have the same dimensions.\",\n \"Joule\\n\\nThe use of newton-metres for torque and joules for energy is useful in helping avoid misunderstandings and miscommunications.\",\n \"Joule\\n\\nAn additional solution is to realize that joules are scalars – they are the dot product of a vector force and a vector displacement whereas torque is a vector. Torque is the cross product of a distance vector and a force vector. Drawing a traditional vector arrow over \\\"newton-metre\\\" in a torque resolves the ambiguity.\",\n \"Joule\\n\\nPractical examples\",\n \"Joule\\n\\nOne joule in everyday life represents approximately:\\n* The energy required to lift a medium-size tomato (100 g) 1 meter vertically from the surface of the Earth. \\n* The energy released when that same tomato falls back down to the ground.\\n* The energy required to accelerate a 1 kg mass at 1 m·s−2 through a 1 m distance in space.\\n* The heat required to raise the temperature of 1 g of water by 0.24 K. \\n* The typical energy released as heat by a person at rest every 1/60 second (approximately 17 ms). \\n* The kinetic energy of a 50 kg human moving very slowly ().\\n* The kinetic energy of a 56 g tennis ball moving at 6 m/s. \\n* The kinetic energy of an object with mass 1 kg moving at √2 ≈ 1.4 m/s.\\n* The amount of electricity required to light a 1 watt LED for 1 s.\",\n \"Joule\\n\\nSince the joule is also a watt-second and the common unit for electricity sales to homes is the kW·h (kilowatt-hour), a kW·h is thus 1000 (kilo) watt × 3600 seconds = 3.6 megajoules (MJ).\",\n \"Joule\\n\\nMultiples\",\n \"Joule\\n\\nFor additional examples, see: Orders of magnitude (energy)\",\n \"Joule\\n\\nZeptojoule\",\n \"Joule\\n\\nThe zeptojoule (zJ) is equal to one sextillionth (10−21) of one joule. 160 zeptojoules is equivalent to one electronvolt.\",\n \"Joule\\n\\nNanojoule\",\n \"Joule\\n\\nThe nanojoule (nJ) is equal to one billionth (10−9) of one joule. One nanojoule is about 1/160 of the kinetic energy of a flying mosquito.\",\n \"Joule\\n\\nMicrojoule\",\n \"Joule\\n\\nThe microjoule (μJ) is equal to one millionth (10−6) of one joule. The Large Hadron Collider (LHC) produces collisions of the microjoule order (7 TeV) per particle.\",\n \"Joule\\n\\nMillijoule\",\n \"Joule\\n\\nThe millijoule (mJ) is equal to one thousandth (10−3) of a joule.\",\n \"Joule\\n\\nKilojoule\",\n \"Joule\\n\\nThe kilojoule (kJ) is equal to one thousand (103) joules. Nutritional food labels in some countries express energy in kilojoules (kJ).\",\n \"Joule\\n\\nOne square metre of the Earth receives about 1.4 kilojoules of solar radiation every second in full daylight.\",\n \"Joule\\n\\nMegajoule\",\n \"Joule\\n\\nThe megajoule (MJ) is equal to one million (106) joules, or approximately the kinetic energy of a one megagram (tonne) vehicle moving at 160 km/h.\",\n \"Joule\\n\\nOne kilowatt hour of electricity is 3.6 megajoules.\",\n \"Joule\\n\\nGigajoule\",\n \"Joule\\n\\nThe gigajoule (GJ) is equal to one billion (109) joules. 6 GJ is about the amount of potential chemical energy in 160 L (approximately one US standard barrel) of oil, when combusted.\",\n \"Joule\\n\\nTerajoule\",\n \"Joule\\n\\nThe terajoule (TJ) is equal to one trillion (1012) joules. About 63 TJ of energy was released by the atomic bomb that exploded over Hiroshima. The International Space Station, with a mass of approximately 450 megagrams and orbital velocity of 7.7 km/s, has a kinetic energy of roughly 13 TJ.\",\n \"Joule\\n\\nPetajoule\",\n \"Joule\\n\\nThe petajoule (PJ) is equal to one quadrillion (1015) joules. 210 PJ is equivalent to about 50 megatons of TNT. This is the amount of energy released by the Tsar Bomba, the largest man-made nuclear explosion ever.\",\n \"Joule\\n\\nExajoule\",\n \"Joule\\n\\nThe exajoule (EJ) is equal to one quintillion (1018) joules. The 2011 Tōhoku earthquake and tsunami in Japan had 1.41 EJ of energy according to its 9.0 on the moment magnitude scale. Energy in the United States used per year is roughly 94 EJ.\",\n \"Joule\\n\\nZettajoule\",\n \"Joule\\n\\nThe zettajoule (ZJ) is equal to one sextillion (1021) joules. The human annual global energy consumption is approximately 0.5 ZJ.\",\n \"Joule\\n\\nYottajoule\",\n \"Joule\\n\\nThe yottajoule (YJ) is equal to one septillion (1024) joules. This is approximately the amount of energy required to heat all the water on Earth by 1 °C. The thermal output of the Sun is approximately 400 YJ per second.\",\n \"Joule\\n\\nConversions\",\n \"Joule\\n\\n1 joule is equal to:\\n* (exactly) \\n* \\n* (gram calories)\\n* (food calories)\\n* \\n* \\n* (foot-poundal)\\n* \\n* \\n* (litre-atmosphere)\\n* (by way of mass-energy equivalence)\\n* (exactly)\",\n \"Joule\\n\\nUnits defined exactly in terms of the joule include:\\n* 1 thermochemical calorie 4.184 J[http://www.fao.org/docrep/meeting/009/ae906e/ae906e17.htm The adoption of joules as units of energy], FAO/WHO Ad Hoc Committee of Experts on Energy and Protein, 1971. A report on the changeover from calories to joules in nutrition.\\n* 1 International Table calorie = 4.1868 J \\n* 1 watt hour = 3600 J (or 3.6 kJ)\\n* 1 kilowatt hour = (or 3.6 MJ)\\n* 1 watt second = \\n* 1 ton TNT =\"\n]","isConversational":false}}}],"truncated":false,"partial":false},"paginationData":{"pageIndex":17,"numItemsPerPage":100,"numTotalItems":138384,"offset":1700,"length":100}},"jwt":"eyJhbGciOiJFZERTQSIsImtpZCI6IjVHZDBvd0g5MTM2eDZjc1FvbE1zcktNWUZoRVFoUm5PVVVybEpjOUhaUEEifQ.eyJyZWFkIjp0cnVlLCJwZXJtaXNzaW9ucyI6eyJyZXBvLmNvbnRlbnQucmVhZCI6dHJ1ZX0sImlhdCI6MTc5MDcwNDEyOCwianRpIjoiMTZiZDBhZTctMGIwZC00NmZmLWFhNmMtZWMzZmU4ZWVkZjJhIiwic3ViIjoiL2RhdGFzZXRzL01lbW9yeUFzTW9kYWxpdHkvVHJpdmlhUUEiLCJleHAiOjE3OTA3MDc3MjgsImlzcyI6Imh0dHBzOi8vaHVnZ2luZ2ZhY2UuY28ifQ.PClIGRLDTkBo3X0XVcm9VCktF3itYiYTTl56DE-tvicC1eaXxHbJ7-g9tPzaAd_NzqhIfJ6ESadzd4iG9UKcBQ","displayUrls":true,"splitSizeSummaries":[{"config":"default","split":"train","numRows":138384,"numBytesParquet":4149441207},{"config":"default","split":"validation","numRows":17944,"numBytesParquet":531588839},{"config":"default","split":"test","numRows":17210,"numBytesParquet":506953567}]},"discussionsStats":{"closed":0,"open":0,"total":0},"fullWidth":true,"hasGatedAccess":true,"hasFullAccess":true,"isEmbedded":false,"savedQueries":{"community":[],"user":[]}}">
id stringlengths 4 10 | question stringlengths 18 1.2k | answer stringlengths 1 179 | answer_aliases listlengths 0 358 | documents listlengths 1 1.63k |
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tc_2642 | How many readings does an act of Parliament have in the House of Commons before being given royal assent? | Three | [
"three",
"3"
] | [
"Act of Parliament\n\nAn Act of Parliament is a statute enacted as primary legislation by a national or sub-national parliament. In the Republic of Ireland the term Act of the Oireachtas is used, and in the United States the term Act of Congress is used.",
"Act of Parliament\n\nIn Commonwealth countries, the term... |
tc_2643 | In which city did Karl Marx write Das Kapital? | London | [
"london uk",
"london united kingdom",
"londra",
"london greater london",
"climate in london",
"metropolis",
"united kingdom london",
"un locode gblon",
"london england united kingdom",
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"london on thames",
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"gblon",
"climate of... | [
"Karl Marx\n\nKarl MarxThe name \"Karl Heinrich Marx\", used in various lexicons, is based on an error. His birth certificate says \"Carl Marx\", and elsewhere \"Karl Marx\" is used. \"K. H. Marx\" is used only in his poetry collections and the transcript of his dissertation; because Marx wanted to honour his fathe... |
tc_2645 | Which party did F W de Klerk represent as South African president? | National Party | [
"partido nacionalista",
"nationalist party",
"national party uk",
"national party disambiguation",
"national party ireland",
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"F. W. de Klerk\n\nFrederik Willem de Klerk (; born 18 March 1936) is a South African politician who served as the country's State President from September 1989 to May 1994. He was the seventh and last head of state of South Africa under the apartheid era. De Klerk was also leader of the National Party (which later... |
