Poncelet’s theorem and Billiard knots
نویسنده
چکیده
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. keywords: Poncelet’s theorem, Jacobian elliptic functions, Billiard knots , Lissajous knots, Cylinder knots Mathematics Subject Classification 2000: 57M25,
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