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arXiv · 1403.3894

A lower bound on opaque sets

Akitoshi Kawamura·Sonoko Moriyama·Yota Otachi·János Pach
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Abstract

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 established by Jones in 1964. A similar bound is proved for all convex sets U other than a triangle.

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Akitoshi Kawamura, Sonoko Moriyama, Yota Otachi, János Pach. 2014-04-10. A lower bound on opaque sets. https://arxiv.org/abs/1403.3894

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