{"title":"The Horizontal Chord Set","authors":"Diana Davis, Serge Troubetzkoy","doi":"10.1080/00029890.2024.2325862","DOIUrl":null,"url":null,"abstract":"We study the set of lengths of the horizontal chords of a continuous function. We give a new proof of Hopf’s characterization of this set, and show that it implies that no matter which function we ...","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"32 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The American Mathematical Monthly","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/00029890.2024.2325862","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We study the set of lengths of the horizontal chords of a continuous function. We give a new proof of Hopf’s characterization of this set, and show that it implies that no matter which function we ...
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