Lebesgue universal covering problem
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Lebesgue's universal covering problem seeks the convex shape with minimum area that can cover any planar set of diameter one. This means finding the least upper bound of distances between all pairs of points in the set. The problem was introduced by Henri Lebesgue in a letter to Gyula Pál in 1914. Within this file, you'll find Pál's universal cover along with several sets with unit diameter. Recently, new universal covers with smaller areas have been discovered, and the smallest area is still unknown. For more information, see: https://www.quantamagazine.org/amateur-mathematician-finds-smallest-universal-cover-20181115
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