A smaller cover for closed unit curves
Wacharin Wichiramala · Miskolc mathematical notes/Mathematical notes · 2018
Forty years ago Schaer and Wetzel showed that a 1 1 2 p 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 Füredi 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.