
A $1 ProblemMichael Mossingoff, Davidson College
Abstract: Suppose you need to design a $1 coin with a polygonal shape, fixed diameter, and maximal area or maximal perimeter. Are regular polygons optimal? Does the answer depend on the number of sides? With the aid of a computer algebra system, we investigate these two extremal problems for polygons, and show how to construct polygons that are optimal, or very nearly so, in almost every case. 