tc_2646 | What is the term used when a sitting MP is removed as the candidate for a forthcoming election? | Deselection | [
"deselection",
"candidate selection",
"reselected",
"deselect",
"preselection",
"pre selection"
] | [
"BBC News - Labour MP Nigel Griffiths to quit at election\n\nBBC News - Labour MP Nigel Griffiths to quit at election\nLabour MP Nigel Griffiths to quit at election\nNigel Griffiths has been the Edinburgh South MP for 23 years\nFormer Labour minister Nigel Griffiths has announced he will quit as MP for Edinburgh So... |
tc_2647 | Who played the part of Piers Fletcher Dervish, personal assistant to MP Alan B'stard, in the television comedy series The New Statesman? | Michael Troughton | [
"michael troughton"
] | [
"The New Statesman\n\nThe New Statesman is a British television comedy drama series made in the late 1980s and early 1990s satirising the United Kingdom's Conservative Party Government of the period. It was written by Laurence Marks and Maurice Gran at the request of, and as a starring vehicle for, its principal ac... |
tc_2648 | Which MP entered Parliament as a Tory in 1833, but became Liberal prime minister in 1868? | Gladstone | [
"gladstone disambiguation",
"mr gladstone",
"gladstone",
"gladstone s"
] | [
"Liberal Party (UK)\n\nThe Liberal Party was a liberal political party which was one of the two major parties in the United Kingdom in the 19th and early 20th century.",
"Liberal Party (UK)\n\nThe party arose from an alliance of Whigs and free-trade Peelites and Radicals in the 1850s. By the end of the nineteenth... |
tc_2650 | Who was the last foreign secretary to serve in Margaret Thatcher's cabinet, an MP who also contested the leadership after her resignation? | Douglas Hurd | [
"baron hurd of westwell",
"douglas richard hurd",
"lord hurd",
"douglas hurd",
"douglas hurd baron hurd of westwell",
"douglas richard hurd baron hurd of westwell",
"lord hurd of westwell",
"douglas heard"
] | [
"Premiership of Margaret Thatcher\n\nThe premiership of Margaret Thatcher spanned throughout the entire duration of the 1980s in Britain, between early May 1979 and late November 1990.",
"Premiership of Margaret Thatcher\n\nThatcher is the third and most recent Prime Minister whose consecutive administrations hav... |
tc_2651 | Which publication documents all proceedings of the British parliament? | Hansard | [
"parliamentary debates",
"lords hansard",
"hansard lords",
"parliamentary hansard",
"hansard s debates",
"parliamentary proceeding",
"hansard"
] | [
"Parliament of the United Kingdom\n\nThe Parliament of the United Kingdom of Great Britain and Northern Ireland, commonly known as the UK Parliament, the British Parliament or Parliament, is the supreme legislative body in the United Kingdom, British Crown dependencies and British overseas territories. It alone po... |
tc_2652 | Which British minister of health inaugurated the National Health Service? | Aneurin Bevan | [
"celticus",
"anuerin bevan",
"nye bevan",
"anurin bevin",
"aneurin bevan",
"bevan aneurin"
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"Which British minister of health inaugurated the National ...\n\nWhich British minister of health inaugurated the National Health Service? View the step-by-step solution to:\nWhich British minister of health inaugurated the National Health Service? This question was answered on May 22, 2016. View the Answer\nWhich... |
tc_2654 | What is the name for the group of opposition spokesmen who comment on the policies of government ministers? | Shadow cabinet | [
"shadcab",
"shadow front bench",
"british shadow government",
"members of shadow cabinet",
"shadow secretary of state for transport and environment",
"official shadow cabinet",
"opposition critic",
"official opposition shadow cabinet",
"shadow cabinet uk",
"shadow secretary of state for education ... | [
"What is the name for the group of opposition spokesmen who\n\nWhat is the name for the group of opposition spokesmen who comment on the policies of government ministers? Sign up\nView the step-by-step solution to:\nWhat is the name for the group of opposition spokesmen who comment on the policies of government min... |
tc_2655 | "Who was ""Britain's first ever Labour prime minister in 1924?" | James Ramsey MacDonald | [
"ramsay macdonald",
"ramsay mcdonald",
"ramsey mcdonald",
"macdonald ramsay",
"macdonald james ramsay",
"ramsey macdonald",
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"james ramsay macdonald",
"macdonald ramsey"
] | [
"Labour Party (UK)\n\nThe Labour Party is a centre-left political party in the United Kingdom. Growing out of the trade union movement and socialist parties of the nineteenth century, the Labour Party has been described as a \"broad church\", encompassing a diversity of ideological trends from strongly socialist to... |
tc_2657 | "What became known s ""the F-word"" at the 1991 Maastricht summit, where Britain wanted it removed from the treaty?" | Federalism | [
"federal system",
"federal state",
"european federalist movements",
"federal future of belgium",
"federalism",
"federalism in french revolution",
"federalisation",
"horizontal federalism",
"federalization",
"union system",
"federalistic",
"federal power"
] | [
"European Council, Maastricht (Hansard, 25 November 1991)\n\nEuropean Council, Maastricht (Hansard, 25 November 1991)\nLord Cledwyn of Penrhos\nMy Lords, we are grateful to the noble Lord the Leader of the House for setting the scene for the debate and for his comprehensive speech in which he explained some aspects... |
tc_2658 | Which British actress won the Hampstead and Highgate seat for Labour in the 1992 General Election? | Glenda Jackson | [
"glenda jackson",
"glenda may jackson",
"jackson glenda",
"glenda may jackson cbe"
] | [
"Hampstead and Highgate (UK Parliament constituency)\n\nHampstead & Highgate was a parliamentary constituency covering the northern half of the London Borough of Camden which includes the village of Hampstead and part of that of Highgate.",
"Hampstead and Highgate (UK Parliament constituency)\n\nIt was abolished ... |
tc_2659 | Whose book Inside NO 10 described Harold Wilson's Downing Street years? | Lady Falkender | [
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"falkender",
"marcia williams",
"baroness falkender",
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"marcia matilda falkender baroness falkender",
"marcia matilda falkender"
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"Harold Wilson\n\nJames Harold Wilson, Baron Wilson of Rievaulx, (11 March 1916 - 24 May 1995) was a British Labour Party politician who served as the Prime Minister of the United Kingdom from 1964 to 1970 and 1974 to 1976.",
"Harold Wilson\n\nFirst entering Parliament in 1945, Wilson was immediately appointed t... |
tc_2661 | What is the Swedish name of the official who acts for the private citizen in complaints against the government? | Ombudsman | [
"ombudsmen thailand",
"ombudsmand",
"public ombudsman",
"ombudsperson",
"ombudsman",
"ombuds officers",
"ombudsman greece",
"ombudsman programs",
"consumer ombudsman",
"ombuds",
"ombudswoman",
"ombudsmann",
"ombudsmen",
"ombudspersons",
"defender of rights",
"ombudspeople",
"office o... | [
"The Swedish system of government - sweden.se\n\nThe Swedish system of government\nHome / Society / The Swedish system of government\nThe Swedish system of government\nAll public power proceeds from the people. This is the foundation of parliamentary democracy in Sweden. Everyone has the same rights and is free to ... |
tc_2662 | Which US president introduced the New Deal in 1933 to counter the depression? | Franklin Roosevelt | [
"f d roosevelt",
"franklin d roosevelt administration",
"f d roosevelt administration",
"franklin deleno roosevelt",
"president franklin roosevelt",
"franklin rosevelt",
"frankilin delano roosevelt",
"president franklin d roosevelt",
"fd roosevelt",
"f roosevelt administration",
"summary of life... | [
"President of the United States\n\nThe President of the United States of America (POTUS) is the elected head of state and head of government of the United States. The president leads the executive branch of the federal government and is the commander-in-chief of the United States Armed Forces.",
