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Forty years ago Schaer and Wetzel showed that a $\frac{1}{\pi}\times\frac{1}{2\pi}\sqrt{\pi^{2}-4}$ rectangle, whose area is about $0.122\,74,$ is thesmallest rectangle that is a cover for the family of all closed unit arcs. Morerecently F\"{u}redi and Wetzel showed that one corner of this rectangle can beclipped to form a pentagonal cover having area $0.11224$ for this family ofcurves. Here we show that then the opposite corner can be clipped to form ahexagonal cover of area less than $0.11023$ for this same family. Thisirregular hexagon is the smallest cover currently known for this family ofarcs.

A smaller cover for closed unit curves