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.[1] The result was further generalized by Yamabe and Yujobô to higher dimensions,[2] and by Floyd to other circumscribed parallelepipeds.[3]
References
- doi:10.2307/1968964
- ^ Yamabe, H.; Yujobô, Z. (1950), "On the continuous function defined on a sphere", Osaka Math. J., 2 (1): 19–22
- doi:10.2307/2033116
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