Periodic trajectories in the regular pentagon, II

Fuchs Dmitry; Serge Tabachnikov

doi:10.17323/1609-4514-2013-13-1-19-32

Periodic trajectories in the regular pentagon, II

Fuchs Dmitry, Serge Tabachnikov

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Abstract

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.

Original language	English (US)
Pages (from-to)	19-32
Number of pages	14
Journal	Moscow Mathematical Journal
Volume	13
Issue number	1
DOIs	https://doi.org/10.17323/1609-4514-2013-13-1-19-32
State	Published - 2013

All Science Journal Classification (ASJC) codes

General Mathematics

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10.17323/1609-4514-2013-13-1-19-32

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title = "Periodic trajectories in the regular pentagon, II",

abstract = "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.",

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AB - 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.

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Periodic trajectories in the regular pentagon, II

Abstract

All Science Journal Classification (ASJC) codes

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