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Ray in a Square

A ray enters a square at point , reflects off the top and bottom of the square, and leaves at point with integer coordinates. What is the ratio , where is the length of the side of the square?

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Reference
[1] A. F. Dunn, Second Book of Mathematical Bafflers, New York: Dover Publications, 1983, p. 50.

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 Izidor Hafner
"Ray in a Square"
 http://demonstrations.wolfram.com/RayInASquare/
 Wolfram Demonstrations Project
 Published: September 28, 2012
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