Mathematics Colloquium: Combinatorial Trigonometry (and a method to DIE for)
3:00 PM Neill 5W (refreshments in Neill Hall 216 Hacker Lounge 216 at 2:30 PM)
Arthur T. Benjamin Harvey Mudd College
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, zig-zag permutations, and Chebyshev polynomials.