16-Apr-1995
Unsolved Problem 16:
Does every obtuse triangle admit a periodic
orbit for the path of a billiard ball?
We assume that the billiard ball bounces off each
side so that the angle of incidence equals the
angle of reflection. If it hits a vertex, it
rebounds along the reflection of its entry path in
the angle bisector of the angle at that vertex.
The orbit (or trajectory) is periodic, if after
a finite number of reflections, it returns to
its starting point.
Reference:
- [Croft 1991]
- Hallard T. Croft, Kenneth J. Falconer, and Richard K. Guy,
Unsolved Problems in Geometry.
Springer-Verlag. New York: 1991.
Page 16.
Revision 1 posted 4/25/95.
A Billiards Problem
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