Today on Twitter John D. Cook, writing as @AlgebraFact, posted the following tweet: In radians, sin(11) is very nearly -1. (It happens to be -0.9999902…) I thought that was awesome! So, I (@divbyzero) replied that cos(333) is approximately 1. (It is 0.999961…) Then @michiexile chimed in, pointing out that cos(355) is closer to -1 than…

# Tag: continued fraction

## A new continued fraction for pi

I love continued fractions. The golden ratio: The square root of 2: The base of the natural logarithm: Pi: In the most recent American Mathematical Monthly (December 2008) Thomas J. Pickett and Ann Coleman, in their note “Another Continued Fraction for ,” present the following beautiful continued fraction in which the terms down the diagonal…