Functions and Analysis

    

Approximating Roots and π Using Pythagorean Triples

Authors: Joseph Bakhos

Methods approximating the square root of a number use recursive sequences. They do not have a simpleformula for generating the seed value for the approximation, so instead they use various algorithms for choosing the first term of the sequences. Section 1 introduces a new option, based upon the number of digits of the radicand, for selecting the first term. This new option works well at all scales. This first term will then be used in a traditional recursive sequence used to approximate roots. Section 2 will apply the method shown in Section 1 to approximate pi using Archimedes’ method, which then no longer requires different algorithms at different scales for seed values. Section 3 will introduce new recursive sequences for approximating rootsusing Pythagorean triples. Section 4 will then use the same new method to approximate pi.

Comments: 7 Pages. Published December 18, 2022: Applied Mathematical Sciences, Vol. 16, 2022, no. 12, 665-677 doi: 10.12988/ams.2022.917217 Link: http://www.m-hikari.com/ams/ams-2022/ams-9-12-2022/p/bakhosAMS9-12-2022.pdf

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Submission history

[v1] 2022-08-05 00:47:45
[v2] 2022-08-16 20:38:56
[v3] 2022-10-29 19:20:21

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