Currie's Mysterious Pattern and Iterated Functions
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908559124463616 |
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| author | Kalman, Dan |
| author_facet | Kalman, Dan |
| contents | In his book "Mathematics Rhyme and Reason," Currie discusses what he calls a $mysterious$ $pattern$ involving the sequence
$ a_{n} = 2^n \sqrt{2 - \sqrt{2 + \sqrt{2 + \cdots + \sqrt{2}}}},$
where $n$ is the number of radicals. Part of the mystery is that $a_n$ converges to $π.$ In this paper we discuss a general framework for results like the mysterious pattern in the context of iterated functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21409 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Currie's Mysterious Pattern and Iterated Functions Kalman, Dan General Mathematics 40A05 In his book "Mathematics Rhyme and Reason," Currie discusses what he calls a $mysterious$ $pattern$ involving the sequence $ a_{n} = 2^n \sqrt{2 - \sqrt{2 + \sqrt{2 + \cdots + \sqrt{2}}}},$ where $n$ is the number of radicals. Part of the mystery is that $a_n$ converges to $π.$ In this paper we discuss a general framework for results like the mysterious pattern in the context of iterated functions. |
| title | Currie's Mysterious Pattern and Iterated Functions |
| topic | General Mathematics 40A05 |
| url | https://arxiv.org/abs/2509.21409 |