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.
➤ Version 1 (2019-08-01)
Philip Gibbs (2019). An Upper Bound for Lebesgue's Covering Problem. Researchers.One, https://researchers.one/articles/an-upper-bound-for-lebesgue-s-covering-problem/5f52699c36a3e45f17ae7dde/v1.