A small cover for convex unit arcs (Q701784)

Moser's worm problem asks for convex sets of least area which contain a congruent copy of every arc of length \(1\). Wetzel noticed that an isosceles right triangle of hypotenuse \(1\), with area 0.2500, contains a congruent copy of every convex arc of length \(1\) (a convex arc being a simple arc which lies on the boundary of its convex hull). The authors improve Wetzel's result by providing a convex set with area less than 0.2466 which contains a congruent copy of every convex arc of length \(1\).