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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2412.05190 |
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| _version_ | 1866912149827223552 |
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| author | Kovács, Zoltán |
| author_facet | Kovács, Zoltán |
| contents | We give an alternative proof of the statement, by using elimination from algebraic geometry, that the only set $S\subset\mathbb{R}^2$, $\left|S\right|=6$ such that all subsets that form a triangle are isosceles triangles, is the regular pentagon with its center. Our proof can be extended to answer some related questions raised by Erdős. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05190 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on Erdős's mysterious remark Kovács, Zoltán Computational Geometry Metric Geometry 13P05, 68W30 We give an alternative proof of the statement, by using elimination from algebraic geometry, that the only set $S\subset\mathbb{R}^2$, $\left|S\right|=6$ such that all subsets that form a triangle are isosceles triangles, is the regular pentagon with its center. Our proof can be extended to answer some related questions raised by Erdős. |
| title | A note on Erdős's mysterious remark |
| topic | Computational Geometry Metric Geometry 13P05, 68W30 |
| url | https://arxiv.org/abs/2412.05190 |