Lebesgue universal covering problem

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Lebesgue's Universal Covering Problem: Unveiling the Smallest Convex Shape The quest for the most efficient convex shape that can cover any planar set of diameter one has been an ongoing challenge. The problem revolves around finding the least upper bound of distances between all pairs of points within a given set. Henri Lebesgue first proposed this enigma in a letter to Gyula Pál back in 1914, sparking a mathematical puzzle that continues to intrigue experts today. Within this document lies Pál's pioneering work on universal covers, accompanied by various sets with unit diameter. Recent breakthroughs have led to the discovery of new universal covers with smaller areas, yet the cover with minimal area remains elusive. For further insights, refer to: https://www.quantamagazine.org/amateur-mathematician-finds-smallest-universal-cover-20181115 Note: A shape is considered a universal cover if it can envelop any set by rotating, translating, or reflecting it.