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 the smallest rectangle that is a cover for the family of all closed unit arcs. More recently F\"{ u}redi and Wetzel showed that one corner of this rectangle can be clipped to form a pentagonal cover having area $0.11224$ for this family of curves. Here we show that then the opposite corner can be clipped to form a hexagonal cover of area less than $0.11023$ for this same family. This irregular hexagon is the smallest cover currently known for this family of arcs.
Categories: cs.CG
