MathDB

We will assume that the sides of a square are reflective and we will designate them with the names of the four cardinal points. Marking a point on the side

N

, determine in which direction a ray of light should exit (into the interior of the square) so that it returns to it after having undergone

n

reflections on the side

E

, another

n

on the side

W

m

on the

S

and

m - 1

on the

N

, where

n

and

m

are known natural numbers. What happens if m and

n

are not prime to each other? Calculate the length of the light ray considered as a function of

m

and

n

, and of the length of the side of the square.

Problem Statement