π$的两期马钦式的合理近似值

arXiv - MATH - General Mathematics Pub Date : 2024-06-07 DOI:arxiv-2406.08510

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

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摘要

在这项工作中，我们考虑了双项马钦类公式的性质，并开发了一种利用其有理近似值计算 $\pi$ 位数的算法。在这种近似中，两个项都是通过使用二进制形式的 1/\pi$ 来构造的。这种方法在计算 $\pi$ 的位数时提供了平方收敛性，而不需要任何三角函数和苏德数。本文给出了一些示例的 Mathematica 代码。

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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 $\pi$ by using its rational approximation. In this approximation, both terms are constructed by using a representation of $1/\pi$ in the binary form. This approach provides the squared convergence in computing digits of $\pi$ without any trigonometric functions and surd numbers. The Mathematica codes showing some examples are presented.

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arXiv - MATH - General Mathematics

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