On the Circumcenters of Triangular Orbits in Elliptic Billiard

Corentin Fierobe (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

On an elliptic billiard, we study the set of the circumcenters of all triangular orbits and we show that this is an ellipse. This article follows Romaskevich (L’Enseig Math 60:247–255, 2014), which proves the same result with the incenters, and Glutsyuk (Moscow Math J 14:239–289, 2014), which among others, introduces the theory of complex reflection in the complex projective plane. The result we present was found at the same time in Garcia (Amer Math Monthly 126:491–504, 2019). His proof uses completely different methods of real differential calculus.

Domaines: Mathématiques [math]

Corentin Fierobe. On the Circumcenters of Triangular Orbits in Elliptic Billiard. Journal of Dynamical and Control Systems, In press, ⟨10.1007/s10883-021-09537-2⟩. ⟨hal-03151412⟩