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Hello, I want to ask you following question: I heard, that there is proof, that for every $n$, the area of a largest cross-section of a $n$-dimensional unit cube is $\sqrt{2}$. Google give me this link: What is known about unit cubes, but it only gives the estimate that it's no greater than $5$. So, is this problem solved?

There is related question: Area of cross-section (at midpoint perpendicular to longest diagonal) in the unit cube of dimension N

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Just to make sure, you ask about codimension one cross-sections right? If so, doesn't theorem 1.3 in that paper answer your question? – Gjergji Zaimi Oct 14 2011 at 6:20
Oh, you absolutely right, I missed it. How can I close the question? – Nurdin Takenov Oct 14 2011 at 6:29
OK, I close the qusetion. – Nurdin Takenov Oct 14 2011 at 6:30

closed as no longer relevant by Nurdin Takenov, Denis Serre, Gjergji Zaimi, S. Carnahan♦ Oct 14 2011 at 7:33

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