从Rauzy-Veech归纳法推导三个间隙定理
Deducing Three Gap Theorem From Rauzy-Veech Induction
摘要：
三间隙定理指出，如果将$n$点放置在圆上，与起始点成$z, 2z, 3z, \ldots nz$角，则最多存在三个不同长度的间隙。该定理首先证明了在1958年的索斯和许多证明已经发现，从那时起。在本文中，我们展示了如何三间隙定理可以很容易地推导出使用Rauzy-Veech归纳法。
英文摘要：
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 $z, 2z, 3z, \ldots nz$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
