How is this done in practice?
Monte Carlo simulations?
What can be achieved on a regular computer?
How is this done in practice?
Monte Carlo simulations?
What can be achieved on a regular computer?
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I don't know what the optimal method is, but Parseval's theorem can be used to prove that (π^4)/90 = Σ (n^-4), with n starting at 1 and extending to infinity. It would be simple to throw that into a loop and calculate π to your desired precision. There's probably simpler equations for π as well
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How do you deal with rounding?
How do you check if those numbers are correct?
It says they used
numberworld.org
in this and the previous attempts.
I'd assume since the summation terms get progressively smaller, you could just keep adding them until the addition of another term has no affect on the nth digit. After that rounding shouldn't matter