Power of Patterns
Follow this link to see how a high school student can perform and memorize a complex calculation of two infinite power series to prove trigonometric identities using the binomial expansion and pascal triangle as the reference patterns;
http://www.youtube.com/watch?v=7qilS6LHEWo
He then challenges you to perform the same feat and to send your succesful challenge to the Face Book page of the Math & Physics Exploration. Under Activities, Math, and trigonometry you can follow his example.
