# How is pi generated?

## Main Question or Discussion Point

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.

phyzguy
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.

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

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