An Iterative Method for Computing π by Argument Reduction of the Tangent Function-Reference-Cited by-同舟云学术

An Iterative Method for Computing π by Argument Reduction of the Tangent Function

Published:2024-02-25 Issue:2 Volume:29 Page:17
ISSN:2297-8747
Container-title:Mathematical and Computational Applications
language:en
Short-container-title:MCA

Author:

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

Affiliation:

1. Algonquin Radio Observatory, Thoth Technology Inc., 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 develop a new iterative method for computing the digits of π by argument reduction of the tangent function. This method combines a modified version of the iterative formula for π with squared convergence that we proposed in a previous work and a leading arctangent term from the Machin-like formula. The computational test we performed shows that algorithmic implementation can provide more than 17 digits of π per increment. Mathematica codes, showing the convergence rate for computing the digits of π, are presented.

Publisher

MDPI AG

Link

https://www.mdpi.com/2297-8747/29/2/17/pdf

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