{"title":"On the Maximal Distance Between the Centers of Mass of a Planar Convex Body and Its Boundary","authors":"Fedor Nazarov, Dmitry Ryabogin, Vladyslav Yaskin","doi":"10.1007/s00454-024-00650-0","DOIUrl":null,"url":null,"abstract":"<p>We prove that the length of the projection of the vector joining the centers of mass of a convex body on the plane and of its boundary to an arbitrary direction does not exceed <span>\\(\\frac{1}{6}\\)</span> of the body width in this direction. It follows that the distance between these centers of mass does not exceed <span>\\(\\frac{1}{6}\\)</span> of the diameter of the body and <span>\\(\\frac{1}{12}\\)</span> of its boundary length. None of those constants can be improved.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00454-024-00650-0","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 prove that the length of the projection of the vector joining the centers of mass of a convex body on the plane and of its boundary to an arbitrary direction does not exceed \(\frac{1}{6}\) of the body width in this direction. It follows that the distance between these centers of mass does not exceed \(\frac{1}{6}\) of the diameter of the body and \(\frac{1}{12}\) of its boundary length. None of those constants can be improved.
分享
京公网安备 11010802042870号
京ICP备2023020795号-1
求助内容：
应助结果提醒方式：
扫码关注我们
