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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
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Page Count: 6
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Isoperimetric Sets of Integers
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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.

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