"President of th... |
tc_2663 | Mario Soares became the first socialist president of which country in 1986? | Portugal | [
"portugul",
"portugallu",
"portugalska",
"pòtigal",
"portugaul",
"portugalujo",
"portuguese republic",
"iso 3166 1 pt",
"republic of portugal",
"portugalsko",
"portugual",
"bồ đào nha",
"portugall",
"portûnga",
"bo dao nha",
"phortaingeil",
"portugale",
"portugal",
"portugál",
... | [
"Mário Soares\n\nMário Alberto Nobre Lopes Soares, GColTE, GCC, GColL (; born 7 December 1924) is a Portuguese politician who served as Prime Minister of Portugal from 1976 to 1978 and from 1983 to 1985, and subsequently as the 17th President of Portugal from 1986 to 1996.",
"Mário Soares\n\nFamily",
"Mário Soa... |
tc_2665 | What is the title of the member of the upper house equivalent to that of the Speaker in the lower house? | Lord Chancellor | [
"chancellor of england",
"lord chancellors",
"lord commissioner of great seal",
"lord chancellor of great britain",
"lords commissioners of great seal",
"lord high chancellor of england",
"lord chancellor",
"chancellor of great britain",
"lords chancellor",
"lord chancellor of england",
"lord hi... | [
"Speaker (politics)\n\nThe Speaker of a deliberative assembly, especially a legislative body, is its presiding officer (chair). The title was first used in 1377 in England.",
"Speaker (politics)\n\nUsage",
"Speaker (politics)\n\nThe speaker's official role is to moderate debate, make rulings on procedure, annou... |
tc_2666 | Who was the first president of France's Fifth Republic? | Charles de Gaulle | [
"charles degaulle",
"general degaulle",
"charles andre joseph marie de gaulle",
"general de gaulle",
"charles de gaulle",
"general charles de gaulle",
"charles de gualle",
"charles de gaule",
"de gaulle charles andré joseph marie",
"de gaulle",
"charles de gaul",
"degaulle",
"charles de gaul... | [
"President of France\n\nThe President of the French Republic (,), is the executive head of state of the French Fifth Republic. The powers, functions and duties of prior presidential offices, and their relation with the first minister and cabinets has over time differed with the various French constitutions.",
"Pr... |
tc_2667 | Who was dismissed from office as Australian prime minister in 1975 after refusing to call a general election? | Gough Whitlam | [
"edward gough whitlam",
"gough whitlam",
"whitlam",
"whitlamism",
"edward whitlam"
] | [
"1975 Australian constitutional crisis\n\nThe 1975 Australian constitutional crisis, also known simply as \"the Dismissal\", has been described as the greatest political and constitutional crisis in Australian history. It culminated on 11 November 1975 with the dismissal from office of the Prime Minister, Gough Whi... |
tc_2670 | "Which word, meaning ""I forbid"" in Latin, means the right to prevent a law being enacted or an action being taken?" | Veto | [
"vetoer",
"legislative override",
"executive veto",
"presidential veto",
"u s presidential veto",
"veto override",
"vetoes",
"veto power",
"vetoed",
"suspensive veto",
"amendatory veto",
"neitunarvald",
"presidential vetoes",
"vetos",
"vetoing",
"veto",
"president s veto"
] | [
"Law\n\nLaw is a system of rules that are enforced through social institutions to govern behavior. Laws can be made by a collective legislature or by a single legislator, resulting in statutes, by the executive through decrees and regulations, or by judges through binding precedent, normally in common law jurisdic... |
tc_2671 | What collective name is given to the first ten amendments to the US constitution? | Bill of Rights | [
"bill of responsibilities",
"bill of duties",
"bill of obligations",
"bor",
"bill of right",
"bill of rights"
] | [
"United States Bill of Rights\n\nThe Bill of Rights is the collective name for the first ten amendments to the United States Constitution. Proposed following the oftentimes bitter 1787–88 battle over ratification of the U.S. Constitution, and crafted to address the objections raised by Anti-Federalists, the Bill of... |
tc_2672 | What is the collective name of the international agreements signed by all the member states of the European Community? | Treaties of Rome | [
"ec treaty",
"formation of eu",
"treaty on european community",
"rome treaty",
"tfue treaty",
"treaty of rome 1957",
"formation of european union",
"foundation of european union",
"eec treaty",
"treaty establishing european community",
"treaties of rome 1957",
"establishment of european union"... | [
"European Economic Community\n\nThe European Economic Community (EEC) was a regional organisation which aimed to bring about economic integration among its member states. It was created by the Treaty of Rome of 1957. Upon the formation of the European Union (EU) in 1993, the EEC was incorporated and renamed as the... |
tc_2673 | In which year did Mikhail Gorbachev resign as Soviet president? | 1991 | [
"one thousand nine hundred and ninety one"
] | [
"Mikhail Gorbachev\n\nMikhail Sergeyevich Gorbachev (; ; born 2 March 1931) is a former Soviet statesman. He was the eighth and last leader of the Soviet Union, having served as General Secretary of the Communist Party of the Soviet Union from 1985 until 1991 when the party was dissolved. He served as the country... |
tc_2674 | Which political commentator has presented both Weekend World and A Week in Politics? | Peter Jay | [
"peter jay",
"jay peter"
] | [
"Weekend World\n\nWeekend World is a British television political series, made by London Weekend Television (LWT) and broadcast from 1972 to 1988.",
"Weekend World\n\nCreated by John Birt, not long after he had joined LWT, the series was broadcast on the ITV network at lunchtimes on Sundays. Produced by Nick Elli... |
tc_2675 | How many countries are there in the British Commonwealth? | 50 | [
"fifty"
] | [
"Commonwealth of Nations\n\nThe Commonwealth of Nations, or the Commonwealth (formerly the British Commonwealth), is an intergovernmental organisation of 53 member states that were mostly territories of the former British Empire. The Commonwealth operates by intergovernmental consensus of the member states, orga... |
tc_2676 | What is the Irish house of representatives called? | Dáil Éireann | [
"dail",
"dail eireann",
"dáil",
"irish lower chamber",
"irish dáil",
"dála",
"house of representatives of ireland",
"dáil eireann",
"irish dail",
"dail eirrean",
"dáil éireann",
"dail éireann"
] | [
"United States House of Representatives\n\nThe United States House of Representatives is one of the two houses of the United States Congress (a bicameral legislature) alongside the Senate.",
"United States House of Representatives\n\nThe composition and powers of the House are established in Article One of the Un... |
tc_2678 | Who was Pope for only 33 days in 1978? | John Paul I | [
"smiling pope",
"pope john paul 1",
"263rd pope",
"john paul i",
"albino luciano",
"smile of god",
"pope john paul i",
"john paul i of rome",
"albino luciani",
"september pope",
"ioannes paulus pp i",
"edoardo luciani",
"albino cardinal luciani"
] | [
"Pope John Paul I\n\nPope John Paul I (; ), born Albino Luciani (; 17 October 1912 - 28 September 1978), served as Pope from 26 August 1978 to his sudden death 33 days later. His reign is among the shortest in papal history, resulting in the most recent Year of Three Popes, the first to occur since 1605. John Paul ... |
tc_2679 | Who was lead singer with the group Queen? | Freddie Mercury | [
"farrokh bomi bulsara",
"fredy mercury",
"mercury film",
"kind of magic film",
"fred mercury",
"farrokh busara",
"ફરોખ બલ્સારા",
"frederick bulsara",
"mr fahrenheit",
"faroukh bulsara",
"freddy mercury",
"farookh bulsara",
"aids attack",
"freddie mercury",
"farrokh pluto bulsara",
"far... | [
"Queen (band)\n\nQueen are a British rock band that formed in London in 1970. Their classic line-up was Freddie Mercury (lead vocals, piano), Brian May (lead guitar, vocals), Roger Taylor (drums, vocals), and John Deacon (bass guitar). Queen's earliest works were influenced by progressive rock, hard rock and heavy ... |
tc_2680 | Which author had the real name Charles Dodgson? | Lewis Carroll | [
