Pi

March 14th, 2017

$\pi = 0+\cfrac{4}{1+\cfrac{1^2}{3+\cfrac{2^2}{5+\cfrac{3^3}{7+\cfrac{4^2}{9+\cfrac{5^2}{\ddots\cfrac{}{2n-1+\cfrac{n^2}{\ddots}}}}}}}}$

Happy $$\pi$$ day! This uses my continued fraction library to compute digits of $$\pi$$. This continued fraction representation is due to John Wallis, with his famous Wallis product formula for $$\pi$$. (I actually cheated, and used the much faster converging simple continued fraction for the numerical value at the bottom, but it's just not as pretty.)