Billiards in ellipses revisited

Arseniy Akopyan, Richard Schwartz, Serge Tabachnikov

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We prove some recent experimental observations of Dan Reznik concerning periodic billiard orbits in ellipses. For example, the sum of cosines of the angles of a periodic billiard polygon remains constant in the 1-parameter family of such polygons (that exist due to the Poncelet porism). In our proofs, we use geometric and complex analytic methods.

Original languageEnglish (US)
Pages (from-to)1313-1327
Number of pages15
JournalEuropean Journal of Mathematics
Issue number4
StatePublished - Dec 2022

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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