{"title":"平面凸体的中心点位置","authors":"Marek Lassak","doi":"10.1007/s00010-024-01058-0","DOIUrl":null,"url":null,"abstract":"<div><p>It is well known that any planar convex body <i>A</i> permits to inscribe an affine-regular hexagon <span>\\(H_A\\)</span>. We prove that the centroid of <i>A</i> belongs to the homothetic image of <span>\\(H_A\\)</span> with ratio <span>\\(\\frac{4}{21}\\)</span> and the center in the center of <span>\\(H_A\\)</span>. This ratio cannot be decreased.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"98 3","pages":"687 - 695"},"PeriodicalIF":0.9000,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01058-0.pdf","citationCount":"0","resultStr":"{\"title\":\"Position of the centroid of a planar convex body\",\"authors\":\"Marek Lassak\",\"doi\":\"10.1007/s00010-024-01058-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>It is well known that any planar convex body <i>A</i> permits to inscribe an affine-regular hexagon <span>\\\\(H_A\\\\)</span>. We prove that the centroid of <i>A</i> belongs to the homothetic image of <span>\\\\(H_A\\\\)</span> with ratio <span>\\\\(\\\\frac{4}{21}\\\\)</span> and the center in the center of <span>\\\\(H_A\\\\)</span>. This ratio cannot be decreased.</p></div>\",\"PeriodicalId\":55611,\"journal\":{\"name\":\"Aequationes Mathematicae\",\"volume\":\"98 3\",\"pages\":\"687 - 695\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-04-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00010-024-01058-0.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Aequationes Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00010-024-01058-0\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Aequationes Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00010-024-01058-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
众所周知，任何平面凸体 A 都允许刻画一个仿射正六边形 \(H_A\)。我们证明 A 的中心点属于 \(H_A\)的同面像，其比率为 \(\frac{4}{21}\)，中心位于 \(H_A\)的中心。这个比率不能减小。
It is well known that any planar convex body A permits to inscribe an affine-regular hexagon \(H_A\). We prove that the centroid of A belongs to the homothetic image of \(H_A\) with ratio \(\frac{4}{21}\) and the center in the center of \(H_A\). This ratio cannot be decreased.
期刊介绍：
aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
