AppliedMath (Jul 2024)

A Rational Approximation of the Two-Term Machin-like Formula for <i>π</i>

  • Sanjar M. Abrarov,
  • Rehan Siddiqui,
  • Rajinder Kumar Jagpal,
  • Brendan M. Quine

DOI
https://doi.org/10.3390/appliedmath4030047
Journal volume & issue
Vol. 4, no. 3
pp. 868 – 888

Abstract

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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.

Keywords