Poncelet’s theorem and billiard knots |
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Authors: | Daniel Pecker |
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Institution: | 1. Facult?? de Math??matiques, U. Pierre et Marie Curie (Paris 6), Paris, France
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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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