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How is pi generated?

  1. Mar 16, 2010 #1
    I was thinking about this recently since it was pi a few days ago :) How is pi, the number, generated in a way that can go on forever? How are extra characters discovered? Thanks.
     
  2. jcsd
  3. Mar 16, 2010 #2

    phyzguy

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  4. Mar 16, 2010 #3
    We usually use an infinite series that converges to pi or some other iterative method.

    For example arctan(x) = x - x^3/3 + x^5/5 - x^7/7 + ... up to infinity. If x=1 then arctan(1) = pi/4 so you can see that you could calculate pi in such a way. The problem is that this infinite series converges (approaches) pi very slowly. What this means is that you need to add a lot of terms before the number starts to look like pi.

    Currently, there are much better infinite series to use for example: http://planetmath.org/encyclopedia/RamanujansFormulaForPi.html [Broken] is a much better infinite series to use to calculate pi.

    Typically the computations are done, well, by computers that are able of doing calculations very fast. I think that currently pi has been calculated to like 10 billion digits or something ridiculous like that.
     
    Last edited by a moderator: May 4, 2017
  5. Mar 16, 2010 #4
  6. Mar 17, 2010 #5
    Is there a way to calculate the number of the nth digit without expanding out pi?
     
  7. Mar 17, 2010 #6
    Last edited: Mar 17, 2010
  8. Mar 17, 2010 #7
    ^ Yes! That's what I was looking for. Thank you.
     
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