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Mirror Bounces

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Author:Ivars Peterson (MathLand)
Description: In a game of mathematical billiards, one ball moves across the table at a constant speed forever. There's no friction to slow the ball down. It simply travels in a straight line until it hits a cushion and rebounds according to the rule that the angle of reflection equals the angle of incidence. What makes the game interesting is the table's geometry. Depending on the ball's initial position and direction, its path can vary considerably within the confines of tables having different shapes. For example, on a circular table, a ball can follow paths that never penetrate an inner circular region of a certain diameter in the middle of the table. A stadium-shaped billiard table leads to unpredictable paths reminiscent of chaos (see Billiards in the Round).

Levels: High School (9-12), College
Languages: English
Resource Types: Games, Articles
Math Topics: Euclidean Plane Geometry

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