{"title":"The dual of Philo's shortest line segment problem","authors":"Yagub N. Aliyev","doi":"arxiv-2406.05702","DOIUrl":null,"url":null,"abstract":"We study the dual of Philo's shortest line segment problem which asks to find\nthe optimal line segments passing through two given points, with a common\nendpoint, and with the other endpoints on a given line. The provided solution\nuses multivariable calculus and geometry methods. Interesting connections with\nthe angle bisector of the triangle are explored.","PeriodicalId":501570,"journal":{"name":"arXiv - CS - Computational Geometry","volume":"191 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Computational Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2406.05702","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We study the dual of Philo's shortest line segment problem which asks to find
the optimal line segments passing through two given points, with a common
endpoint, and with the other endpoints on a given line. The provided solution
uses multivariable calculus and geometry methods. Interesting connections with
the angle bisector of the triangle are explored.
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