Discovering Patterns in Pi: Is It Possible?

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Discussion Overview

The discussion revolves around the possibility of discovering patterns in the digits of pi, particularly in the context of its irrationality and the implications of finding such patterns. Participants explore theoretical scenarios and the nature of irrational numbers, focusing on whether patterns can exist within them.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants question whether any patterns in pi, such as every 97th digit being a specific number, could exist despite pi being known as an irrational number.
  • Others assert that pi is irrational and therefore does not exhibit patterns, although they acknowledge that no proof exists to definitively rule out the existence of such patterns.
  • A hypothetical scenario is presented where a pattern is found in an irrational number, prompting questions about the implications for its irrationality and the reasons behind the existence of such a pattern.
  • Some participants note that irrational numbers can have patterns, provided they do not repeat a fixed sequence indefinitely.
  • There is a discussion about how the existence of a pattern might depend on the numerical base used, suggesting that patterns could vary across different representations.

Areas of Agreement / Disagreement

Participants express differing views on the existence of patterns in pi, with some asserting that no patterns can exist while others entertain the possibility of patterns in irrational numbers more generally. The discussion remains unresolved regarding the implications of finding patterns in pi or other irrational numbers.

Contextual Notes

Participants highlight the lack of proof regarding the existence of patterns in pi and the dependence of potential patterns on the numerical base used, indicating that the discussion is limited by these unresolved aspects.

thetexan
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Has anyone every discovered any patterns in pi such as...every 97th digit is a 3? or something similar?

I know there is no repeatable pattern of digits but is there anything that precludes other patterns such as the above?

tex
 
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Pi is irrational. There is simply no pattern and it's not like anything prevents a pattern from occurring. Pi is just pi.
 
thetexan said:
Has anyone every discovered any patterns in pi such as...every 97th digit is a 3? or something similar?
No. It is expected that no such pattern exists ("normal number"), and billions to trillions of digits have been analyzed to look for patterns (for a huge amount of things you could call "pattern"), but there is no proof that no such pattern exists.
ProfuselyQuarky said:
Pi is irrational. There is simply no pattern and it's not like anything prevents a pattern from occurring. Pi is just pi.
There are irrational numbers with patterns like the one described by thetexan.
 
mfb said:
There are irrational numbers with patterns like the one described by thetexan.
You are right.
 
Well, that brings up this question.

Let's say they did find a pattern in an irrational number...every 105th digit is a 7. What would that imply? Would it still be irrational? Would we be able to figure out why the pattern exists?

tex
 
thetexan said:
Well, that brings up this question.

Let's say they did find a pattern in an irrational number...every 105th digit is a 7. What would that imply? Would it still be irrational? Would we be able to figure out why the pattern exists?

tex
If we include a 7 at every 107th digit of ##\pi## I would bet the new number will still be transcendental. There are still 106 digits where anything can happen.
 
There are irrational numbers where every 105th digit is 7. That is perfectly fine - as long as the number does not have a fixed sequence (and nothing else after some point) repeated to infinity in its decimal expansion it is irrational.

As an example, if you replace every 105th digit in the decimal expansion of pi by 7, you get an irrational number with that pattern.
thetexan said:
Would we be able to figure out why the pattern exists?
What does "why" even mean? Why is pi larger than 3?

It would be extremely odd, because such a pattern would depend on the base we use - we use base 10, in binary, ternary or whatever else you would not have that pattern.
 

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