• Corpus ID: 244346106

Long and Short Periodic Billiard Trajectories in the Regular Pentagon

@inproceedings{Everett2021LongAS,
  title={Long and Short Periodic Billiard Trajectories in the Regular Pentagon},
  author={Samuel Everett and Vanessa Lin and Aidan Mager},
  year={2021}
}
In any periodic direction on the regular pentagon billiard table, there exists two combinatorially different billiard paths, with one longer than the other. For each periodic direction, McMullen asked if one could determine whether the periodic trajectory through a given point is long, short, or a saddle connection. In this paper we present an algorithm resolving this question for trajectories emanating from the midpoints of the pentagon. 

References

SHOWING 1-10 OF 13 REFERENCES

Periodic trajectories in the regular pentagon

The study of billiards in rational polygons and of directional flows on flat surfaces is a fast-growing and fascinating area of research. A classical construction reduces the billiard system in a

Obtuse Triangular Billiards II: One Hundred Degrees Worth of Periodic Trajectories

We give a rigorous computer-assisted proof that a triangle has a periodic billiard path when all its angles are at most one hundred degrees.

Periodic billiard trajectories in polygons: generating mechanisms

CONTENTSIntroduction §1. Billiard trajectories in a plane domain §2. Fagnano's problem. Mechanical interpretations of periodic trajectories in triangles §3. An extremal property of billiard

Geometry and billiards

Motivation: Mechanics and optics Billiard in the circle and the square Billiard ball map and integral geometry Billiards inside conics and quadrics Existence and non-existence of caustics Periodic

Billiard dynamics: an updated survey with the emphasis on open problems.

This is an updated and expanded version of the earlier survey article "Billiard dynamics: a survey with the emphasis on open problems," which introduced the subject matter and reported on the recent work pertaining to the problems and conjectures exposed.

Rational billiards and flat structures

1 Polygonal billiards, rational billiards 1 1.1 Polygonal billiards . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Examples: a pair of ellastic point-masses on a segment and a triple

Translation surfaces and their orbit closures: An introduction for a broad audience

This survey is an invitation for mathematicians from different backgrounds to become familiar with the subject, and top priority is given to presenting a view of the subject that is at once accessible and connected to many areas of mathematics.

Billiards in polygons: Survey of recent results

We review the dynamics of polygonal billiards

Closed trajectories for quadratic differentials with an application to billiards

On considere les orbites periodiques pour le systeme dynamique d'une table polygonale avec des angles multiples rationnels de π: le billard rationnel

Periodic paths on the pentagon, double pentagon and golden L

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