A proof of irrationality of $π$ based on the nested radicals with roots of $2$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917384572370944 |
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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 prove the irrationality of $π$ based on the nested radicals with roots of $2$ of kind $c_k = \sqrt{2 + c_{k - 1}}$ and $c_0 = 0$. Sample computations showing how the rational approximation tends to $π$ with increasing the integer $k$ are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21776 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A proof of irrationality of $π$ based on the nested radicals with roots of $2$ Abrarov, Sanjar M. Siddiqui, Rehan Jagpal, Rajinder Kumar Quine, Brendan M. General Mathematics In this work, we prove the irrationality of $π$ based on the nested radicals with roots of $2$ of kind $c_k = \sqrt{2 + c_{k - 1}}$ and $c_0 = 0$. Sample computations showing how the rational approximation tends to $π$ with increasing the integer $k$ are presented. |
| title | A proof of irrationality of $π$ based on the nested radicals with roots of $2$ |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2511.21776 |