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Monthly Article Explores Arranging Stars on U.S. Flag

A June 13 Inside Science TV spot highlighted work by Emory University mathematician Skip Garibaldi on the question of how to adjust the arrangement of stars on the American flag to accommodate a 51st star. A paper that appeared in the June/July 2012 issue of The American Mathematical Monthly explores a related but more general problem: for which numbers of stars between 1 and 100 do "nice" arrangements exist?


In "Arrangements of Stars on the American Flag," Dimitris Koukoulopoulos (University of Montreal) and Johann Thiel (United States Military Academy) take a Slate article by Chris Wilson—which also focuses on Garibaldi's work—as a starting point and fold in results (due to Paul Erdős) about multiplication tables of integers. The authors characterize the rarity of nice arrangements and show that for some numbers—29, for example—no such arrangement exists.

Read the paper (pdf).

News Date: 
Thursday, June 20, 2013