On the incenters of triangular orbits in elliptic billiard

Abstract

We consider 3-periodic orbits in an elliptic billiard. Numerical experiments conducted by Dan Reznik have shown that the locus of the centers of inscribed circles of the corresponding triangles is an ellipse. We prove this fact by the complexification of the problem coupled with the complex law or rfelection.

6 pages, 1 figure

References in corpus (1)

• Ellipsoidal billiards in pseudo-Euclidean spaces and relativistic quadrics

Cited by in corpus (4)

• Loci of 3-periodics in an Elliptic Billiard: why so many ellipses?
• The Ballet of Triangle Centers on the Elliptic Billiard
• On the circumcenters of triangular orbits in elliptic billards
• Thesis manuscript: Projective and complex billiards, periodic orbits and Pfaffian systems