Pappas, Eckel, and Betz: The Purple-Hair Theorem

The Purple-Hair Theorem

printer friendly email this article

Peter Pappas, professor of mathematics, Sandy Eckel '04, and Rachel Betz '05 (two of his Undergraduate Research Summer Institute fellows from the summer of 2004) discovered and developed a theory of "telling time in higher dimensions," using a new class of objects called lag-time torus knots which they have completely classified.

During their work, Pappas and his group developed a conjecture on the behavior of these objects, and he told them that he'd give them anything they wanted if they could prove this conjecture. "What I had in mind was a nice dinner, or a 'free-food event' as they used to call it," said Pappas. Early one evening at his apartment, the doorbell rang, and "there were Sandy and Rachel with huge grins on their faces, looking very tired, holding this box of purple hair dye. They handed me their proof of the conjecture, and told me that I had to dye my hair purple and give a talk in front of all of URSI the following week. So I did it--their proof was correct and ingenious."

When Pappas speaks on lag-time torus knots at conferences, mathematicians always ask for "The Frequency Result" by its popular name, "The Purple-Hair Theorem."