Alternating Billiards

math
A new version of billiards where the ball bounces by alternating between two fixed directions, from my research on placements of chess pieces.
Author

Christopher R. H. Hanusa

Published

January 8, 2019

This post was originally a Twitter thread.

I am excited to share with you an article that I posted to the arXiv today. My collaborator and I worked on an interesting question related to my long-running research in counting placements of chess pieces. 1/3

We ended up creating a new version of billiards with a different rule for bouncing off a wall: instead of obeying the law of reflection, the ball “bounces” by alternating between two fixed directions.

I’m very pleased by its arXiv number: https://arxiv.org/abs/1901.01917

Even if you don’t read it for its math, do check out our pictures. :)

Oh, and here are two pictures. (4/3)

An alternating billiard path in a square table: colored circles numbered from -2 to 7 sit on the dotted edges of the square, joined in order by line segments that zigzag up the table

An alternating billiard path on an elliptical table: six colored circles numbered 1 to 6 on a dotted ellipse, joined by line segments that form a closed path

Citation

BibTeX citation:
@online{hanusa2019,
  author = {Hanusa, Christopher R. H.},
  title = {Alternating {Billiards}},
  date = {2019-01-08},
  url = {https://hanusa.xyz/blog/posts/2019-01-08-alternating-billiards/},
  langid = {en}
}
For attribution, please cite this work as:
Hanusa, Christopher R. H. 2019. “Alternating Billiards.” January 8. https://hanusa.xyz/blog/posts/2019-01-08-alternating-billiards/.