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Ask HN: How do you calculate Pi to N digits?

6 points by eddtries ↗ HN
How do you actually calculate pi to say 1000 digits? or 10,000? Most info I found on google take you to pre-solved lists of digits OR code that is optimised beyond recognition so I'm unsure how you actually do the calculation to begin with.

12 comments

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FrankWilhoit
Search "infinite series for pi". Several sources contain historical surveys of series: the earliest-discovered converge slowly, the best recent ones I think quadruple the number of digits on each iteration.
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Someone
https://en.wikipedia.org/wiki/Approximations_of_π

The method of using inscribed and circumscribed n-gons conceptually is the simplest (1), but converges very slowly. See https://arxiv.org/pdf/2008.07995.pdf.

(1) at least to non-mathematicians. Pure mathematicians will want to prove the claims that the circumference of a circle is larger than/smaller than that of its inscribed/circumscribed polygon and that both can get arbitrarily close to it if the number of sides gets large enough.

westurner
To approximate an arbitrary number of digits of pi with sympy:

  #! pip install sympy gmpy
  import sympy
  sympy.evalf(sympy.pi)
  sympy.N(sympy.pi)
https://docs.sympy.org/latest/modules/evalf.html

RosettaCode > [Python] lists quite a few more: https://rosettacode.org/wiki/Pi#Python

eddtries
I want to try write the underlying code myself, but thanks!
westurner
gmpy2.const_pi(precision=0: =53bits) probably isn't too helpful then either: https://gmpy2.readthedocs.io/en/latest/mpfr.html#gmpy2.const... https://github.com/aleaxit/gmpy/issues/253#issue-499509692

RosettaCode has only one solution to the "Approximate Pi with Rationals (not float64s)" in Python problem.

I remember having seen a few statistical manifestation of Pi demos on YouTube