Moser's worm problem [SEP] named after
Moser's worm problem
Moser's worm problem (also known as mother worm's blanket problem) is an unsolved problem in geometry 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. In some variations of the problem, the region is restricted to be convex.
Examples.
For example, a circular
-area partitions of space into equal-volume cells, and the optimality of the Weaire–Phelan structure as a solution to the Kelvin problem
- Lebesgue's universal covering problem on the minimum-area convex shape in the plane that can cover any shape of diameter one
- Moser's worm problem – what is the smallest area of a shape that can cover every unit-length curve in the plane?
- The moving sofa problem – what is the largest area of a shape that can be maneuvered through a