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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.09568 |
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| _version_ | 1866911954834030592 |
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| author | Macrae, Roderick M. |
| author_facet | Macrae, Roderick M. |
| contents | In a recent Note (Am. J. Phys. 92:397, 2024; arXiv:2309.10826), Vallejo and Bove provide a physical argument based nominally on the second law of thermodynamics as a way of resolving the mathematical question appearing in the title. A remarkable aspect of their argument is that it does not depend on the numerical value of $π$, because $e^{x} \ge x^{e}$ for all positive $x$, with equality occurring only when $x = e$. Moreover, their argument does not depend on the validity of the second law but is rather a limited proof of it for this particular case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09568 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Comment on "Which is greater: $e^π$ or $π^{e}$? An unorthodox physical solution to a classic puzzle" Macrae, Roderick M. Classical Physics In a recent Note (Am. J. Phys. 92:397, 2024; arXiv:2309.10826), Vallejo and Bove provide a physical argument based nominally on the second law of thermodynamics as a way of resolving the mathematical question appearing in the title. A remarkable aspect of their argument is that it does not depend on the numerical value of $π$, because $e^{x} \ge x^{e}$ for all positive $x$, with equality occurring only when $x = e$. Moreover, their argument does not depend on the validity of the second law but is rather a limited proof of it for this particular case. |
| title | Comment on "Which is greater: $e^π$ or $π^{e}$? An unorthodox physical solution to a classic puzzle" |
| topic | Classical Physics |
| url | https://arxiv.org/abs/2407.09568 |