{"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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"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\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"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\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00010-024-01058-0\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00010-024-01058-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.
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