Billiards in near rectangles

TL;DR

This paper proves that quadrilaterals close to rectangles always have a periodic billiard path, extending understanding of billiard dynamics in near-rectangular shapes.

Contribution

It establishes the existence of periodic billiard paths in quadrilaterals near rectangles, a new result in billiard dynamics.

Findings

Quadrilaterals close to rectangles have periodic billiard paths.

The result applies to all sufficiently near-rectangular quadrilaterals.

The work was conducted as an REU project at ICERM in Summer 2012.

Abstract

For every quadrilateral sufficiently close to a rectangle, we shall show that it possess a periodic billiard path. This is an REU work done at ICERM in Summer 2012.