Billard (Mathematics)

A billiard in mathematics is a model of a particle moving in a straight line within a bounded, convex shape, reflecting off the boundary without losing speed. The study of billiards explores how the particle's path evolves over time—whether it eventually repeats, fills the space uniformly, or exhibits chaotic behavior. This area connects to dynamical systems, geometry, and chaos theory, providing insights into how simple rules lead to complex motion. It helps mathematicians understand fundamental properties of motion, stability, and pattern formation in constrained environments.