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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2411.16935 |
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| _version_ | 1866909404207513600 |
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| author | Dannenberg, M. Hagerstrom, W. Hart, G. Iosevich, A. Le, T. Li, I. Skerrett, N. |
| author_facet | Dannenberg, M. Hagerstrom, W. Hart, G. Iosevich, A. Le, T. Li, I. Skerrett, N. |
| contents | We solve a variant of the classical Buffon Needle problem. More specifically, we inspect the probability that a randomly oriented needle of length $l$ originating in a bounded convex set $X\subset\mathbb{R}^2$ lies entirely within $X$. Using techniques from convex geometry, we prove an isoperimetric type inequality, showing that among sets $X$ with equal perimeter, the disk maximizes this probability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16935 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Buffon Needle Problem Over Convex Sets Dannenberg, M. Hagerstrom, W. Hart, G. Iosevich, A. Le, T. Li, I. Skerrett, N. Classical Analysis and ODEs Metric Geometry 42B10 We solve a variant of the classical Buffon Needle problem. More specifically, we inspect the probability that a randomly oriented needle of length $l$ originating in a bounded convex set $X\subset\mathbb{R}^2$ lies entirely within $X$. Using techniques from convex geometry, we prove an isoperimetric type inequality, showing that among sets $X$ with equal perimeter, the disk maximizes this probability. |
| title | Buffon Needle Problem Over Convex Sets |
| topic | Classical Analysis and ODEs Metric Geometry 42B10 |
| url | https://arxiv.org/abs/2411.16935 |