Position of the centroid of a planar convex body

IF 0.9 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae Pub Date : 2024-04-23 DOI:10.1007/s00010-024-01058-0

Marek Lassak

引用次数: 0

Abstract

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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平面凸体的中心点位置

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Aequationes Mathematicae MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

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.