Counting Regions in Billiard Trajectories
Dave Auckly, Betsy Giles
TL;DR
This paper investigates how the number of parallelograms formed in billiard trajectories within rectangles varies with the rectangle's normalized dimensions.
Contribution
It introduces a new analysis of billiard paths focusing on parallelogram counts based on rectangle dimensions.
Findings
Number of parallelograms depends on rectangle dimensions
Derived formulas relating dimensions to parallelogram counts
Insights into geometric patterns in billiard trajectories
Abstract
This paper explores the number of parallelograms that appear in a billiard path that enters one corner of a rectangle and leaves a second corner of a rectangle as a function of the normalized dimensions of the rectangle.
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Taxonomy
TopicsScientific Research and Discoveries · Mathematical Dynamics and Fractals · Quantum chaos and dynamical systems