A Smaller Cover of the Moser’s Worm Problem

Abstract

The Moser’s worm problem asks for a smallest set on the plane that contains a congruent copy of every unit arc. Such smallest covering set has not been found yet. The smallest known cover constructed by Norwood and Poole in 2003 [6] has area 0.260437. In this work, we adapt their idea to construct a smaller cover of area 0.26007. We also simplify the proof that the set constructed this way contains a congruent copy of every unit arc.