Kakutani'S Theorem

(Geometry)

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Geometry
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What is Kakutani's theorem (geometry)?

Kakutani's theorem is a result in geometry named after Shizuo Kakutani. It states that every convex body in 3-dimensional space has a circumscribed cube, i.e. a cube all of whose faces touch the body. The result was further generalized by Yamabe and Yujobô to higher dimensions, and by Floyd to other circumscribed parallelepipeds.

Technology Types

geometrymathematical theoremmeasure theoryprobability theorempropositionstatementtheoremtheorems in convex geometrytheorems in measure theory

Synonyms

Kakutani equivalence

Translations

Satz von Kakutani-Yamabe-Yujobô (de)Stelling van Kakutani (nl)

Tech Info


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