Virginia Mathematics Teacher Fall 2016

that are almost squares. Perhaps, for instance, there is a way to morph from Dudeney's construction to the -turn construction. The open question is: Given a rectangle R (where ), what is the smallest value x so that three rectangles can be arranged to cover R ? Coverings of sets play an important theoretical role in many fields of mathematics, particularly those that are related to topology. However, in those fields, it is usually only necessary to know that the right kinds of coverings are possible. It is not particularly important that they be optimally arranged, so this problem has not been studied extensively. Recently, there has been some interest in related problems of coverings by circles, squares, and other regular polygons. A gallery of best-known results may be found at the webpage www2.stetson.edu/~efriedma/ packing.html.

Matt Harvey Associate Professor of Mathe­ matics The University of Virginia’s College at Wise msh3e@uvawise.edu

Virginia Mathematics Teacher vol. 43, no. 1

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