{"title":"A lower bound on opaque sets","authors":"A. Kawamura, Sonoko Moriyama, Y. Otachi, J. Pach","doi":"10.4230/LIPIcs.SoCG.2016.46","DOIUrl":null,"url":null,"abstract":"It is proved that the total length of any set of countably many rectifiable curves, whose union meets all straight lines that intersect the unit square U, is at least 2.00002. This is the first improvement on the lower bound of 2 by Jones in 1964. A similar bound is proved for all convex sets U other than a triangle.","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"9 1","pages":"13-22"},"PeriodicalIF":0.0000,"publicationDate":"2014-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discret. Comput. Geom.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4230/LIPIcs.SoCG.2016.46","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
Abstract
It is proved that the total length of any set of countably many rectifiable curves, whose union meets all straight lines that intersect the unit square U, is at least 2.00002. This is the first improvement on the lower bound of 2 by Jones in 1964. A similar bound is proved for all convex sets U other than a triangle.
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