# A Set of Pi for Ellipses

On last Pi-Day, I’ve sent some friends a poster showing an approximation of $$\pi$$ that is individual to them. You can find an example of “my” $$\pi$$ here. This time, however, I wanted to calculate the actual Pi as accurate as I could. By hand. Entirely. So I decided to do it up to the 20th decimal place, fairly accurate and the involved numbers will be small enough to fit on printing paper. The method I wanted to use was invented by the great Newton in 1666: \[\pi = 2\, \sum^{\infty}_{k=0}{\...