A rational approximation of the two-term Machin-like formula for $π$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910539747164160 |
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| author | Abrarov, Sanjar M. Siddiqui, Rehan Jagpal, Rajinder Kumar Quine, Brendan M. |
| author_facet | Abrarov, Sanjar M. Siddiqui, Rehan Jagpal, Rajinder Kumar Quine, Brendan M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08510 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A rational approximation of the two-term Machin-like formula for $π$ Abrarov, Sanjar M. Siddiqui, Rehan Jagpal, Rajinder Kumar Quine, Brendan M. General Mathematics 11Y60 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. |
| title | A rational approximation of the two-term Machin-like formula for $π$ |
| topic | General Mathematics 11Y60 |
| url | https://arxiv.org/abs/2406.08510 |