A $1 Problem

Michael Mossingoff, Davidson College

June 22nd, 2005 at 3:30pm in K9509.

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.