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arXiv · 2001.08469

Dan Reznik's identities and more

Misha Bialy·Serge Tabachnikov
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Abstract

Dan Reznik found, by computer experimentation, a number of conserved quantities associated with periodic billiard trajectories in ellipses. We prove some of his observations using a non-standard generating function for the billiard ball map. In this way, we also obtain some identities valid for all smooth convex billiard tables.

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Misha Bialy, Serge Tabachnikov. 2020-01-23. Dan Reznik's identities and more. https://arxiv.org/abs/2001.08469

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