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.