Explicit Constructions for Poncelet Polygons
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| author | Berman, Leah Wrenn Gévay, Gábor Richter-Gebert, Jürgen Tabachnikov, Serge |
| author_facet | Berman, Leah Wrenn Gévay, Gábor Richter-Gebert, Jürgen Tabachnikov, Serge |
| contents | We study the geometric structure of Poncelet $n$-gons from a projective point of view. In particular we present explicit constructions of Poncelet $n$-gons for certain $n$ and derive algebraic characterisations in terms of bracket polynomials. Via the connections of Poncelet polygons and $(N_4)$-configurations, the results of this article can be used to construct a large class of specific movable $(N_4)$-configurations, the trivial celestial 4-configurations, which up to this point were all thought to be rigid and to require regular polygons for their construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09225 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explicit Constructions for Poncelet Polygons Berman, Leah Wrenn Gévay, Gábor Richter-Gebert, Jürgen Tabachnikov, Serge Combinatorics Metric Geometry 51A20, 52C35 We study the geometric structure of Poncelet $n$-gons from a projective point of view. In particular we present explicit constructions of Poncelet $n$-gons for certain $n$ and derive algebraic characterisations in terms of bracket polynomials. Via the connections of Poncelet polygons and $(N_4)$-configurations, the results of this article can be used to construct a large class of specific movable $(N_4)$-configurations, the trivial celestial 4-configurations, which up to this point were all thought to be rigid and to require regular polygons for their construction. |
| title | Explicit Constructions for Poncelet Polygons |
| topic | Combinatorics Metric Geometry 51A20, 52C35 |
| url | https://arxiv.org/abs/2408.09225 |