Abstract
Consider a d-dimensional closed ball B whose center coincides with that of the hypercube [0, 1]d. Pick the radius of B in such a way that the vertices of the hypercube are outside of B and the midpoints of its edges in the interior of B. It is known that, when d ≥ 3, the (d − 1)-dimensional volume of H∩[0, 1]d, where H is a hyperplane of ℝd tangent to B, is largest possible if and only if H is orthogonal to a diagonal of the hypercube. It is shown here that the same holds when d ≥ 5 but the interior of B is only required to contain the centers of the square faces of the hypercube.
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