"manlet",
"carroll lewis",
"charles l dodgson",
"lewis carol",
"charles lutwidge dodgson",
"lewis caroll",
"c l dodgson",
"lewis carrol",
"reverend charles lutwidge dodgson",
"carrollian",
"cl dodgson",
"lewis carroll"
] | [
"Lewis Carroll\n\nCharles Lutwidge Dodgson (; 27 January 1832 – 14 January 1898), better known by his pen name Lewis Carroll, was an English writer, mathematician, logician, Anglican deacon, and photographer. His most famous writings are Alice's Adventures in Wonderland, its sequel Through the Looking-Glass, whi... |
tc_2682 | Who was the Lord Chancellor beheaded for refusing to recognize Henry VIII as head of the church? | Thomas More | [
"saint thomas moore",
"sir st thomas more",
"t more",
"st thomas more",
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"tomas moore",
"saint thomas more",
"tomas more",
"sir saint thomas more",
"more thomas saint",
"thomas morus",
"sir tho... | [
"Henry VIII of England\n\nHenry VIII (28 June 1491 – 28 January 1547) was King of England from 21 April 1509 until his death. He was the first English King of Ireland, and continued the nominal claim by English monarchs to the Kingdom of France. Henry was the second monarch of the Tudor dynasty, succeeding his fath... |
tc_2684 | Who led the Free French forces during World War II? | Charles de Gaulle | [
"charles degaulle",
"general degaulle",
"charles andre joseph marie de gaulle",
"general de gaulle",
"charles de gaulle",
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"charles de gaule",
"de gaulle charles andré joseph marie",
"de gaulle",
"charles de gaul",
"degaulle",
"charles de gaul... | [
"Free France\n\nFree France and its Free French Forces (French: France Libre and Forces françaises libres) were the government-in-exile led by Charles de Gaulle during the Second World War and its military forces that continued to fight against the Axis powers as one of the Allies after the fall of France. It was s... |
tc_2685 | Which battle of 1876 was Custer's last stand? | Little Bighorn | [
"little bighorn disambiguation",
"little bighorn",
"little big horn"
] | [
"Battle of the Little Bighorn\n\nThe Battle of the Little Bighorn, known to Lakota as the Battle of the Greasy Grass, and commonly referred to as Custer's Last Stand, was an armed engagement between combined forces of the Lakota, Northern Cheyenne, and Arapaho tribes, against the 7th Cavalry Regiment of the United... |
tc_2686 | Which actor, comedian and singer was born David Daniel Kaminski? | Danny Kaye | [
"david daniel kaminski",
"david daniel kaminsky",
"danny kay",
"danny kaye show",
"danny kaye"
] | [
"Danny Kaye\n\nDavid Daniel Kaminsky (January 18, 1911 – March 3, 1987), better known by his screen name Danny Kaye, was an American actor, singer, dancer, comedian, and musician. His performances featured physical comedy, idiosyncratic pantomimes, and rapid-fire novelty songs.",
"Danny Kaye\n\nKaye starred in 17... |
tc_2688 | What nationality was the spy Mata Hari? | Dutch | [
"dutc",
"dutch",
"dutch disambiguation",
"dtuch"
] | [
"Espionage\n\nEspionage (colloquially, spying) is the obtaining of information considered secret or confidential without the permission of the holder of the information. Espionage can be committed by an individual or a spy ring (a cooperating group of spies), in the service of a government or a company, or operati... |
tc_2689 | "Who said: ""The customer is always right""?" | Harry Gordon Selfridge | [
"harry selfridge",
"harry gordon selfridge",
"earl of oxford street",
"hg selfridge"
] | [
"The customer is always right\n\n\"The customer is always right\" is a motto or slogan which exhorts service staff to give a high priority to customer satisfaction. It was popularised by pioneering and successful retailers such as Harry Gordon Selfridge, John Wanamaker and Marshall Field. They advocated that cust... |
tc_2691 | "What pen name was used by the Spanish orator Dolores Ibarruri, who said ""It is better to die on your feet than to live on your knees""?" | La Pasionaria | [
"dolores ibarruri",
"la pasionare",
"la pasionaria",
"dolores ibárruri gómez",
"passionaria",
"dolores ibarruri gomez",
"dolores ibárruri",
"la pasionara",
"ibarruri dolores",
"pasionaria"
] | [
"Dolores Ibárruri\n\nIsidora Dolores Ibárruri Gómez (9 December 1895 - 12 November 1989) – known as \"La Pasionaria\" (Spanish, \"the Passionflower\") – was a Spanish Republican heroine of the Spanish Civil War and communist politician of Basque origin, known for her famous slogan ¡No Pasarán! (\"They shall not pa... |
tc_2692 | For what purpose did Melvil Dewey devise his decimal system in 1876? | Classifying books | [
"classifying books"
] | [
"Full text of \"Major classification systems : the Dewey ...\n\nFull text of \"Major classification systems : the Dewey Centennial\"\nSee other formats\n020.715 A434 no. 21 Major Classification Systems: The Dewey Centennial LIBRARY OF THE UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN 020/715 A434 ... |
tc_2693 | Who was the king of rock and roll? | Elvis Presley | [
"elivs",
"gladys love presley",
"apron strings",
"elvis aaron presley",
"elvis presly",
"elvis aaron pressley",
"king actor singer",
"elvis pres",
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"elvisesque",
"mr aaron",
"elvis pres ey",
"jesse presley",
"elvis aron presley",
"lovely mamie",
"keep your hands off of i... | [
"The King of Rock and Roll\n\nThe King of Rock and Roll was Little Richard's second album for Reprise Records, a follow-up album that contained one original Little Richard song, the Gospel-Rock \"In The Name\" and a new song co-written by Producer H. B. Barnum, \"Green Power\", the single release; and versions of t... |
tc_2694 | Who was Sherlock Holmes' assistant? | Dr. Watson | [
"dr john watson",
"doctor watson",
"john hamish watson",
"watsonish",
"john watson sherlock holmes",
"john h watson",
"dr john h watson",
"watson sherlock holmes",
"dr watson",
"doctor john h watson"
] | [
"Sherlock Holmes\n\nSherlock Holmes is a fictional private detective created by British author Sir Arthur Conan Doyle. Known as a \"consulting detective\" in the stories, Holmes is known for a proficiency with observation, forensic science, and logical reasoning that borders on the fantastic, which he employs when... |
tc_2695 | What are the indigenous people of new Zealand called? | Maoris | [
"maori people",
"maori social issues",
"māori classic period",
"maoridom",
"maoris",
"list of maoris",
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"maori history",
"te tipunga",
"māori people",
"list of maori people",
"māori health",
"māoridom",
"maori"
] | [
"New Zealand\n\nNew Zealand () is an island nation in the southwestern Pacific Ocean. The country geographically comprises two main landmasses – that of the North Island, or Te Ika-a-Māui, and the South Island, or Te Waipounamu – and numerous smaller islands. New Zealand is situated some 1500 km east of Australia a... |
tc_2696 | Who was the film star who married Prince Rainier III of Monaco? | Grace Kelly | [
"grace kelly princess of monaco",
"princess grace",
"grace kelly",
"grace of monaco",
"gracepatriciakelly",
"grace princess of monaco",
"grace patricia kelly",
"gracekelly",
"princess grace of monaco",
"gracia princess of monaco",
"grace de monaco"
] | [
"Rainier III, Prince of Monaco\n\nRainier III (Rainier Louis Henri Maxence Bertrand Grimaldi; 31 May 1923 – 6 April 2005) ruled the Principality of Monaco for almost 56 years, making him one of the longest ruling monarchs in European history.\nThough internationally known for his marriage to the American actress Gr... |
tc_2697 | What was the first name of the politician Gladstone, the composer Walton, and the reformer Wilberforce? | William | [
"william disambiguation",
"william"
] | [
"William Ewart Gladstone\n\nWilliam Ewart Gladstone (; 29 December 1809 – 19 May 1898) was a British Liberal politician. In a career lasting over sixty years, he served as Prime Minister four separate times (1868–74, 1880–85, February–July 1886 and 1892–94), more than any other person, and served as Chancellor of ... |
tc_2698 | Of which tribe was Goliath the champion? | Philistines | [
"phillistines",
"plishtim",
"phillistine",
