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

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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)
Pages (from-to)	1313-1327
Number of pages	15
Journal	European Journal of Mathematics
Volume	8
Issue number	4
DOIs	https://doi.org/10.1007/s40879-020-00426-9
State	Published - Dec 2022

All Science Journal Classification (ASJC) codes

General Mathematics

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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.",

author = "Arseniy Akopyan and Richard Schwartz and Serge Tabachnikov",

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AU - Akopyan, Arseniy

AU - Schwartz, Richard

AU - Tabachnikov, Serge

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N2 - 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.

AB - 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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JO - European Journal of Mathematics

JF - European Journal of Mathematics

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Billiards in ellipses revisited

Abstract

All Science Journal Classification (ASJC) codes

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