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).


Integral Solution Diophantine Equation Isosceles Triangle Irrational Number Easy Problem 
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Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.College of Letters, Arts and SciencesUniversity of Colorado at Colorado SpringsColorado SpringsUSA

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