File:Examples for calculating the square root of 2 with Heron's method.svg

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Description
English: First elements of the sequence we get, when we calculate with Heron's Method via the recursion with the starting points , and .
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Source Own work
Author Stephan Kulla (User:Stephan Kulla)
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Python code

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")

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I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

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Date/TimeThumbnailDimensionsUserComment
current20:15, 13 May 2016Thumbnail for version as of 20:15, 13 May 2016720 × 540 (28 KB)Stephan Kulla (talk | contribs)lesser elements...
20:06, 13 May 2016Thumbnail for version as of 20:06, 13 May 2016720 × 540 (30 KB)Stephan Kulla (talk | contribs)User created page with UploadWizard

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