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Geometriae Dedicata

, Volume 161, Issue 1, pp 323–333 | Cite as

Poncelet’s theorem and billiard knots

  • Daniel PeckerEmail author
Original Paper

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.

Keywords

Poncelet’s theorem Jacobian elliptic functions Billiard knots Lissajous knots Cylinder knots 

Mathematics Subject Classification (2000)

57M25 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Faculté de MathématiquesU. Pierre et Marie Curie (Paris 6)ParisFrance

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