"philistean",
"philistim",
"philistines",
"philisteins",
"philistine",
"philistéan",
"pilishtim",
"list of battles between israel and philistines"
] | [
"Goliath\n\nGoliath (; ; Arabic: جالوت, Ǧālūt (Qur'anic term), جليات Ǧulyāt (Christian term)) of Gath (one of five city states of the Philistines) was a giant Philistine warrior defeated by the young David, the future king of Israel. The story is told in the Bible's Books of Samuel (1 Samuel 17).",
"Goliath\n\nTh... |
tc_2700 | What nickname was given to General Thomas Jackson because of his stern defense at the battle of Bull Run? | Stonewall | [
"stonewall disambiguation",
"stone wall",
"stonewall film",
"stonewall",
"stone wall disambiguation"
] | [
"Stonewall Jackson\n\nThomas Jonathan \"Stonewall\" Jackson (January 21, 1824 – May 10, 1863) was a Confederate general during the American Civil War, and the best-known Confederate commander after General Robert E. Lee. His military career includes the Valley Campaign of 1862 and his service as a corps commander ... |
tc_2702 | Which Christian martyr was first bishop of Rome? | St. Peter | [
"simon cephas",
"shemayon keppa",
"cephas",
"san petro",
"saint peter",
"st peter",
"pope saint peter",
"pope peter",
"peter apostle",
"1st pope",
"simon caiaphas",
"s petro",
"rock of faith",
"saint peter apostle",
"shim on bar yona",
"holy peter",
"letters of st peter",
"st peter... | [
"Pope\n\nThe Pope ( from pappas, a child's word for \"father\") is the Bishop of Rome and the leader of the worldwide Catholic Church. The primacy of the Roman bishop is largely derived from his role as the traditional successor to Saint Peter, to whom Jesus is supposed to have given the keys of Heaven and the ... |
tc_2703 | Who was the most famous of English lexicographers? | Samuel Johnson | [
"dr samuel johnson",
"doctor johnson",
"johnson samuel",
"samuel johnson",
"great cham of literature",
"johnsonism",
"dr johnson",
"probus brittanicus",
"johnsonian",
"johnsoniana"
] | [
"What Samuel Johnson Really Did | Humanities\n\nWhat Samuel Johnson Really Did | Humanities\nWhat Samuel Johnson Really Did\nHe Made Dictionaries Matter\n+ Click on image to enlarge. Plagued by financial problems for much of his life, Johnson, who, in fact, had to drop our of Pembroke College in Cambridge, before e... |
tc_2704 | In which of the arts has Richard Avedon distinguished himself? | Photography | [
"photographing",
"photographic technique",
"photographics",
"early photography",
"photo picture",
"yachting photography",
"photography as art form",
"technology of photography",
"photographic",
"photography techniques",
"photography business",
"commercial photographer",
"print finishing",
... | [
"Visual arts\n\nThe visual arts are art forms such as ceramics, drawing, painting, sculpture, printmaking, design, crafts, photography, video, filmmaking and architecture. Many artistic disciplines (performing arts, conceptual art, textile arts) involve aspects of the visual arts as well as arts of other types. Als... |
tc_2705 | Which religious grou0p migrated westward to the Great Salt Lake, Utah, in 1847? | Mormons | [
"mormons",
"mormon",
"mormon population statistics",
"liberal mormon",
"utah mormon"
] | [
"Great Salt Lake\n\nThe Great Salt Lake, located in the northern part of the U.S. state of Utah, is the largest salt water lake in the Western Hemisphere, and the eighth-largest terminal lake in the world. In an average year the lake covers an area of around 1700 sqmi, but the lake's size fluctuates substantially... |
tc_2706 | "Which 18th-century dictionary compiler defined himself as a ""harmless drudge""?" | Samuel Johnson | [
"dr samuel johnson",
"doctor johnson",
"johnson samuel",
"samuel johnson",
"great cham of literature",
"johnsonism",
"dr johnson",
"probus brittanicus",
"johnsonian",
"johnsoniana"
] | [
"Depatment Meeting Jeopardy Jeopardy Template\n\nDepatment Meeting Jeopardy Jeopardy Template\nWhat is the number of days of summer? 93\nWhat is the year the school was establishe? 1926\nWhat is an alternate Acronym? Shhh,Texas, Ain't, Assessing, Rigor\nWhich 18th century dictionary compiler defined himself as a \"... |
tc_2707 | Who was president of the USSR from 1985-91? | Mikhail Gorbachev | [
"michail gorbatschow",
"mikhail gorbachov",
"gorbachov",
"gorbachev",
"gorbachof",
"mihail gorbaciov",
"mihail gorbachyov",
"михаил сергеевич горбачёв",
"gorbachyov",
"mihail sergejevič gorbačëv",
"mihail gorbachev",
"mihail sergeevic gorbacev",
"new thinking",
"mikhail gorbachyov",
"gor... | [
"President of the Soviet Union\n\nThe President of the Soviet Union (), officially called President of the USSR () or President of the Union of the Soviet Socialist Republics (), was the head of state of the Soviet Union from 15 March 1990 to 25 December 1991. Mikhail Gorbachev was the only person to occupy the o... |
tc_2708 | What was the name of the Thracian slave who led an ultimately unsuccessful gladiator revolt against Rome in 73 BC? | Spartacus | [
"spartakus",
"espartaco",
"spartacus",
"sparticus",
"spartacus person"
] | [
"Thracians\n\nThe Thracians (; Thrāikes, ) were a group of Indo-European tribes inhabiting a large area in southeastern Europe. They spoke the Thracian language – a scarcely attested branch of the Indo-European language family. The study of Thracians and Thracian culture is known as Thracology.",
"Thracians\n\n... |
tc_2709 | Which English king abdicated and became Duke of Windsor? | Edward VIII | [
"edward viii of great britain",
"edward 8th",
"edward 1st duke of windsor",
"prince edward of cornwall and york",
"prince edward 1st duke of windsor",
"david windsor",
"edward viii of england",
"edward duke of windsor",
"edward viii of canada",
"edward of cornwall and york",
"king edward viii of... | [
"Abdication\n\nAbdication is the act of formally relinquishing monarchical authority.",
"Abdication\n\nTerminology",
"Abdication\n\nThe word abdication derives from the Latin abdicatio meaning to disown or renounce (from ab, away from, and dicare, to dedicate or relinquish). In its broadest sense abdication is ... |
tc_2710 | Who was the first man in space in 1961? | Yuri Gagarin | [
"youri gagarine",
"jurij gagarin",
"iurii gagarin",
"yury gagarin",
"valentina goryacheva",
"gagarin",
"ю́рий алексе́евич гага́рин",
"juri gagarin",
"first human in space",
"first person in space",
"yuri gagarin",
"yury alekseyevich gagarin",
"юрий гагарин",
"yuri gegarin",
"yuri aleksey... | [
"Yuri Gagarin\n\nYuri Alekseyevich Gagarin (; 9 March 1934 – 27 March 1968) was a Russian Soviet pilot and cosmonaut. He was the first human to journey into outer space, when his Vostok spacecraft completed an orbit of the Earth on 12 April 1961.",
"Yuri Gagarin\n\nGagarin became an international celebrity, and w... |
tc_2712 | What invention made the fortune of Alfred Noel, founder of the Nobel prize? | Dynamite | [
"dynamite",
"dynamited",
"dinamite"
] | [
"Nobel Prize\n\nThe Nobel Prize (,; Swedish definite form, singular: Nobelpriset; ) is a set of annual international awards bestowed in a number of categories by Swedish and Norwegian committees in recognition of academic, cultural and/or scientific advances.",
"Nobel Prize\n\nThe will of the Swedish inventor Alf... |
tc_2713 | Whose circus did General Tom Thumb join at the age of five in 1843? | P T Barnum | [
"phineas barnum",
"phineas t barnum",
"philo f barnum",
"p barnum",
"p t barnum s",
"barnum",
"p t barnum",
"pt barnum",
"greatest showman on earth book",
"phineas taylor barnum"
] | [
"General Tom Thumb\n\nCharles Sherwood Stratton (January 4, 1838 – July 15, 1883), better known by his stage name \"General Tom Thumb\", was a dwarf who achieved great fame as a performer under circus pioneer P.T. Barnum.",
"General Tom Thumb\n\nChildhood and early life",
"General Tom Thumb\n\nStratton was a so... |
tc_2715 | Of which country was de Valera the prime minister, and later the president? | Ireland | [
"irlandia",
"erin s isle",
"héireann",
"airlann",
"ireland",
"irelanders",
"airlan",
"mikra britannia",
"irelander",
"population of ireland",
"west coast of ireland",
"scotia major",
"symbol of ireland",
"irland",
"auld sod",
"island of ireland",
"ireland region",
"irlanda",
"ire... | [
