Poncelet's theorem and Billiard knots

Details Poncelet's theorem and Billiard knots Poncelet's theorem and Billiard knots

2011-10-03

arxiv.org/abs/1110.0415v1

Mathematics

Algebraic Geometry

Scientific paper

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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