Anyone familiar with the BBP formula?

Here's a link for convenience: http://en.wikipedia.org/wiki/Bailey%E2%8...fe_formula

Wow. I knew there are algorithms for calculating the digits of transcendent numbers directly, but I didn't know how it worked. This is a beauty! Amazing!

It's beautiful to me too...

...in the way that a hammer to the skull appears...

...when I see what smart people find beautiful.

The point is that we have a formula which gives pi as a sum with powers of 1/16, so the first four terms for example come with pre-factors 1/16^k =

k=0: 1
k=1: 1/16
k=2: 1/256
K=3: 1/4096 ....

Since this becomes small so quickly, the formula yields an impressive precision using very few of these terms. Taking the sum to k=3 only, we already obtain seven digit precision,

47/15 + 53/6552 + 829/5026560 + 79/15590400 = 3.1415924....

as opposed to pi= 3.1415926....

Edit: description has slightly changed

More importantly, since this pre-factor becomes smaller in this very particular fashion, one can reverse engineer how these terms in the sum contribute to any particular arbitrary digit of pi. This allows us to calculate the, say, quadrillion and oneth digit of pi without having to calculate the quadrillion digits preceding it, with minimal calculational effort of a tiny fraction of the computing time one would otherwise need. Edit: finding the quadrillionth digit is still a huge computing problem using this method, but would be completely unreachable otherwise.

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

http://www.ams.org/samplings/feature-column/fcarc-pi

Mhm. Uh-huh. Yeah.

I know some of these words.

Some people have way too much time on their hands. I suppose I get the fact that mutiple computers working simultaneously could conceivably save computing time and space, but I'm confident that the number of digits we're talking about to make this a consideration is absurd. I'm struggling to think of any other practical application.

(February 3, 2015 at 12:32 pm)Cato Wrote: Some people have way too much time on their hands. I suppose I get the fact that mutiple computers working simultaneously could conceivably save computing time and space, but I'm confident that the number of digits we're talking about to make this a consideration is absurd. I'm struggling to think of any other practical application.

We rarely see what useful things pure research will yield, but it always results in knowledge.

It seems to me to be mathematician's art.