Update app.py

app.py

@@ -10,7 +10,10 @@ def calculate_distance(x1, y1, x2, y2):
 
 # Function to calculate angles using the Law of Cosines
 def calculate_angle(a, b, c):
-    angle = math.degrees(math.acos((b ** 2 + c ** 2 - a ** 2) / (2 * b * c)))
+    try:
+        angle = math.degrees(math.acos((b ** 2 + c ** 2 - a ** 2) / (2 * b * c)))
+    except ValueError:
+        angle = 0  # Handle possible domain error in acos
     return angle
 
 # Function to calculate area using Heron's formula
@@ -25,21 +28,21 @@ def calculate_perimeter(a, b, c):
 
 # Function to calculate the radius of the inscribed circle
 def calculate_radius_inscribed_circle(a, b, c):
-    s = (a + b + c) / 2
-    area = calculate_area(a, b, c)
     try:
+        s = (a + b + c) / 2
+        area = calculate_area(a, b, c)
         radius = area / s
     except ZeroDivisionError:
-        radius = 0
+        radius = 0  # Handle case where area or perimeter is zero
     return radius
 
 # Function to calculate the radius of the circumscribed circle
 def calculate_radius_circumscribed_circle(a, b, c):
-    area = calculate_area(a, b, c)
     try:
+        area = calculate_area(a, b, c)
         radius = (a * b * c) / (4 * area)
     except ZeroDivisionError:
-        radius = 0
+        radius = 0  # Handle case where area is zero
     return radius
 
 # Function to calculate the centroid coordinates
@@ -54,7 +57,7 @@ def calculate_incenter(x1, y1, x2, y2, x3, y3, a, b, c):
         I_x = (a * x1 + b * x2 + c * x3) / (a + b + c)
         I_y = (a * y1 + b * y2 + c * y3) / (a + b + c)
     except ZeroDivisionError:
-        I_x, I_y = 0, 0
+        I_x, I_y = 0, 0  # Handle division by zero if sides sum to zero
     return I_x, I_y
 
 # Function to calculate the circumcenter coordinates
@@ -64,9 +67,22 @@ def calculate_circumcenter(x1, y1, x2, y2, x3, y3, a, b, c):
         Ux = ((x1**2 + y1**2) * (y2 - y3) + (x2**2 + y2**2) * (y3 - y1) + (x3**2 + y3**2) * (y1 - y2)) / D
         Uy = ((x1**2 + y1**2) * (x3 - x2) + (x2**2 + y2**2) * (x1 - x3) + (x3**2 + y3**2) * (x2 - x1)) / D
     except ZeroDivisionError:
-        Ux, Uy = 0, 0
+        Ux, Uy = 0, 0  # Handle division by zero in circumcenter calculation
     return Ux, Uy
 
+# Function to calculate midpoints of sides
+def calculate_midpoints(x1, y1, x2, y2, x3, y3):
+    # Midpoint of AB
+    M1_x = (x1 + x2) / 2
+    M1_y = (y1 + y2) / 2
+    # Midpoint of BC
+    M2_x = (x2 + x3) / 2
+    M2_y = (y2 + y3) / 2
+    # Midpoint of CA
+    M3_x = (x3 + x1) / 2
+    M3_y = (y3 + y1) / 2
+    return (M1_x, M1_y), (M2_x, M2_y), (M3_x, M3_y)
+
 # Function to format values close to zero as 0
 def format_zero(val):
     if abs(val) < 1e-6:
@@ -74,40 +90,47 @@ def format_zero(val):
     return val
 
 # Function to plot the triangle with all points in different colors and a legend
-def plot_triangle(x1, y1, x2, y2, x3, y3, I_x, I_y, Ux, Uy, G_x, G_y):
+def plot_triangle(x1, y1, x2, y2, x3, y3, I_x, I_y, Ux, Uy, G_x, G_y, midpoints):
     fig, ax = plt.subplots(figsize=(8, 6))
     triangle = Polygon([(x1, y1), (x2, y2), (x3, y3)], closed=True, edgecolor='b', facecolor='lightblue')
     ax.add_patch(triangle)
     
