I did some quick research and discovered that the Chudnovsky algorithm is the fastest and most accurate way for calculating Pi. But does anyone know how it works?
The explanation of why the Chudnovsky series converges to pi is quite involved:
it involves Generalized Geometric Series, Ramanujan Series, J-invariants, Fourier Series, Elliptic functions, Modular Groups … and a whole lot more advanced math concepts.
Some aspects were only understood very recently (2012).
If you want to start understanding the ideas behind these types of series you may start with Fourier Series and Generalized Geometric Series.
I’ll pass. 
Haha. Maybe I will start smaller and then get somewhere.
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What if you try making the hexadecimal Pi spigot (the one that gives you one digit in base 16, independent from others)?
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