add py file

Author: j2doll

polygon.circle.py

@@ -0,0 +1,64 @@
+
+# polygon.circle.py
+
+import math
+import matplotlib.pyplot as plt
+
+def calculate_radii(s, n):
+    # Calculate the radius R of the circumcircle
+    R = s / (2 * math.sin(math.pi / n))
+    # Calculate the radius r of the inscribed circle
+    r = s / (2 * math.tan(math.pi / n))
+    return R, r
+
+def plot_polygon_and_circles(s, n):
+    R, r = calculate_radii(s, n)
+    
+    # Calculate vertex coordinates of regular polygons
+    vertices = [
+        (R * math.cos(2 * math.pi * i / n), R * math.sin(2 * math.pi * i / n))
+        for i in range(n)
+    ]
+    vertices.append(vertices[0])  # Add the first point for closed shapes
+
+    # Plot Settings
+    fig, ax = plt.subplots()
+    ax.set_aspect('equal')
+    ax.grid(True, which='both')
+
+    # Drawing an extracorporeal circle
+    outer_circle = plt.Circle((0, 0), R, color='blue', fill=False, linestyle='--', label='Circle circumscribed by a polygon')
+    ax.add_artist(outer_circle)
+
+    # Draw an inversion circle
+    inner_circle = plt.Circle((0, 0), r, color='red', fill=False, linestyle='--', label='Circle inscribed in a polygon')
+    ax.add_artist(inner_circle)
+
+    # Draw regular polygons
+    polygon = plt.Polygon(vertices, edgecolor='green', fill=None, label=f'Definite {n} polygon')
+    ax.add_artist(polygon)
+
+    # axis setting
+    max_radius = max(R, r)
+    ax.set_xlim(-max_radius * 1.1, max_radius * 1.1)
+    ax.set_ylim(-max_radius * 1.1, max_radius * 1.1)
+
+    # Add legend
+    ax.legend()
+
+    # Plot display
+    plt.title(f'Definite {n} squares with side length {s} and other inscribed and inscribed circles')
+    plt.xlabel('X coordinate')
+    plt.ylabel('Y coordinate')
+    plt.show()
+
+# User Input
+s = float(input("Enter the length s of one side of a regular polygon: "))
+n = int(input("Enter the number n of sides of a regular polygon (in integers greater than three): "))
+
+if n < 3:
+    print("n must be an integer greater than or equal to 3.")
+else:
+    plot_polygon_and_circles(s, n)
+
+