Satz von Thales

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%matplotlib notebook


    

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import numpy as np
import numpy.linalg as la

import matplotlib.pyplot as plt
from matplotlib.patches import Arc

alpha = 60.
alp = alpha * np.pi/180.
x0 = np.sin(alp)
y0 = np.cos(alp)

fig = plt.figure(1)
ax = fig.gca()
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_xlim(-1.25, 1.25)
ax.set_ylim(-1.25, 1.25)
ax.set_aspect('equal')
ax.scatter(-x0, -y0)
ax.scatter(x0, -y0)
ax.plot([-x0, x0], [-y0, -y0])


    

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def onclick(event):
    delta = 5 * np.pi/180.
    
    x_data = event.xdata
    y_data = event.ydata
    r_data = np.sqrt(x_data**2+y_data**2)
    phi_data = np.arctan2(y_data, x_data)
    
    alp_data = (x_data+x0)*(x_data-x0) + (y_data+y0)**2
    alp_data /= np.sqrt((x_data+x0)**2+(y_data+y0)**2)
    alp_data /= np.sqrt((x_data-x0)**2+(y_data+y0)**2)
    alp_data = np.arccos(alp_data)
    print 'alpha = {}'.format(alp_data*180./np.pi)
    
    if alp_data > alp-delta and alp_data < alp+delta:
        plt.scatter(x_data, y_data, c='g')
        x = [-x0, x_data]
        y = [-y0, y_data]
        plt.plot(x, y, 'g')
        x = [x0, x_data]
        y = [-y0, y_data]
        plt.plot(x, y, 'g')

cid = fig.canvas.mpl_connect('button_press_event', onclick)


    

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ax.scatter(0., 0.)
x = [-x0, 0.]
y = [-y0, 0.]
ax.plot(x, y, 'b')
x = [x0, 0.]
y = [-y0, 0.]
ax.plot(x, y, 'b')

arc = Arc((0., 0.), 2., 2., 0., alpha-90., 270.-alpha, color='k', fill=False)
ax.add_artist(arc)


    

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