Number Theory and the American Flag

The Union Jack is the top left corner of the American flag that contains one star for each state. In 2010, the Puerto Rico Democracy Act allowed for the potential addition of Puerto Rico as the 51st state, which would force the addition of a new star to the American flag. The work of Skip Garibaldi showed that "nice" arrangements for stars on the Union Jack exist for 1 to 100 stars with three exceptions. In this talk, we will introduce some modern results in number theory to examine just how unexpected these exceptions really are as the number of stars increases. We will show that the resolution of this design problem is closely related to a number theory problem of Paul Erdos. This is joint work with Dimitris Koukoulopoulos.

Johann Thiel