论平面凸体质量中心与其边界之间的最大距离

Pub Date : 2024-05-06 DOI:10.1007/s00454-024-00650-0

Fedor Nazarov, Dmitry Ryabogin, Vladyslav Yaskin

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引用次数: 0

摘要

我们证明，连接平面上凸体质量中心及其边界的矢量在任意方向上的投影长度不超过该方向上体宽的\(\frac{1}{6}\)。由此可见，这些质心之间的距离不会超过凸体直径的 \(\frac{1}{6}\) 和边界长度的 \(\frac{1}{12}\) 。这些常数都无法改进。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On the Maximal Distance Between the Centers of Mass of a Planar Convex Body and Its Boundary

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On the Maximal Distance Between the Centers of Mass of a Planar Convex Body and Its Boundary

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.

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