A lower bound on opaque sets
Computational Geometry
2014-04-11 v2
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.
Cite
@article{arxiv.1403.3894,
title = {A lower bound on opaque sets},
author = {Akitoshi Kawamura and Sonoko Moriyama and Yota Otachi and János Pach},
journal= {arXiv preprint arXiv:1403.3894},
year = {2014}
}
Comments
13 pages, 10 figures