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High Quality Content by WIKIPEDIA articles! 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 whose faces touch the body. The result was further generalized by Yamabe and Yujobô to higher dimension, and by Floyd to other circumscribed parallelepipeds. Kakutani attended Tohoku University in Sendai, where his advisor was Tatsujir Shimizu. Early in his career he spent two years at the Institute for Advanced Study in Princeton at the invitation of the German mathematician Hermann Weyl. While there, he also met John von Neumann.