import numpy as np
import matplotlib.pyplot as plt

n_max = 5.0

def square_root_seg(a, x_0):
    x_n = x_0

    while True:
        yield x_n
        x_n = (x_n + a / x_n) / 2.0

ns = np.arange(0, n_max + 0.01, 1.)

plt.plot([0,n_max],[np.sqrt(2),np.sqrt(2)], color="black")

for x_0 in [ 2.0, 4.0, 8.0 ]:
    xs = np.fromiter(square_root_seg(2.0, x_0), np.float, ns.size)
    plt.plot(ns, xs, "o", label="$x_0=%d$" % int(x_0))

plt.text(7.2, np.sqrt(2)-0.1, "$\sqrt{2}$")
plt.legend(loc='upper right')
plt.savefig("Examples for calculating the square root of 2 with Heron's method.svg")