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arXiv:1810.11310math.DS

Periodic paths on the pentagon, double pentagon and golden L

Diana Davis, Samuel Lelièvre

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Abstract

We give a tree structure on the set of all periodic directions on the golden L, which gives an associated tree structure on the set of periodic directions for the pentagon billiard table and double pentagon surface. We use this to give the periods of periodic directions on the pentagon and double pentagon. We also show examples of many periodic billiard trajectories on the pentagon, which are strikingly beautiful, and we describe some of their properties. Finally, we give conjectures and future directions based on experimental computer evidence.

arXiv comments
32 pages, 24 figures; Sage code in .tex file. v2 incorporates reviewers' suggestions and adds a few new sections
Journal reference
DOI
Subjects
math.DSDynamical Systems

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  1. I am mesmerized by our new robotic vacuum (2019) 1 comment

    • The algorithm of going straight until you hit a wall, and then turning a (constant) angle has some really cool properties -- some angles/starting positions will eventually let you cover the entire floor, while others will produce beautiful repeating patterns [1]. One key insight…

      eat_veggiesView on HNParent context

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