mathoverflow.net/questions/247882 the maximal area is $\sqrt{2}$
it is attained only if the hyperplane has a normal unit vector with two nonzero coordinates with absolute value $1/\sqrt2$
As far as I know this is Ball's theorem. Fedja wrote a simple proof once many years ago math.spbu.ru/analysis/f-doska/cube.pdf Pooley2012.pdf(635.45 KB, Downloads: 41)
mathoverflow.net/questions/430553/
Let $1<n\in\mathbb N,$ $S(n)$ is the greatest $(n-1)$-area of $L\cap I^n$ where $I^n\subseteq\mathbb R^n$ is the unit cube, and $L$ runs over all possible affine $(n-1)$-hyperplanes.
For all $n>1$, $S(n)=\sqrt2$, it is a result of Keith Ball PDF K. M. Ball. Cube slicing in Rn. Proc Amer Math Soc 97:3 (1986), pp. 465-473
hbghlyj
posted 2023-4-14 20:10
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