Finding a Digit of Pi Without Previous Knowledge

[STAii]

I heard there is a certain way to find a certain digit of Pi without knowing the digits before it.
Now i tried to make a search on it, and i got some pages, but frankly couldn't understand anything in them !
So i would appreciate if someone could explain to me in a simple way how to figure out a certain digit of Pi without the digits before.
Thanks in advance.

 

[Integral]

I have seen this algorithm on the web, I do not have a link and cannot point you to it, but it does exist.

One thing it was not, was simple. It was a very complex algorithm that I could not even begin to sort out. I do not think there is a simple way to do it, sorry.
Staii,
Glad to see that you are still posting.

 

[Moni]

I also need that, would please try to remember where you got that ?

 

[lethe]

just check mathworld. http://mathworld.wolfram.com/Bailey-Borwein-PlouffeAlgorithm.html

 

[Integral]

That is not the algorithm I saw, nor is it clear to me exatly how the linked one works. Is n the number of the digit you need to generate? if so it means you must sum to n, how does that differ from generating all preceding digits?

 

[lethe]

Originally posted by Integral
That is not the algorithm I saw, nor is it clear to me exatly how the linked one works. Is n the number of the digit you need to generate? if so it means you must sum to n, how does that differ from generating all preceding digits?

that infinite sum there has a (1/16)ⁿ. that means that the nth term of the series is the nth digit in a hexadecimal representation. in general, what is meant by a representation in some base is an infinite sum with a geometric term in the base of the number.

 

[Hurkyl]

The bibliography on that link links to a page (I think by the inventors) that describes the formula and how one can actually go about evaluating it fairly quickly).

Hurkyl

 

[STAii]

Umm ...
Well the problem i faced was only in knowning how to apply the formula !
I just got this idea yesterday, i can program an application that can use ONLY the processing power that is not used in each one's PC (the Idle Proccess) to make something usefull.
So the first thing i could thing of, was caclulating Pi.
And, it will be inpractical to use any formula that depends on preceeding data (iow, forumlas that do not calculate each digit alone), cause there will be thousands of computers working at the same time, but not connected.
So each computer has to work on a certain range of digits, without depending on previous data (which may be not completed yet !).
Anyways ... i will try to make some more research, and will come back here to discuss it (and ask for help for sure ).

Staii,
Glad to see that you are still posting.

Thank you Integral, people like you on the forums are those who keep me going on .