A rational approximation of the two-term Machin-like formula for $π$

Fuente: arXiv
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Bibliographic Details
Main Authors: Abrarov, Sanjar M., Siddiqui, Rehan, Jagpal, Rajinder Kumar, Quine, Brendan M.
Format: Preprint
Published: 2024
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author Abrarov, Sanjar M.
Siddiqui, Rehan
Jagpal, Rajinder Kumar
Quine, Brendan M.
author_facet Abrarov, Sanjar M.
Siddiqui, Rehan
Jagpal, Rajinder Kumar
Quine, Brendan M.
contents In this work, we consider the properties of the two-term Machin-like formula and develop an algorithm for computing digits of $π$ by using its rational approximation. In this approximation, both terms are constructed by using a representation of $1/π$ in the binary form. This approach provides the squared convergence in computing digits of $π$ without any trigonometric functions and surd numbers. The Mathematica codes showing some examples are presented.
format Preprint
id arxiv_https___arxiv_org_abs_2406_08510
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A rational approximation of the two-term Machin-like formula for $π$
Abrarov, Sanjar M.
Siddiqui, Rehan
Jagpal, Rajinder Kumar
Quine, Brendan M.
General Mathematics
11Y60
In this work, we consider the properties of the two-term Machin-like formula and develop an algorithm for computing digits of $π$ by using its rational approximation. In this approximation, both terms are constructed by using a representation of $1/π$ in the binary form. This approach provides the squared convergence in computing digits of $π$ without any trigonometric functions and surd numbers. The Mathematica codes showing some examples are presented.
title A rational approximation of the two-term Machin-like formula for $π$
topic General Mathematics
11Y60
url https://arxiv.org/abs/2406.08510