Deducing Three Gap Theorem From Rauzy-Veech Induction

2018/07/30 by Christian Weiß, Weiß, Christian
Computer Science · Engineering · Mathematics · #Computational Geometry and Mesh Generation #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1807.11273

openalex publication_date 2018/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Three Gap Theorem states that there are at most three distinct lengths of gaps if one places n points on a circle, at angles of z, 2z, 3z, … nz from the starting point. The theorem was first proven in 1958 by Sós and many proofs have been found since then. In this note we show how the Three Gap Theorem can easily be deduced by using Rauzy-Veech induction.

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