A rational approximation of the two-term Machin-like formula for $\pi$

Abstract

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.

30 pages

References in corpus (2)

• A generalized series expansion of the arctangent function based on the enhanced midpoint integration
• Algorithmic determination of a large integer in the two-term Machin-like formula for pi