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#kakeya_set

Kakeya set

Shape containing unit line segments in all directions

In mathematics, a Kakeya set, or Besicovitch set, is a set of points in Euclidean space which contains a unit line segment in every direction. For instance, a disk of radius 1/2 in the Euclidean plane, or a ball of radius 1/2 in three-dimensional space, forms a Kakeya set. Much of the research in this area has studied the problem of how small such sets can be. Besicovitch showed that there are Besicovitch sets of measure zero.

Sun 9th

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Kakeya set Kakeya Moser's worm problem Sōichi Kakeya Polynomial method in combinatorics Falconer's conjecture Proofs from THE BOOK Geometric measure theory Nikodym set Lebesgue's universal covering problem
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