Geometry

   

An Upper Bound for Lebesgue’s Universal Covering Problem

Authors: Philip Gibbs

The universal covering problem as posed by Henri Lebesgue in 1914 seeks to find the convex planar 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 cover can be refined and extended to provide an improved upper bound for the optimal area. An upper bound of 0.8440935944 is found.

Comments: 21 Pages.

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Submission history

[v1] 2018-01-22 15:19:04

Unique-IP document downloads: 156 times

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