A Rational Approximation of the Two-Term Machin-like Formula for π-Reference-Cited by-同舟云学术

A Rational Approximation of the Two-Term Machin-like Formula for π

Published:2024-07-19 Issue:3 Volume:4 Page:868-888
ISSN:2673-9909
Container-title:AppliedMath
language:en
Short-container-title:AppliedMath

Author:

Abrarov Sanjar M.¹²³,Siddiqui Rehan²³⁴^ORCID,Jagpal Rajinder Kumar²⁴,Quine Brendan M.¹³⁴

Affiliation:

1. Thoth Technology Inc., Algonquin Radio Observatory, Achray Rd., RR6, Pembroke, ON K8A 6W7, Canada

2. Epic College of Technology, 5670 McAdam Rd., Mississauga, ON L4Z 1T2, Canada

3. Department Earth and Space Science and Engineering, York University, 4700 Keele St., Toronto, ON M3J 1P3, Canada

4. Department Physics and Astronomy, York University, 4700 Keele St., Toronto, ON M3J 1P3, Canada

Abstract

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.

Publisher

MDPI AG

Link

https://www.mdpi.com/2673-9909/4/3/47/pdf

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