Billiards in ellipses revisited

Arseniy Akopyan; Richard Schwartz; Serge Tabachnikov

doi:10.1007/s40879-020-00426-9

Billiards in ellipses revisited

Arseniy Akopyan, Richard Schwartz, Serge Tabachnikov

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English (US)
Journal	European Journal of Mathematics
DOIs	https://doi.org/10.1007/s40879-020-00426-9
State	Accepted/In press - 2020

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1007/s40879-020-00426-9

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title = "Billiards in ellipses revisited",

abstract = "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.",

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AU - Schwartz, Richard

AU - Tabachnikov, Serge

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