Also fun: The Arithmetic-Geometric Mean can be used to calculate Pi! (Most usefully, the AGM of 1 and sqrt(1/2).)

I was confused by this because pi is not between 1 and sqrt(1/2). But I found https://www.cs.miami.edu/home/burt/manuscripts/gaussagm/agma... and it clarifies that this AGM is used in the course of approximating pi not that it’s sufficient on its own to do so.