How is pi generated?

• Epic Sandwich

Epic Sandwich

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.

Answers and Replies

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:
Is there a way to calculate the number of the nth digit without expanding out pi?

What do you mean Anonymous217?

Oh! You mean like take pi and you want to find a number in pi at a particular digit?

http://www.math.hmc.edu/funfacts/ffiles/20010.5.shtml

Last edited:
^ Yes! That's what I was looking for. Thank you.