Billiards in ellipses revisited

Billiards in ellipses revisited

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 proof...

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Veröffentlicht in:European journal of mathematics 2022-12, Vol.8 (4), p.1313-1327
Hauptverfasser: Akopyan, Arseniy, Schwartz, Richard, Tabachnikov, Serge
Format: Artikel
Sprache:eng
Schlagworte:
Algebraic Geometry
Angles (geometry)
Ellipses
Mathematics
Mathematics and Statistics
Polygons
Research Article
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Zusammenfassung: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.
ISSN:2199-675X
2199-6768
DOI:10.1007/s40879-020-00426-9