Determine the solution of Moser’s worm problem

Determine the minimum-area planar region containing a congruent copy of every unit arc, thereby resolving Moser’s worm problem, which remains unresolved despite the established bounds for convex universal covers.

Background

Moser’s worm problem asks for the least-area planar region that contains a congruent copy of every arc of length one. The paper improves the known lower and upper bounds in the convex case but does not determine the exact optimum.

The unresolved issue concerns the unrestricted minimum-area covering region, while the paper specifically proves new bounds for convex universal covers. The authors explicitly state that the problem remains open and that the optimal region is unknown.