不透明集合上的下界

Discret. Comput. Geom. Pub Date : 2014-03-16 DOI:10.4230/LIPIcs.SoCG.2016.46

A. Kawamura, Sonoko Moriyama, Y. Otachi, J. Pach

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引用次数: 6

摘要

证明了任意可数多条可整流曲线的集合，其并集满足与单位平方U相交的所有直线，其总长度至少为2.00002。这是琼斯在1964年对2下界的第一次改进。对于除三角形以外的所有凸集U，证明了一个相似的界。

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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A lower bound on opaque sets

It is proved that the total length of any set of countably many rectifiable curves, whose union meets all straight lines that intersect the unit square U, is at least 2.00002. This is the first improvement on the lower bound of 2 by Jones in 1964. A similar bound is proved for all convex sets U other than a triangle.

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Discret. Comput. Geom.

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