Moser's worm problem

Moser's worm problem: Moser's worm problem was formulated by the Austrian-Canadian mathematician Leo Moser in 1966. The problem asks for the region of smallest area that can accommodate every plane curve of length 1. Here "accommodate" means that the curve may be rotated and translated to fit inside the region.

For example, a disk of radius 1/2 can accommodate any plane curve of length 1 by placing the midpoint of the curve at the center of the disk. This is not the smallest such region.

The problem remains open, though the minimum shape is known to have area between 0.232239 and 0.2738.

See also

Moving sofa problem

References

Tirasan Khandhawit; Sira Sriswasdi (2007). "An Improved Lower Bound for Moser's Worm Problem". arXiv:math/0701391 [math.MG].

Tirasan Khandhawit; Dimitrios Pagonakis; Sira Sriswasdi (2011). "Lower Bound for Convex Hull Area and Universal Cover Problems". arXiv:1101.5638 [math.MG].

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