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Arrangements of Stars on the American Flag

by Dimitris Koukoulopoulos and Johann Thiel

Year of Award: 2013

Award: Halmos-Ford

Publication Information: The American Mathematical Monthly, vol. 119, 2012, pp. 443-450

Summary: (Adapted from the MathFest 2013 Prizes and Awards Booklet) Reasonable star patterns on the American flag correspond to special factorizations; the density of such factorizations is less than the density of values in a multiplication table; Paul Erdös showed this density asymptotically approaches zero by considering the average number of prime factors of an integer.

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About the Authors: (From the MathFest 2013 Prizes and Awards Booklet)

Dimitris Koukoulopoulos is an Assistant Professor at - the University of Montreal. He received his bachelor's degree from the Aristotle University of Thessaloniki before moving to the University of Illinois at Urbana-Champaign for his doctoral studies. He wrote his thesis on Erdos's multiplication problem and it's generalizations under the direction of Kevin Ford. Prior to joining the faculty of the University of Montreal, he spent two years as a postdoc at the Centre de Recherches Mathematiques at Montreal. His interests lie in analytic, multiplicative, additive, elementary, and probabilistic number theory.

DJohann Thiel is an Assistant Professor at the United States Military Academy in West Point, NY. He received his bachelor's and master's degrees from the University of Florida before attending the University of Illinois at Urbana-Champaign to continue his graduate studies. There, under the supervision of A. J. Hildebrand, he developed his appreciation for number theory, where his main interests currently lie.

Subject classification(s): Number Theory | Primes | Geometry and Topology | Plane Geometry | Patterns
Publication Date: 
Monday, August 19, 2013

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