Just a note to self, so I don't lose some of these sites I've found.

I've been looking at algorithms to calculate π (pi) recently. I've not actually installed and learned anything like GMP, MAPM, MPFR, or other so-called "bignum" libraries, so I'm pretty much limited to the digits that can be stored in a double. *sniff* Well, I'll get around to it eventually, eh?

So, the major algorithms I've found are as follows:

- Archimedes' iterative algorithm for approximating Pi
- Archimedes' Algorithm for Pi
- Archimedes' Approximation of Pi
- http://physics.weber.edu/carroll/Archimedes/pi.htm
- Archimedes and the Computation of Pi

*n*-gon (starting with the square, or 4-gon) can yield a*2n*-gon,*ad infinitum*. The only limitation is the precision with which you can store numbers, in particular the square root of two (as your initial calculation of the diameter, given a 1×1 inscribed square). - The Bailey, Borwein, and Plouffe (BPP) formula
- Series expansions and Fibonacci numbers
- Pi and the Fibonacci Numbers (Talks about several series-expansion algorithms such as arctangent, Gregory's series, and Machin's formula.)

I've implemented Aristotle's algorithm and Gregory's series, and filled a double with accurate values for π (pi) fairly quickly. Actually, the expansion of Gregory's series rand several orders of magnitude faster. I suppose now I should install GMP and play with actual numbers instead of these piddly little doubles.

See also: History of numerical approximations of pi on Wikipedia