There are a lot of ways to calculate digits of $\pi$ using Mathematica. The most naïve way I can think of is
Of course, there are a lot of fast classic formulas (Chudnovsky, Ramanujan) to achieve this goal. I'm wondering what is the fastest way to calculate digits of $\pi$ using Mathematica. The reason that this question may be interesting is that Mathematica has a lot of unique features that can make this calculation faster (or can improve known classic ways of calculating $\pi$).
What are your ideas for calculating digits of $\pi$ using Mathematica in the fastest way possible?
A good answer will involve:
- Explanation of the reason of choosing a particular formula / algorithm.
- Why this particular Method is optimal (in Mathematica at least).
- Optional: Why this Method suits best the use of Mathematica compared with other languages.
Note: As @J.M. points, Mathematica implements the Chudnovsky formula for the default calculation.