Combinatorial Trigonometry (and a method to DIE for)

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.

Speaker Bio: Arthur Benjamin grew up in Cleveland, Ohio, and earned his B.S. at Carnegie Mellon University in 1983 and his PhD in Mathematical Sciences at Johns Hopkins University in 1989. Since then he has been a Professor of Mathematics at Harvey Mudd College, in Claremont, California, where he has served as department chair. He has written three books and is co-Editor of Math Horizons magazine, published by the Mathematical Association of America (MAA). In 2000, the MAA awarded him the Haimo Prize for Distinguished University Teaching. Arthur Benjamin is also a professional magician, and frequently performs at the Magic Castle in Hollywood. He is the author of several books, including "Secrets of Mental Math" and the DVD course "The Joy of Mathematics," produced by The Teaching Company. He has demonstrated and explained his calculating talents to audiences all over the world and has appeared on numerous television and radio programs, including The Today Show, CNN, and National Public Radio. He has been featured in Scientific American, Omni, Discover, People, Esquire, New York Times, Los Angeles Times, and Reader's Digest. In 2005, Reader's Digest called him "America's Best Math Whiz."

Presentation Slides: PDF

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