Note 1 in this MO question seems to suggest the maximal area inscribed rectangle in a planar convex region is also the maximal perimeter rectangle in convex shape. I am not entirely convinced this is always the case so I am asking for help in making a formal argument for it. Both area and perimeter are functions of the lengths of the sides of the rectangle, so it seems like a reasonable statement. How to find out a counterexample or show both characterize the same object?
2026-03-28 13:22:09.1774704129
Equivalent characterizations of inscribed rectangle in convex region
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