Title: Combinatorial Trigonometry (and a method to DIE for)
Speaker: Arthur T. Benjamin (Smallwood Family Professor of Mathematics, Harvey Mudd College)
Hosted by Chris Butler
Abstract: Many trigonometric identities, including the Pythagorean theorem, have combinatorial proofs. Furthermore, some combinatorial problems have trigonometric solutions. All of these problems can be reduced to alternating sums, and are attacked by a technique we call D.I.E. (Description, Involution, Exception). This technique offers new insights to identities involving binomial coefficients, Fibonacci numbers, derangements,and Chebyshev polynomials.