Harmonious loci of Poncelet triangles about the incircle and their degeneracies
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911337999761408 |
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| author | Helman, Mark Garcia, Ronaldo A. Reznik, Dan |
| author_facet | Helman, Mark Garcia, Ronaldo A. Reznik, Dan |
| contents | We tour several Euclidean properties of Poncelet triangles inscribed in an ellipse and circumscribing the incircle, including loci of triangle centers and envelopes of key objects. We also show that a number of degenerate behaviors are triggered by the presence of an equilateral triangle in the family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19464 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Harmonious loci of Poncelet triangles about the incircle and their degeneracies Helman, Mark Garcia, Ronaldo A. Reznik, Dan Dynamical Systems Computational Geometry 51M04, 51N20, 51N35, 68T20 We tour several Euclidean properties of Poncelet triangles inscribed in an ellipse and circumscribing the incircle, including loci of triangle centers and envelopes of key objects. We also show that a number of degenerate behaviors are triggered by the presence of an equilateral triangle in the family. |
| title | Harmonious loci of Poncelet triangles about the incircle and their degeneracies |
| topic | Dynamical Systems Computational Geometry 51M04, 51N20, 51N35, 68T20 |
| url | https://arxiv.org/abs/2409.19464 |