Finding a Digit of Pi Without Previous Knowledge

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Discussion Overview

The discussion revolves around methods for calculating a specific digit of Pi without needing the preceding digits. Participants explore the complexity of existing algorithms and share resources, while expressing challenges in understanding and applying these methods.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks a simple explanation for finding a digit of Pi without prior knowledge of the digits.
  • Another participant mentions having encountered a complex algorithm online but finds it difficult to understand.
  • A suggestion is made to check MathWorld for the Bailey-Borwein-Plouffe algorithm, which is believed to relate to the topic.
  • There is uncertainty about the algorithm's workings, particularly regarding the role of 'n' in generating the desired digit.
  • A participant explains that the infinite sum in the algorithm has a term (1/16)^n, indicating that it relates to hexadecimal representation.
  • One participant expresses a desire to develop an application that utilizes idle processing power to calculate Pi, emphasizing the need for a method that does not rely on previous digits.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the simplicity or clarity of the algorithms discussed. There are multiple viewpoints regarding the complexity of the methods and their applicability to the problem at hand.

Contextual Notes

Participants express challenges in understanding the algorithms and their applications, indicating potential limitations in their explanations or the resources referenced.

STAii
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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.
 
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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.
 
I also need that, would please try to remember where you got that ?
 
just check mathworld. http://mathworld.wolfram.com/Bailey-Borwein-PlouffeAlgorithm.html
 
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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?
 
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.
 
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
 
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 :smile:).
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 :smile:.
 

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