{"title":"由Rauzy-Veech归纳法推导出三间隙定理","authors":"Christian Weiss","doi":"10.15446/recolma.v54n1.89777","DOIUrl":null,"url":null,"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, … 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.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Deducing Three Gap Theorem from Rauzy-Veech induction\",\"authors\":\"Christian Weiss\",\"doi\":\"10.15446/recolma.v54n1.89777\",\"DOIUrl\":null,\"url\":null,\"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, … 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.\",\"PeriodicalId\":38102,\"journal\":{\"name\":\"Revista Colombiana de Matematicas\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-07-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Revista Colombiana de Matematicas\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15446/recolma.v54n1.89777\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista Colombiana de Matematicas","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15446/recolma.v54n1.89777","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Deducing Three Gap Theorem from Rauzy-Veech induction
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, … 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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