Buffon's Problem determines Gaussian Curvature in three Geometries
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866917669148557312 |
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| author | Abelgas, Aizelle Carrillo, Bryan Palacios, John Weisbart, David Yassine, Adam |
| author_facet | Abelgas, Aizelle Carrillo, Bryan Palacios, John Weisbart, David Yassine, Adam |
| contents | A version of the classical Buffon problem in the plane naturally extends to the setting of any Riemannian surface with constant Gaussian curvature. The Buffon probability determines a Buffon deficit. The relationship between Gaussian curvature and the Buffon deficit is similar to the relationship that the Bertrand-Diguet-Puiseux Theorem establishes between Gaussian curvature and both circumference and area deficits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_06755 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Buffon's Problem determines Gaussian Curvature in three Geometries Abelgas, Aizelle Carrillo, Bryan Palacios, John Weisbart, David Yassine, Adam Probability 60D99 A version of the classical Buffon problem in the plane naturally extends to the setting of any Riemannian surface with constant Gaussian curvature. The Buffon probability determines a Buffon deficit. The relationship between Gaussian curvature and the Buffon deficit is similar to the relationship that the Bertrand-Diguet-Puiseux Theorem establishes between Gaussian curvature and both circumference and area deficits. |
| title | Buffon's Problem determines Gaussian Curvature in three Geometries |
| topic | Probability 60D99 |
| url | https://arxiv.org/abs/2009.06755 |