Patterns in Pi

  • B
  • Thread starter thetexan
  • Start date
  • #1
thetexan
255
9
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
 

Answers and Replies

  • #2
ProfuselyQuarky
Gold Member
831
542
Pi is irrational. There is simply no pattern and it's not like anything prevents a pattern from occurring. Pi is just pi.
 
  • #3
36,025
12,923
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.
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.
 
  • #4
ProfuselyQuarky
Gold Member
831
542
There are irrational numbers with patterns like the one described by thetexan.
You are right.
 
  • #5
thetexan
255
9
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
 
  • #6
fresh_42
Mentor
Insights Author
2021 Award
16,883
16,547
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.
 
  • #7
36,025
12,923
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.
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.
 

Suggested for: Patterns in Pi

  • Last Post
Replies
21
Views
3K
  • Last Post
Replies
17
Views
4K
  • Last Post
Replies
21
Views
4K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
13
Views
2K
  • Last Post
Replies
17
Views
991
  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
3K
Top