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Moser's worm problem
Moser's worm 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 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. Another possible solution has the shape of a rhombus with vertex angles of /3 and 2/3 and with a long diagonal of unit length.〔.〕 However, these are not optimal solutions; other shapes are known that solve the problem with smaller areas.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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