The aim of this paper is to share with the mathematical community a list of 33 problems that I
have found along the years in my research. I believe that it is worth to think about them and …

Mathematical billiards describe the motion of a mass point in a domain with elastic
reflections off the boundary or, equivalently, the behavior of rays of light in a domain with …

Handbook of DISCRETE AND COMPUTATIONAL GEOMETRY Page 1 i “K25063” — 2017/9/15
— 18:58 — page 875 — i i i 33 VISIBILITY Joseph O’Rourke INTRODUCTION In a …

Obtuse Triangular Billiards II: One Hundred Degrees Worth of Periodic Trajectories Page 1
Obtuse Triangular Billiards II: One Hundred Degrees Worth of Periodic Trajectories Richard …

The shortest loop traced out by a billiard ball in an acute triangle is the pedal subtriangle,
connecting the feet of the altitudes. In this paper we prove a similar result for loops in the …

This is an updated and expanded version of our earlier survey article [E. Gutkin,“Billiard
dynamics: a survey with the emphasis on open problems,” Regular Chaotic Dyn. 8, 1–13 …

Let S ε denote the set of Euclidean triangles whose two small angles are within ε radians of
and respectively. In this paper we prove two complementary theorems:(1) For any ε> 0 there …

This paper contains a collection of open problems from the the workshop “Emerging
applications of measure rigidity” held at the American Institute of Mathematics in June, 2004 …

1. INTRODUCTION. The trajectory of a billiard ball in motion on a frictionless billiards table is
completely determined by its initial position, direction, and speed. When the ball strikes a …

We prove that any sufficiently small perturbation of an isosceles triangle has a periodic
billiard path. Our proof involves the analysis of certain infinite families of Fourier series that …