How is Pi Generated? Answers to Your Questions

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Discussion Overview

The discussion centers around the generation of the mathematical constant pi, exploring how its digits can be calculated and the methods used to discover additional digits. The scope includes theoretical approaches, mathematical reasoning, and references to computational techniques.

Discussion Character

  • Exploratory, Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant expresses curiosity about how pi can be generated indefinitely and how additional digits are discovered.
  • Another participant mentions that there are many formulae for calculating pi, providing a link to a reference.
  • A participant describes the use of infinite series, specifically mentioning the arctan series, and notes that while it can converge to pi, it does so slowly, requiring many terms for accuracy.
  • It is suggested that there are better infinite series available for calculating pi, with a reference to Ramanujan's formula.
  • A participant inquires about calculating the nth digit of pi without expanding it, prompting clarification from another participant.
  • A later reply confirms the interest in finding a specific digit of pi, indicating a desire for methods related to digit extraction.

Areas of Agreement / Disagreement

Participants present various methods for calculating pi, but there is no consensus on a single approach or method. The discussion includes both theoretical and computational perspectives without resolving which is superior.

Contextual Notes

Some methods mentioned may depend on specific mathematical assumptions or definitions, and the discussion does not resolve the efficiency or accuracy of the various approaches presented.

Who May Find This Useful

Readers interested in mathematical constants, computational methods in mathematics, or the history and theory of pi may find this discussion relevant.

Epic Sandwich
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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.
 
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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 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?
 
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.
 

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