Billiards in ellipses revisited

2020/01/09 by Akopyan, Arseniy, Schwartz, Richard, Tabachnikov, Serge · 1 citation
#Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2001.02934

Abstract

We prove some recent experimental observations of D. 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 one-parameter family of such polygons (that exist due to the Poncelet porism). In our proofs, we use geometric and complex analytic methods.

Cited by

• The stationary focus of the Kiepert parabola over a special Poncelet triangle family

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