This question was inspired by this Quora question.
I'm sure lots of you are familiar with the fact that we have many different representations of $\pi$, things like
$$
\begin{align}
\pi & = \sqrt{6\zeta(2)} \\
& = \frac{4}{1 + \frac{1^2}{3 + \frac{2^2}{5 + \frac{3^2}{7 + \frac{4^2}{9 + \ddots}}}...
Just this evening I had to remove the hamel-basis twice. The second time was almost exclusively old questions. I wish we had a 20k rep limit on new tags.
