# A $1 Problem Year of Award: 2007 Award: Lester R. Ford Publication Information: The American Mathematical Monthly, vol. 113, (2006), pp. 385-402 Summary: (from the author's 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? We investigate these two extremal problems for polygons, and show how to construct polygons that are optimal, or very nearly so, in each case.

About the Author: (from The American Mathematical Monthly, (2006)) Michael J. Mossinghoff earned his B.S. in mathematics at Texas A&M University in 1986, completed his M.S. in computer science at Stanford in 1988, and earned his Ph.D. in number theory at the University of Texas at Austin in 1995. He has taught mathematics at Appalachian State University and computer science at UCLA, and he now teaches both subjects at Davidson College. His research focuses on extremal problems on polynomials, especially on problems involving Mahler’s measure. An avid coin collector in his youth, he remains interested in all sorts of pecuniary peculiarities.

Author (old format):
Michael J. Mossinghoff
Author(s):
Michael J. Mossinghoff
Flag for Digital Object Identifier:
Publication Date:
Wednesday, October 22, 2008
Publish Page:
Summary:

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? We investigate these two extremal problems for polygons, and show how to construct polygons that are optimal, or very nearly so, in each case.