An Upper Bound for Lebesgue's Covering Problem
Metric Geometry
2018-10-25 v1
Abstract
A covering problem posed by Henri Lebesgue in 1914 seeks to find the convex shape of smallest area that contains a subset congruent to any point set of unit diameter in the Euclidean plane. Methods used previously to construct such a covering can be refined and extended to provide an improved upper bound for the optimal area. An upper bound of 0.8440935944 is found.
Keywords
Cite
@article{arxiv.1810.10089,
title = {An Upper Bound for Lebesgue's Covering Problem},
author = {Philip Gibbs},
journal= {arXiv preprint arXiv:1810.10089},
year = {2018}
}
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21 pages