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.
Original language | English (US) |
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Pages (from-to) | 1341-1354 |
Number of pages | 14 |
Journal | European Journal of Mathematics |
Volume | 8 |
Issue number | 4 |
DOIs | |
State | Published - Dec 2022 |
All Science Journal Classification (ASJC) codes
- General Mathematics