Kakutani's theorem (geometry): Difference between revisions
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'''Kakutani's theorem''' is a result in [[geometry]] named after [[Shizuo Kakutani]]. It states that every [[convex body]] in 3-[[dimension]]al space has a circumscribed [[cube]], i.e. a cube all of whose faces touch the body. The result was further generalized by [[Hidehiko Yamabe|Yamabe]] and Yujobô to higher dimensions, and by Floyd to other circumscribed [[parallelepiped]]s. |
'''Kakutani's theorem''' is a result in [[geometry]] named after [[Shizuo Kakutani]]. It states that every [[convex body]] in 3-[[dimension]]al space has a circumscribed [[cube]], i.e. a cube all of whose faces touch the body. The result was further generalized by [[Hidehiko Yamabe|Yamabe]] and Yujobô to higher dimensions, and by Floyd to other circumscribed [[parallelepiped]]s. |
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Revision as of 21:35, 12 May 2024
 | This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. (May 2024) |
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.
References
- Kakutani, S. (1942), "A proof that there exists a circumscribing cube around any bounded closed convex set in R3", Annals of Mathematics, Second Series, 43 (4): 739–741, doi:10.2307/1968964.
- Yamabe, H.; Yujobô, Z. (1950), "On the continuous function defined on a sphere", Osaka Math. J., 2 (1): 19–22.
- Floyd, E. E. (1955), "Real-valued mappings of spheres", Proceedings of the American Mathematical Society, 6 (6): 957–959, doi:10.2307/2033116.
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