Access

You are not currently logged in.

Access JSTOR through your library or other institution:

login

Log in through your institution.

Isoperimetric Sets of Integers

Steven J. Miller, Frank Morgan, Edward Newkirk, Lori Pedersen and Deividas Seferis
Mathematics Magazine
Vol. 84, No. 1 (February 2011), pp. 37-42
DOI: 10.4169/math.mag.84.1.037
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.84.1.037
Page Count: 6
  • Download ($16.00)
  • Subscribe ($19.50)
  • Cite this Item
Isoperimetric Sets of Integers
Preview not available

Abstract

Summary The celebrated isoperimetric theorem says that the circle provides the least-perimeter way to enclose a given area. In this note we discuss a generalization which moves the isoperimetric problem from the world of geometry to number theory and combinatorics. We show that the classical isoperimetric relationship between perimeter P and area A, namely P = cA1/2, holds asymptotically in the set of nonnegative integers.

Page Thumbnails