"Éamon de Valera\n\nÉamon de Valera (; first registered as George de Valero; changed some time before 1901 to Edward de Valera; 14 October 1882 – 29 August 1975) was a prominent politician in twentieth-century Ireland. His political career spanned over half a century, from 1917 to 1973; he served several terms a... |
tc_2716 | "Which actress starred opposite Alan Ladd in the film ""The Blue Dahlia""?" | Veronica Lake | [
"veronica lake",
"constance ockleman",
"constance keane"
] | [
"Alan Ladd\n\nAlan Walbridge Ladd (September 3, 1913 – January 29, 1964) was an American actor and film and television producer. Ladd found success in film the 1940s and early 1950s, particularly in Westerns such as Shane (1953) and film noirs where he was often paired with Veronica Lake, such as This Gun for Hire ... |
tc_2717 | "Which French fashion designer created the ""Little black dress""?" | Coco Chanel | [
"gabrielle chanel",
"gabriella bonheur chanel",
"gabrielle 22coco 22 chanel",
"coco chanel",
"chateau de cremat",
"mademoiselle chanel",
"gabrielle bonheur chanel",
"coco chanel couch"
] | [
"French fashion\n\nFrance is a leading country in the fashion design industry, along with Italy, Germany, the United Kingdom, Japan and the USA. Fashion is an important part of the country's cultural life and society, and the French are well known for their \ngood taste in fashion. Haute couture and the prêt-à-port... |
tc_2719 | What is the sticky wax obtained from sheep? | Lanolin | [
"wool grease",
"wool fat",
"adeps lanæ",
"lanolin",
"e913",
"anhydrous wool fat",
"eucerit",
"adeps lanae",
"wool wax"
] | [
"Sheep\n\nThe sheep (Ovis aries) is a quadrupedal, ruminant mammal typically kept as livestock. Like all ruminants, sheep are members of the order Artiodactyla, the even-toed ungulates. Although the name \"sheep\" applies to many species in the genus Ovis, in everyday usage it almost always refers to Ovis aries. Nu... |
tc_2720 | What is the trade name for the non-stick material used for coating cooking pans? | Teflon | [
"eptfe",
"polytetracfluoroethane",
"tefflon",
"c2f4n",
"teflon trademark",
"ptfe",
"teflon r",
"polytetraflouroethylene",
"teflon coated",
"polytetrafluoroethylene",
"polytetrafluroethylene",
"teflon®",
"polytetrafluorethylene",
"polytetrafluoroethene",
"pfte",
"teflon"
] | [
"Cookware and bakeware\n\nCookware and bakeware are types of food preparation containers, commonly found in a kitchen. Cookware comprises cooking vessels, such as saucepans and frying pans, intended for use on a stove or range cooktop. Bakeware comprises cooking vessels intended for use inside an oven. Some utensil... |
tc_2721 | What name is given to the brittle kind of iron used for making engine blocks and manhole covers? | Cast Iron | [
"white iron",
"chilled casting",
"white cast iron",
"cast iron"
] | [
"Iron\n\nIron is a chemical element with symbol Fe (from , ultimately from ferre to bear or carry) and atomic number 26. It is a metal in the first transition series. It is by mass the most common element on Earth, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's cr... |
tc_2722 | Which scientific unit gives a measure of loudness? | Decibel | [
"decible",
"dbrnc",
"dbi1",
"decibel acoustics",
"20 log rule",
"bel unit",
"dbμv",
"decibels",
"bell unit",
"relative db",
"㏈",
"decibal",
"bel acoustics",
"dbu",
"decibel",
"decibel scale",
"bel acustics",
"dbhz",
"dbi",
"millibel",
"absolute db",
"dbv",
"dbuv"
] | [
"Loudness\n\nLoudness is the characteristic of a sound that is primarily a psychological correlate of physical strength (amplitude). More formally, it is defined as \"that attribute of auditory sensation in terms of which sounds can be ordered on a scale extending from quiet to loud\".",
"Loudness\n\nLoudness, a ... |
tc_2723 | The behavior of sound in rooms and concert halls is a separate science. what is its name? | Acoustics | [
"acoustical science",
"acoustics",
"acoustician",
"acoustic measurements and instrumentation",
"acoustical",
"acoustical data",
"history of acoustics",
"acustica"
] | [
"Behavior of Sound Waves - Sound - Science | HowStuffWorks\n\nBehavior of Sound Waves - Sound | HowStuffWorks\nBehavior of Sound Waves\nLike light waves and other waves, sound waves are reflected, refracted, and diffracted, and exhibit interference. Reflection\nSound is constantly being reflected off many different... |
tc_2724 | What kind of animal is an iguana? | Reptile | [
"reptila",
"reptilian proteins",
"reptiles",
"hepatic piston",
"reptilia",
"reptile migration",
"reptile",
"reptile anatomy",
"class reptilia"
] | [
"Iguana (Iguana Iguana) - Animals - A-Z Animals - Animal ...\n\nIguana (Iguana Iguana) - Animals - A-Z Animals\nFive groups that classify all living things\nAnimalia\nA group of animals within the animal kingdom\nChordata\nA group of animals within a pylum\nReptilia\nA group of animals within a class\nSquamata\nA g... |
tc_2726 | What is the name given to the molten rock beneath the surface of the Earth? | Magma | [
"magma reservoir",
"magma rock",
"magmatic",
"melt geology",
"magmas",
"magma",
"partial magma"
] | [
"Rock (geology)\n\nIn geology, rock or stone is a naturally occurring solid aggregate of one or more minerals or mineraloids. For example, the common rock granite is a combination of the quartz, feldspar and biotite minerals. The Earth's outer solid layer, the lithosphere, is made of rock.",
"Rock (geology)\n\nRo... |
tc_2727 | Which disease is spread in minute water drops? | Legionnaire's disease | [
"legion fever",
"legionnaire s",
"legionnaires disease",
"legionaire s disease",
"legionaires disease",
"2015 san quentin legionnaires disease outbreaks",
"legionairres disease",
"legionairre s disease",
"legionnaires",
"legionnaire disease",
"legionnaire s disease",
"legionellosis",
"legion... | [
"CDC – Control of Infectious Diseases\n\nAchievements in Public Health, 1900-1999: Control of Infectious Diseases\nmmwrq@cdc.gov . Type 508 Accommodation and the title of the report in the subject line of e-mail. Achievements in Public Health, 1900-1999: Control of Infectious Diseases\nDeaths from infectious dise... |
tc_2729 | What is the strong inelastic material found in a human tendon? | Collagen | [
"atc code g04bx11",
"procollagen",
"collagen for wound healing",
"collagen fiber",
"collagenous",
"white fibres",
"zyderm ii",
"receptors collagen",
"type vii collagen",
"atcvet code qb02bc07",
"atcvet code qg04bx11",
"collagenous fibers",
"collagen fibrils",
"collagen fibers",
"atc code... | [
"Tendon\n\nA tendon or sinew is a tough band of fibrous connective tissue that usually connects muscle to bone and is capable of withstanding tension.",
"Tendon\n\nTendons are similar to ligaments; both are made of collagen. Ligaments join one bone to another bone, while tendons connect muscle to bone.",
"Tendo... |
tc_2730 | What material forms the hard outermost layer of a human tooth? | Enamel | [
"enamels",
"enamel",
"enamel disambiguation",
"enamelled"
] | [
"Human tooth\n\nThe human teeth function is mechanically breaking down items of food by cutting and crushing them in preparation for swallowing and digestion. There are four different types of teeth, namely incisors, canines, molars and premolars. Each type of tooth has a different job. The incisors cut the food, t... |
tc_2731 | Snowflakes are symmetrical. How many sides do they have? | Six | [
"six",
"6"
] | [
"Symmetry\n\nSymmetry (from Greek συμμετρία symmetria \"agreement in dimensions, due proportion, arrangement\") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, \"symmetry\" has a more precise definition, that an object is invariant to any of various trans... |
tc_2732 | What name is given to an atomic particle carrying a negative charge? | Electron | [
"negative electron",
"electron",
"antipositron",
"electron movement",
"beta minus particle",
"electron theory",
"electron lepton",
"negaton",
"mass of electron",
"electrons",
"electron mass"
] | [
"Subatomic particle\n\nIn the physical sciences, subatomic particles are particles much smaller than atoms. There are two types of subatomic particles: elementary particles, which according to current theories are not made of other particles; and composite particles. Particle physics and nuclear physics study the... |
