A Pool Table, Irrational Numbers, and Integral Independence
A rectangular p × 2q pool table has pockets in every corner and in themiddle of each 2q-long side (see Figure 1.1). A ball is rolled from a corner pocket at a 45°. angle with respect to the side rails.
Find necessary and sufficient conditions on the real numbers p and q for the ball to eventually get into a pocket (angle of incidence is equal to the angle of reflection).
KeywordsIntegral Solution Diophantine Equation Isosceles Triangle Irrational Number Easy Problem
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