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arXiv · 2408.09225

Explicit Constructions for Poncelet Polygons

Leah Wrenn Berman·Gábor Gévay·Jürgen Richter-Gebert·Serge Tabachnikov
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Abstract

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.

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Leah Wrenn Berman, Gábor Gévay, Jürgen Richter-Gebert, Serge Tabachnikov. 2024-08-17. Explicit Constructions for Poncelet Polygons. https://arxiv.org/abs/2408.09225

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