Poncelet's theorem and Billiard knots
Algebraic Geometry
2011-10-04 v1 Geometric Topology
Abstract
Let be any elliptic right cylinder. We prove that every type of knot can be realized as the trajectory of a ball in 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.
Cite
@article{arxiv.1110.0415,
title = {Poncelet's theorem and Billiard knots},
author = {Daniel Pecker},
journal= {arXiv preprint arXiv:1110.0415},
year = {2011}
}