For questions about billiards; dynamical systems involving point particles (billiard balls) that travel in straight lines on the interior of some bounded domain (the billiard table) and experience perfectly elastic reflections on collision with boundary.
Questions tagged [billiards]
65 questions
3
votes
1 answer
The forever moving billiard ball
Suppose I have a rectangular table, dimensions $x$ by $y$, and a billiard ball is positioned in the very center. For descriptive convenience, let us impose a coordinate system on this table with an origin (0,0) in the center of the table where I…
Kenshin
- 2,152
2
votes
1 answer
Turning a rhombus billiard into an equivalent barrier billiard
I am reading a research paper and the authors map the rhombus billiard (angles $60$-$120$ degrees) to an equivalent barrier billiard. They start with a rhombus standing upright and reflect in a counter clockwise manner:
"after three reflections, we…
recmath
- 2,738
2
votes
1 answer
About trajectories on a circular billiard
Let consider a circular billiard.
You start by putting the ball on the edge off the table. The trajectory then is quite simple (see the picture), with equal angles at each rebound.
Which will eventually gives a trajectory looking something like…
E. Joseph
- 14,843
2
votes
0 answers
Is there an elementary proof for the envelope of an infinitely-bouncing billiard ball?
I was reading this page here
http://cage.ugent.be/~hs/billiards/billiards.html
And was wondering if there existed an elementary proof of proving that the envelopes form certain conic sections (ie: hyperbola or ellipse) depending on the initial angle…
Trogdor
- 10,331
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Construct a mirrored rectangle tunnel unilluminable from one end to another, consisting of only orthogonal rectangles and circles
In a problem there consist of a 2D tunnel, a rectangle with two opposite sides removed as its faces, in which obstacles are only orthogonal rectangles (those whose edges are parallel to one of the edges of the tunnel) and circles. The light come…
