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In any periodic direction on the regular pentagon billiard table, thereexists two combinatorially different billiard paths, with one longer than theother. For each periodic direction, McMullen asked if one could determinewhether the periodic trajectory through a given point is long, short, or asaddle connection. In this paper we present an algorithm resolving thisquestion for trajectories emanating from the midpoints of the pentagon.

Long and Short Periodic Billiard Trajectories in the Regular Pentagon