Combinatorial Properties of Billiards on an Equilateral Triangle
نویسنده
چکیده
We explore periodic orbits on an equilateral triangular billiard table. We prove that there is exactly one periodic orbit with odd period. For any positive integer n, there exist P d|n μ(d)P ¡ n d ¢ periodic orbits of period 2n, where μ(d) is the Möbius transformation function and P (n) = bn+2 2 c− bn+2 3 c. We count periodic orbits by introducing a new type of integer partition.
منابع مشابه
Periodic Orbits for Billiards on an Equilateral Triangle
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 bumper, we assume that the angle of incidence equals the angle of reflection. Once released, the ball continues indefinitely along its trajectory with constant speed unless it strikes a vertex, at which poi...
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