     # Define colors for different points
     vertex_color = 'blue'
-    centroid_color = 'green'
+    centroid_color = 'orange'
     incenter_color = 'red'
     circumcenter_color = 'purple'
-    
+    midpoint_color = 'green'
+
     # Plot the triangle vertices
     vertices = [(x1, y1), (x2, y2), (x3, y3)]
+    vertex_labels = [f"Vertex A ({x1:.1f}, {y1:.1f})", f"Vertex B ({x2:.1f}, {y2:.1f})", f"Vertex C ({x3:.1f}, {y3:.1f})"]
     for i, (vx, vy) in enumerate(vertices):
         ax.scatter(vx, vy, color=vertex_color, zorder=5)
-        ax.text(vx, vy, f"({vx:.1f}, {vy:.1f})", fontsize=10, ha="left", va="bottom", color=vertex_color)
-    
+        
     # Plot key points with their corresponding colors
     key_points = [
-        (I_x, I_y, incenter_color, "Incenter"),
-        (Ux, Uy, circumcenter_color, "Circumcenter"),
-        (G_x, G_y, centroid_color, "Centroid")
+        (I_x, I_y, incenter_color),
+        (Ux, Uy, circumcenter_color),
+        (G_x, G_y, centroid_color)
     ]
     
-    for x, y, color, label in key_points:
+    for x, y, color in key_points:
         ax.scatter(x, y, color=color, zorder=5)
-        ax.text(x, y, f"{label}\n({x:.1f}, {y:.1f})", fontsize=10, ha="left", va="bottom", color=color)
+        ax.text(x, y, fontsize=10, ha="left", va="bottom", color=color)
+
+    # Plot midpoints of sides
+    for i, (mx, my) in enumerate(midpoints):
+        ax.scatter(mx, my, color=midpoint_color, zorder=5)
+        ax.text(mx, my, fontsize=10, ha="left", va="bottom", color=midpoint_color)
     
     # Add legend
     handles = [
         plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=vertex_color, markersize=10, label="Vertices"),
         plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=centroid_color, markersize=10, label="Centroid"),
         plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=incenter_color, markersize=10, label="Incenter"),
-        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=circumcenter_color, markersize=10, label="Circumcenter")
+        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=circumcenter_color, markersize=10, label="Circumcenter"),
+        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=midpoint_color, markersize=10, label="Midpoints")
     ]
     ax.legend(handles=handles, loc='upper left', fontsize=12)
     
@@ -124,6 +147,11 @@ def plot_triangle(x1, y1, x2, y2, x3, y3, I_x, I_y, Ux, Uy, G_x, G_y):
     plt.grid(True)
     st.pyplot(fig)
 
+# Function to check if the sides form a valid triangle
+def is_valid_triangle(a, b, c):
+    # Check if the sum of two sides is greater than the third side (Triangle Inequality Theorem)
+    return a + b > c and b + c > a and c + a > b
+
 # Main function to interact with the user
 def main():
     st.title("Advanced Triangle Solver")
@@ -144,11 +172,21 @@ def main():
         b = calculate_distance(x1, y1, x3, y3)
         c = calculate_distance(x1, y1, x2, y2)
 
+        # Validate if it's a valid triangle
+        if not is_valid_triangle(a, b, c):
+            st.error("The entered points do not form a valid triangle.")
+            return
+        
         # Calculate angles using the Law of Cosines
         A = calculate_angle(a, b, c)
         B = calculate_angle(b, a, c)
         C = calculate_angle(c, a, b)
 
+        # Check if angles sum up to 180 degrees
+        if abs(A + B + C - 180) > 1e-2:
+            st.error("The sum of the angles is not 180 degrees.")
+            return
+
         # Calculate area, perimeter, and radius of inscribed and circumscribed circles
         area = calculate_area(a, b, c)
         perimeter = calculate_perimeter(a, b, c)
@@ -160,6 +198,9 @@ def main():
         I_x, I_y = calculate_incenter(x1, y1, x2, y2, x3, y3, a, b, c)
         Ux, Uy = calculate_circumcenter(x1, y1, x2, y2, x3, y3, a, b, c)
 
+        # Calculate midpoints of the sides
+        midpoints = calculate_midpoints(x1, y1, x2, y2, x3, y3)
+
         # Display results in columns
         col1, col2, col3 = st.columns(3)
         
@@ -199,8 +240,8 @@ def main():
             st.markdown(f"Perimeter: **{perimeter:.3f}** units")
             st.markdown(f"Centroid: **({G_x:.3f}, {G_y:.3f})**")
 
-        # Display triangle graph with colored points and legend
-        plot_triangle(x1, y1, x2, y2, x3, y3, I_x, I_y, Ux, Uy, G_x, G_y)
+        # Display triangle graph with midpoints and colored points
+        plot_triangle(x1, y1, x2, y2, x3, y3, I_x, I_y, Ux, Uy, G_x, G_y, midpoints)
 
 if __name__ == "__main__":
     main()