Otfried Schwarzkopf, Ulrich Fuchs, Günter Rote, and Emo Welzl:
Approximation of convex figures by pairs of rectangles
 (Preliminary extended abstract)
In:
Proceedings of the 7th Annual Symposium on Theoretical
Aspects of Computer Science (STACS'90), Rouen, February 1990.
Lecture Notes in Computer Science 415, SpringerVerlag, 1990,
pp. 240–249, (Zbl 729.68087, MR #91e:68148). doi:10.1007/3540522824_47

(Improved and extended version)
Computational Geometry, Theory and
Applications 10 (1998), pp. 77–87. doi:10.1016/S09257721(96)000193
Abstract
We consider the problem of approximating a convex figure in the plane by
a pair (r,R) of homothetic (i. e., similar and parallel) rectangles with
r contained in C and R containing C. 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 Szegö. 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).