polygon.circle.py

# 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)