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

18 Scopus citations

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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year = "2022",

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doi = "10.1007/s40879-020-00426-9",

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T1 - Billiards in ellipses revisited

AU - Akopyan, Arseniy

AU - Schwartz, Richard

AU - Tabachnikov, Serge

PY - 2022/12

Y1 - 2022/12

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.

UR - https://www.scopus.com/pages/publications/85090796259

UR - https://www.scopus.com/pages/publications/85090796259#tab=citedBy

U2 - 10.1007/s40879-020-00426-9

DO - 10.1007/s40879-020-00426-9

M3 - Article

AN - SCOPUS:85090796259

SN - 2199-675X

VL - 8

SP - 1313

EP - 1327

JO - European Journal of Mathematics

JF - European Journal of Mathematics

IS - 4

ER -

Billiards in ellipses revisited

Abstract

All Science Journal Classification (ASJC) codes

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