An Improved Upper Bound for Leo Moser's Worm Problem
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Abstract. A wormω is a continuous rectifiable arc of unit length in the Cartesian plane. Let W denote the class of all worms. A planar region C is called a cover for W if it contains a copy of every worm in W . That is, C will cover or contain any member ω of W after an appropriate translation and/ or rotation of ω is completed (no reflections). The open problem of determining a cover C of smallest area is attributed to Leo Moser , . This paper reduces the smallest known upper bound for this area from 0.275237  to 0.260437.
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