tc_2733 | DNA is found in which part of the cell? | Nucleus | [
"nucleus disambiguation",
"nuecleus",
"nucleic",
"nucleus",
"nucleas",
"nucleus album",
"nuclei"
] | [
"DNA\n\nDeoxyribonucleic acid (; DNA) is a molecule that carries the genetic instructions used in the growth, development, functioning and reproduction of all known living organisms and many viruses. DNA and RNA are nucleic acids; alongside proteins and complex carbohydrates (polysaccharides), they are one of the... |
tc_2734 | By which name is the drug acetylsalicylic acid better known? | Aspirin | [
"junior aspirin",
"myoprin",
"nu seals aspirin",
"bufferin",
"acetylsalicylate",
"acetophen",
"salacetin",
"neuronika",
"empirin",
"kardegic",
"colfarit",
"8 hour bayer",
"pirseal",
"dolean ph 8",
"atcvet code qa01ad05",
"entericin",
"acetylsalicylic",
"dolopirin",
"baby aspirin"... | [
"Nomenclature\n\nNomenclature is a system of names or terms, or the rules for forming these terms in a particular field of arts or sciences. The principles of naming vary from the relatively informal conventions of everyday speech to the internationally agreed principles, rules and recommendations that govern the ... |
tc_2735 | How many legs has an insect? | Six | [
"six",
"6"
] | [
"Insect\n\nInsects (from Latin ', a calque of Greek ['], \"cut into sections\") are a class of invertebrates within the arthropod phylum that have a chitinous exoskeleton, a three-part body (head, thorax and abdomen), three pairs of jointed legs, compound eyes and one pair of antennae. They are the most diverse gr... |
tc_2739 | Which flower has the same name as a diaphragm in the eye? | Iris | [
"iris",
"iris band",
"iris song",
"iris disambiguation",
"iris genus"
] | [
"Human eye\n\nThe human eye is an organ that reacts to light and has several purposes. As a sense organ, the mammalian eye allows vision. Rod and cone cells in the retina allow conscious light perception and vision including color differentiation and the perception of depth. The human eye can distinguish about 10 ... |
tc_2741 | Which animals are arthropods and have eight legs? | Arachnids | [
"arachnidae",
"arachnids",
"arachnida",
"arachnid",
"list of false scorpions",
"list of common names for non scorpion arachnids commonly called scorpions",
"arachnicide"
] | [
"Arthropod\n\nAn arthropod (from Greek arthro-, joint + podos, foot) is an invertebrate animal having an exoskeleton (external skeleton), a segmented body, and jointed appendages (paired appendages). Arthropods form the phylum Arthropoda, which includes the insects, arachnids, myriapods, and crustaceans. \nArthropo... |
tc_2742 | Which is the modern scientific unit of work and energy? | Joule | [
"femtojoule",
"zettajoule",
"joule",
"kilojoule",
"joule unit",
"decijoule",
"nanojoule",
"terajoule",
"joules",
"zeptojoule",
"joule j",
"gigajoule",
"decajoule",
"yoctojoule",
"ocrajoule",
"petajoule",
"petajoules",
"zetajoule",
"exajoule",
"megajoule",
"μj",
"millijoule"... | [
"BBC Bitesize - KS3 Physics - Energy in the home - Revision 1\n\nBBC Bitesize - KS3 Physics - Energy in the home - Revision 1\nEnergy\nEnergy in the home\nEnergy is measured in J and kJ. Power is the rate of using energy, and is measured in W and kW. Fuel bills show energy used in kWh, and the cost of this can be c... |
tc_2743 | Chlorine, fluorine and bromine belong to which family of elements? | Halogens | [
"halogen group",
"halogens",
"hallogen",
"group 17 elements",
"halide group",
"halogen element",
"group 17 element",
"group 7a",
"group 17",
"halogen elements",
"fluorine family",
"dihalo",
"fluorine group",
"halogen"
] | [
"Chlorine\n\nChlorine is a chemical element with symbol Cl and atomic number 17. It has a relative atomic mass of about 35.5. Chlorine is in the halogen group (17) and is the second lightest halogen, following fluorine. The element is a yellow-green diatomic gas under standard conditions. Chlorine has the highest e... |
tc_2748 | Which was the first antibiotic to be discovered? | Penicillin | [
"penhexal vk",
"permapen",
"penniciline",
"crysticillin",
"penincillin",
"duracillin",
"penacillin",
"pfizerpen",
"penicillian",
"allergic to penicillin",
"pennicilin",
"pennicillin",
"penicilin",
"penicillin",
"pfizerpen g",
"penicilline",
"bicillin",
"peniciline",
"pfizerpen as... | [
"Antibiotics\n\nAntibiotics, also called antibacterials, are a type of antimicrobial drug used in the treatment and prevention of bacterial infections. They may either kill or inhibit the growth of bacteria. A limited number of antibiotics also possess antiprotozoal activity. Antibiotics are not effective agai... |
tc_2750 | What is the boiling point of water? | 100 degrees Celsius | [
"one hundred temp",
"100 degrees celsius",
"100 temp"
] | [
"What Is the Boiling Point of Water? - About.com Education\n\nWhat Is the Boiling Point of Water? What Is the Boiling Point of Water? What Is the Boiling Point of Water? Boiling Point of Water\nThe boiling point of water is 100 degrees Celsius or 212 degrees Fahrenheit at 1 atmosphere of pressure (sea level). Jody ... |
tc_2751 | Ascorbic acid is which vitamin? | Vitamin C | [
"kyselina askorbova",
"vitamin c",
"scorbacid",
"cebicure",
"vitamin c foundation",
"vitacimin",
"cescorbat",
"ciamin",
"cebion",
"cecon",
"ascorbicap",
"vitamisin",
"list of foods containing vitamin c",
"xitix",
"cetebe",
"cetamid",
"cetane caps td",
"antiscorbic vitamin",
"ceve... | [
"Ascorbic acid\n\nAscorbic acid is a naturally occurring organic compound with antioxidant properties. It is a white solid, but impure samples can appear yellowish. It dissolves well in water to give mildly acidic solutions. Ascorbic acid is one form (\"vitamer\") of vitamin C. It was originally called L-hexuronic... |
tc_2753 | What is the generic term for the mechanical, electrical and electronic components of a computer? | Hardware | [
"hardware disambiguation",
"hardware system",
"hardware"
] | [
"Computer\n\nA computer is a device that can be instructed to carry out an arbitrary set of arithmetic or logical operations automatically. Their ability to follow a sequence of operations, called a program, make computers very flexible and popular. Such computers are used as control systems for a very wide variety... |
tc_2754 | Whose research on X-ray diffraction of ?DNA crystals helped Crick and Watson during the race to discover the structure of DNA? | Rosalind Franklin | [
"rosland franklin",
"king s college london dna controversy",
"franklin rosalind",
"rosalind franklin",
"rosalynd franklin",
"rosalind elsie franklin",
"roslayn franklin",
"king s college dna controversy",
"rosalyn franklin",
"rosalind frankin",
"rosland elise franklin",
"rosalind e franklin"
] | [
"X-ray crystallography\n\nX-ray crystallography is a tool used for identifying the atomic and molecular structure of a crystal, in which the crystalline atoms cause a beam of incident X-rays to diffract into many specific directions. By measuring the angles and intensities of these diffracted beams, a crystallograp... |
tc_2755 | Heisenberg is most associated with which branch of physics? | Quantum Mechanics | [
"quantum physical",
"quantam physics",
"quantum mechenics",
"quantum theory",
"quantum physicist",
"quantum dislocation",
"quantum effects",
"quantum mechanical laws",
"quantum hypothesis",
"nonrelativistic quantum theory",
"quantum mechanical",
"quantum mechanic",
"classical quantum mechani... | [
"Werner Heisenberg\n\nWerner Karl Heisenberg (; 5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the key pioneers of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent series of papers with Max Born and Pascual Jordan, during the same year, t... |
tc_2756 | What did Heike Kamerlingh-Onnes discover? | Superconductivity | [
"super conduction manipulation",
"supraconductivity",
"superconducting transition",
"superconduction",
"super conductivity",
"superconducting",
"superconductor engineering",
"super conductors",
"superconductivivty",
"superconductive",
"superconductor engineer",
"superconducting engineer",
"s... | [
"Heike Kamerlingh Onnes\n\nHeike Kamerlingh Onnes (; 21 September 1853 – 21 February 1926) was a Dutch physicist and Nobel laureate. He exploited the Hampson-Linde cycle to investigate how materials behave when cooled to nearly absolute zero and later to liquefy helium for the first time. His production of extreme ... |
