PERIODIC-ORBITS IN TRIANGULAR BILLIARDS

From all orbits described by a ball bouncing elastically inside a triangular billiard some special classes are selected for further numerical investigation. One of these classes consists of all orbits starting in a direction perpendicular to a side. Evidence is presented to show that almost all orbits of this kind are either periodic or end in a corner. The starting points with the same period form intervals, which are distributed in some regular fashion. Even for orbits with very high period the phase portrait and the velocity portrait show peculiar regularities. Although these observations suggest a number of theorems with general validity, the author cannot support them with more than plausibility arguments.