In 1593, Francois Vieta gave an expression equivalent to the infinite product,
expressing ππ using only 2's and square roots. After more than 400 years, even today, it seems that every proof of uses the double angle identity cos2x=2cos2x−1cos2x=2cos2x−1 , having the flavor of Vieta’s idea. The purpose of this note is to show that the convergence of the infinite product in can be proved without using trigonometric identities but using only the mathematics taught in high school, that is, basic algebra, Geometric Mean-Arithmetic Mean Inequality of two positive numbers and induction.
University of Colombo, Sri Lanka
Tue, 19/04/2016 - 12:00pm to 1:00pm
RC-4082, The Red Centre, UNSW