Poncelet porism in singular cases
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915371106172928 |
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| author | Dragovic, Vladimir Radnovic, Milena |
| author_facet | Dragovic, Vladimir Radnovic, Milena |
| contents | The celebrated Poncelet porism is usually studied for a pair of smooth conics that are in a general position. Here we discuss Poncelet porism in the real plane - affine or projective, when that is not the case, i.e. the conics have at least one point of tangency or at least one of the conics is not smooth. In all such cases, we find necessary and sufficient conditions for the existence of an n-gon inscribed in one of the conics and circumscribed about the other. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21514 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Poncelet porism in singular cases Dragovic, Vladimir Radnovic, Milena Algebraic Geometry Exactly Solvable and Integrable Systems 51N15, 14H70 The celebrated Poncelet porism is usually studied for a pair of smooth conics that are in a general position. Here we discuss Poncelet porism in the real plane - affine or projective, when that is not the case, i.e. the conics have at least one point of tangency or at least one of the conics is not smooth. In all such cases, we find necessary and sufficient conditions for the existence of an n-gon inscribed in one of the conics and circumscribed about the other. |
| title | Poncelet porism in singular cases |
| topic | Algebraic Geometry Exactly Solvable and Integrable Systems 51N15, 14H70 |
| url | https://arxiv.org/abs/2504.21514 |