MathDB
Bouncing ray of light

Source: Poland Math Olympiad 1995 Round 1 #8

July 18, 2023
geometrygeometric transformationreflection

Problem Statement

The ray of light starts from the center of a square and reflects from its sides with the principle that the angle of reflection is equal to the angle of incidence. After some time the ray returns to the center of the square. The ray never reached the vertex and has never returned to the center of the square before. Prove that the ray reflected from the sides of the square an odd number of times.