Fun Ways of Wrinting Pi (Pi Day 2020)

\(\pi\) is arguably the most (in)famous number.

Here are three fun ways of representing pi.

  1. \[\pi = 4 \int_{0}^{1}\sqrt{1 - x^2} dx\]

  2. \[\pi = 2 \int_{0}^{1} \frac{dx}{\sqrt{1 - x^2}}\]
  3. \[\pi = \sum_{n=0}^{\infty} \frac{(2n)!}{2^{2n - 1}(n!)^2(2n+1)}\]