L’Enseignement Mathématique

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Volume 60, Issue 3/4, 2014, pp. 247–255
DOI: 10.4171/LEM/60-3/4-2

On the incenters of triangular orbits on elliptic billiards

Olga Romaskevich[1]

(1) UMPA, CNRS, École Normale Supérieure de Lyon, 46 allée d'Italie, 69364, Lyon CEDEX 07, France

We consider 3-periodic orbits in an elliptic billiard. Numerical experiments conducted by Dan Reznik have suggested 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 of reflection.

Keywords: Elliptic billiards, Poncelet theorem, periodic orbits

Romaskevich Olga: On the incenters of triangular orbits on elliptic billiards. Enseign. Math. 60 (2014), 247-255. doi: 10.4171/LEM/60-3/4-2