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Results tagged with billiards
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user 129192
Billiards are a class of dynamical systems in which a point particle moves uniformly in a domain $D\subset \mathbb{R}^d$ except for mirror-like reflections from the boundary. Varying $D$ leads to examples satisfying many ergodic properties. Billiards enhance visual explanations of dynamical concepts to students and the general public. There are many applications in physics and image processing. The free motion and/or reflection rule may be generalized.
4
votes
1
answer
562
views
Types of triangles admitting periodic billiard orbits
It is an open problem in dynamical systems if every triangle has a periodic billiard orbit. So far it has been proven that equilateral triangles, isosceles triangles, right triangles, and obtuse tria …
- 11
3
votes
1
answer
94
views
Finding particular closed paths in geometric plane regions
Let $X_m$ denote a set of $m\geq 3$ lines in $\mathbb{R}^2$ that are not all parallel. Consider the problem of determining a closed path of $kn$ points in $X_m$ $k, n \in \mathbb{Z}^+$, such that the …
- 1,087
0
votes
Accepted
Finding particular closed paths in geometric plane regions
The answer, given in this paper: https://arxiv.org/abs/2112.02207, turns out to be "yes", there always exist such closed curves. The theorem stating the answer to this question is given in the introd …
- 1,087
33
votes
3
answers
2k
views
Why is the billiard problem for obtuse triangles so hard?
This is an incredibly naive question so this may be closed. Nevertheless, I have been reading about the problem asking if every obtuse triangle admits a periodic billiard path, which has been open fo …
- 156k