Abstract
We consider the problem of approximating a convex figure in the plane by a pair (τ, R) of homothetic (i.e. similar and parallel) rectangles with τ⊂C⊂R. We show the existence of such pairs where the sides of the outer rectangle have length at most double the length 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(log3 n).KeywordsConvex HullConvex BodyConvex PolygonBinary SearchExpansion FactorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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