A. Deniz, A. V. Ratiu, “On the Existence of Fagnano Trajectories in Convex Polygonal Billiards”, Regul. Chaotic Dyn., 2009, Volume 14, Issue 2,Pages <nobr>312

This article is cited in 1 paper

On the Existence of Fagnano Trajectories in Convex Polygonal Billiards

A. Deniz^a, A. V. Ratiu^b

^a Anadolu University, Mathematics Department, Eskisehir, Turkey
^b Istanbul Bilgi University, Mathematics Department, Istanbul, Turkey

Abstract: We prove that an $n$-gon $\mathcal F$ is pedal strong Fagnano trajectory in some convex polygonal billiard table $\mathcal A$ if and only if it is a convex Poncelet $n$-gon.

Keywords: polygonal billiards, Poncelet polygons, Fagnano trajectories.

MSC: 37D50, 51N20

Received: 12.01.2009
Accepted: 10.03.2009

Language: English

DOI: 10.1134/S1560354709020075