Question:
Currently what is the fastest algorithm for computing pi?
Replies:
I do not know the details, but I know it is complicated. I think they use
some of the tan formulas. I believe there was a Scientific American article
on this somewhere between 5 and 10 years back. In any case, one part of the
problem is how to store all those digits, and how to multiply numbers with
that many digits, etc. I believe eventually (when you get to billions of
digits) the fastest multiplication of such numbers is by a convolution
approach using a Fast Fourier Transform! Of course, if you only want a
small number of digits its not that bad!
asmith The article asmith refers to was in the February 1988 issue of Scientific
American. Entitled "Ramanujan and pi", it gives a number of formulas for
the calculation of pi (including the one used by the article's authors, who
were the record holders for digits at the time the article was written).
There is also a nice capsule history of the calculation of pi and some
information on the amazing Indian mathematician Ramanujan. Highly recom-
mended reading.
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