tc_2757 | What science is the study of missiles in motion? | Ballistics | [
"science of bullet",
"ballistic trajectories",
"ballistics",
"firearm and tool mark examiners",
"ballistically",
"ballistics test",
"ballistic vehicle",
"forensic ballistics",
"criminal ballistics",
"ballistic body"
] | [
"ballistics - Infoplease\n\nballistics\nEncyclopedia > Science and Technology > Physics > Physics\nballistics\nballistics (bəlĭsˈtĭks) [ key ], science of projectiles. Interior ballistics deals with the propulsion and the motion of a projectile within a gun or firing device. Its problems include the ignition ... |
tc_2759 | What kind of elements are found in a pure state in nature? | Native elements | [
"native elements"
] | [
"Chemical element\n\nA chemical element or element is a species of atoms having the same number of protons in their atomic nuclei (i.e. the same atomic number, Z). There are 118 elements that have been identified, of which the first 94 occur naturally on Earth with the remaining 24 being synthetic elements. There ... |
tc_2760 | "What are classified by their measurement in degrees as ""right"", ""reflex"", ""obtuse"", or ""acute""?" | Angles | [
"angles",
"anglii",
"angles people",
"angle tribe",
"angili",
"angli",
"angles tribe"
] | [
"Degree (angle)\n\nA degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of plane angle, defined by representing a full rotation as 360 degrees.",
"Degree (angle)\n\nIt is not an SI unit, as the SI unit for angles is radian, but it is mentioned i... |
tc_2761 | What is the name given to the longest side of a right-angled triangle? | Hypotenuse | [
"hypothenuse",
"hypotenuse",
"hypoteneuse",
"hypotenus"
] | [
"Right triangle\n\nA right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry.",
"Right triangle\n\nThe side opposite the... |
tc_2762 | Which Swedish scientist had a temperature scale named after him? | Anders Celsius | [
"celsius anders",
"anders celsius"
] | [
"Carl Linnaeus\n\nCarl Linnaeus (; 23 May 1707 – 10 January 1778), also known after his ennoblement as Carl von Linné , was a Swedish botanist, physician, and zoologist, who formalised the modern system of naming organisms called binomial nomenclature. He is known by the epithet \"father of modern taxonomy\". Man... |
tc_2763 | How many colors are there in the spectrum when white light is separated? | Seven | [
"seven",
"7"
] | [
"Color\n\nColor (American English) or colour (Commonwealth English) is the visual perceptual property corresponding in humans to the categories called red, blue, yellow, etc. Color derives from the spectrum of light (distribution of light power versus wavelength) interacting in the eye with the spectral sensitiviti... |
tc_2765 | The discovery of which law provoked the surprised cry 'Eureka!'? | Archimedes Principle | [
"principle of displacement",
"archimedes principle",
"archemedes principle",
"archemides principle"
] | [
"PHYSICS FOLIO |authorSTREAM\n\nPHYSICS FOLIO |authorSTREAM\nPHYSICS FOLIO\n Does not support media & animations\n Automatically changes to Flash or non-Flash embed\n The presentation is successfully added In Your Favorites . Views:\n This Presentation is Public Favorites: \n0\nENTRY NO. 1: Physics A Natura... |
tc_2768 | What is the study and use of frequencies above 20 khz? | Ultrasonic's | [
"from sound to image",
"ultrasonics",
"ultrasonic wave",
"ultrasound",
"ultra sound",
"ultrasonic s",
"biomedical ultrasonic",
"ultrasounds",
"industrial ultrasonography",
"ultrsound",
"ultrasound ct"
] | [
"Hertz\n\nThe hertz (symbol Hz) is the unit of frequency in the International System of Units (SI) and is defined as one cycle per second. It is named for Heinrich Rudolf Hertz, the first person to provide conclusive proof of the existence of electromagnetic waves.",
"Hertz\n\nSome of the unit's most common uses... |
tc_2769 | What is an unchanging position in which forces cancel each other out? | Equilibrium | [
"equilibration",
"equilibrium disambiguation",
"equilibrium album",
"equilibrium",
"equilibria",
"position of equilibrium",
"equillibrium"
] | [
"Equilibria - definition of equilibria by The Free Dictionary\n\nEquilibria - definition of equilibria by The Free Dictionary\nEquilibria - definition of equilibria by The Free Dictionary\nhttp://www.thefreedictionary.com/equilibria\nRelated to equilibria: Punctuated equilibria\ne·qui·lib·ri·um\n (ē′kwə-lĭb′rē-əm, ... |
tc_2770 | Which physicist's law states that equal volumes of all gases, measured at the same temperature and pressure, contain the same number of molecules? | Amadeo Avogadro | [
"avogadro amadeo",
"conte di quaregna e ceretto",
"amedeo avogadro",
"lorenzo romano amedeo carlo avogadro",
"count lorenzo romano amedeo carlo avogadro di quaregna e cerreto",
"amedeo avogadro conte de quaregna",
"lorenzo romano amedeo carlo avogadro di quaregna e cerreto",
"amadeo avogadro",
"avog... | [
"Gas\n\nGas is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or compound molecules made from a variety of atoms (e.g. carbon dioxide)... |
tc_2771 | What is the ability of fluids to offer resistance to flow? | Viscosity | [
"inviscid",
"coefficient of viscosity",
"dynamic kinematic viscosity",
"viscous shear",
"viscosity",
"kinematic viscosity",
"pa·s",
"pascal second",
"sutherland s formula",
"eddy viscosity",
"centistoke",
"viscous force",
"rhe",
"inviscid fluid",
"millipoiseuille",
"centistokes",
"pa... | [
"Fluid\n\nIn physics, a fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids. Fluids are substances that have zero shear modulus or, in simpler terms, a fluid is a sub... |
tc_2773 | What is described as an ionized gas with approximately equal numbers of positive and negative charges? | Plasma | [
"plasmas",
"plasma biology",
"plasma disambiguation",
"biological plasma",
"plasm",
"plasma"
] | [
"Plasma (physics)\n\nPlasma (from Greek πλάσμα, \"anything formed\" ) is one of the four fundamental states of matter, the others being solid, liquid, and gas. A plasma has properties unlike those of the other states.",
"Plasma (physics)\n\nA plasma can be created by heating a gas or subjecting it to a strong ele... |
tc_2774 | What name is given to the very serious chain of events which can follow the failure of the cooling system in a nuclear reactor? | Meltdown | [
"meltdown song",
"meltdown disambiguation",
"meltdown album",
"melt down",
"meltdown"
] | [
"Nuclear reactor\n\nThis article is a subarticle of Nuclear power.",
"Nuclear reactor\n\nA nuclear reactor, formerly known as an atomic pile, is a device used to initiate and control a sustained nuclear chain reaction. Nuclear reactors are used at nuclear power plants for electricity generation and in propulsion ... |
tc_2775 | Which electronic device magnifies the strength of a signal? | Amplifier | [
"common plate",
"class c amplifier",
"power amplifier",
"penguat peralatan",
"electronic amplifier",
"class b amplifier",
"class ab",
"amplifier stage",
"piezo audio amplifier",
"common cathode",
"single stage amplifier",
"class amplifier",
"class ab amplifier",
"common grid",
"piezoelec... | [
"Electronics\n\nElectronics is the science of how to control electric energy, energy in which the electrons have a fundamental role. Electronics deals with electrical circuits that involve active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive electric... |
tc_2776 | What was the name of the unit of heat now replaced by the joule? | Calorie | [
"㎉",
"kcals",
"nutritional calories",
"calorific",
"large calorie",
"nutritional calorie",
"small calorie",
"thermochemical calorie",
"callories",
"calories",
"gigacalorie",
"calory",
"calorie nutrition",
"㎈",
"kilogram calorie",
"kilocalorie",
"gram calorie",
"kilocalories",
"th... | [
"Joule\n\nThe joule, symbol J, is a derived unit of energy in the International System of Units. It is equal to the energy transferred (or work done) to an object when a force of one newton acts on that object in the direction of its motion through a distance of one metre (1 newton metre or N·m). It is also the en... |
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