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arXiv · 1110.0415

Poncelet's theorem and Billiard knots

Daniel Pecker
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Abstract

Let $D$ be any elliptic right cylinder. We prove that every type of knot can be realized as the trajectory of a ball in $D.$ This proves a conjecture of Lamm and gives a new proof of a conjecture of Jones and Przytycki. We use Jacobi's proof of Poncelet's theorem by means of elliptic functions.

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Daniel Pecker. 2011-10-03. Poncelet's theorem and Billiard knots. https://arxiv.org/abs/1110.0415

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