Circle inner reflections.ipynb

Kernel: Python 3 (system-wide)

$$\text{\Huge Inner Circle Reflections}$$

import numpy as np
import matplotlib.pyplot as plt
from numpy import pi

def generate(initial_rad_position, deflection, number_of_points):
    XPoints = [0]*number_of_points
    YPoints = [0]*number_of_points
    angle = initial_rad_position
    for i in range(number_of_points):
        XPoints[i] = np.cos(angle)
        YPoints[i] = np.sin(angle)
        angle = 2 * deflection + angle
    return (XPoints, YPoints)

def plot(angle,bounces):
    fig, ax = plt.subplots(figsize=(7,7))
    ax.set_aspect('equal')
    ax.autoscale()

    x=np.linspace(-1,1,500)
    y_1 = np.sqrt(1-x**2)
    y_2 = -np.sqrt(1-x**2)

    ax.plot(x,y_1,'k');
    ax.plot(x,y_2,'k');
    ax.plot(*generate(0,angle,bounces));

plot(1,100)
plot(pi/6,100)
plot(2*pi/5,100)

plot(11*np.pi/21,100)