A SMALLER COVER FOR CONVEX UNIT ARCS

Abstract

The Moser’s worm problem asks for the smallest set on the plane that can cover every unit arc. The smallest cover known is by Norwood and Poole of which the area is 0.260437. An interesting variant of this problem is to find the smallest cover for every convex unit arc. Thirty years ago, Wetzel proved that the isosceles right triangle with unit hypotenuse and area 0.25 is such a cover. Recently, Johnson and Poole found a convex cover of area 0.2466. In this work, we establish a smaller cover of area 0.2464 obtained from clipping the triangle at height 0.44.