File:Examples for calculating the square root of 2 with Heron's method.svg
Summary
| Description |
English: First elements of the sequence we get, when we calculate with Heron's Method via the recursion with the starting points , and . |
| Date | |
| Source | Own work |
| Author | Stephan Kulla (User:Stephan Kulla) |
| SVG development | |
| Source code | Python codeimport 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")
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Licensing
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