Moscow Mathematical Journal

Volume 13, Issue 1, January–March 2013 pp. 19–32.

Periodic Trajectories in the Regular Pentagon, II

Authors: Dmitry Fuchs (1) and Serge Tabachnikov (2)
Author institution: (1) Department of Mathematics, University of California, Davis, CA 95616, USA
(2) Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA
Summary:

This paper is a continuation of our study of periodic billiard trajectories in the regular pentagon and closed geodesics on the double pentagon. The trajectories are encoded by infinite words in the alphabet consisting of five symbols. The main result of the paper is an algorithmic description of the symbolic periodic trajectories, conjectured in our recent paper.

2010 Mathematics Subject Classification. Primary: 37D40; Secondary: 37B10, 37E15, 37E35.

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