Abstract
We consider the problem of approximating a convex figure in the plane by a pair ( r, R) of homothetic (that is, similar and parallel) rectangles with r ⊆ C ⊆ R. We show the existence of such a pair where the sides of the outer rectangle are at most twice as long as the sides of the inner rectangle, thereby solving a problem posed by Pólya and Szegő. If the n vertices of a convex polygon C are given as a sorted array, such an approximating pair of rectangles can be computed in time O(log 2 n).
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