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Poncelet's theorem and Billiard knots

Abstract

Let DD be any elliptic right cylinder. We prove that every type of knot can be realized as the trajectory of a ball in D.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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