Ray in a Square

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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?

Contributed by: Izidor Hafner (September 2012)
Open content licensed under CC BY-NC-SA


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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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