Hexagon radius approximation

import matplotlib.pyplot as plt
import numpy as np

f = np.linspace(0,  np.pi *2,num= 100)

x = np.sin(f)
y = np.cos(f)

z = np.zeros(100) # approximation of f from coordinates
scale2 = np.zeros(100)

for i in range(100):
    yy = np.abs(y[i])
    xx = np.abs(x[i])
    if xx > yy:
        temp = yy/xx
        z[i] = -(0.97239411 + -0.19194795 * temp * temp) * temp + np.pi/2
    else:
        temp = xx/yy
        z[i] =  (0.97239411 + -0.19194795 * temp * temp) * temp

    w = z[i]
    ww = w*w
    sinw = w * (1 - ww *(1 / 6 - ww/120 ))
    sin3w = 3*sinw - 4* sinw* sinw* sinw
    scale2[i] = 1 - np.abs(sin3w) *  (1-np.cos( np.pi / 6))
    #scale2 = 1 - np.abs(np.sin(nofpoints/2*z))* (1-np.cos( np.pi / nofpoints))




plt.figure(figsize=(10,10))

f2 = np.linspace(0,  np.pi *2,num= 7)
plt.plot(np.sin(f2), np.cos(f2))

plt.plot(np.multiply(x, scale2), np.multiply(y, scale2))
plt.plot(np.multiply(x, scale2)*1.25, np.multiply(y, scale2)*1.25)


plt.xlim([-1.5, 1.5])
plt.ylim([-1.5, 1.5])

plt.show()