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

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 squar...

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Bibliographic Details
Published in:AppliedMath 2024-09, Vol.4 (3), p.868-888
Main Authors: Abrarov, Sanjar M., Siddiqui, Rehan, Jagpal, Rajinder Kumar, Quine, Brendan M.
Format: Article
Language:English
Subjects:
constant pi
iteration
nested radicals
rational approximation
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Summary: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.
ISSN:2673-9909
2673-9909
DOI:10.3390/appliedmath4030047