# Pi inside pi inside pi

1. Jan 15, 2013

### Edi

If pi is infinite and nonrepetive and every number combination is in pi, somewhere, does that mean pi itself is in pi somewhere.. ? (that would make it periodic)

2. Jan 15, 2013

### CompuChip

Yes, it is, starting at the first digit :)

3. Jan 15, 2013

### jbriggs444

If pi is "normal in base ten" then that would mean that every _finite_ sequence of decimal digits occurs somewhere in the decimal expansion of pi.

There can only be countably many non-terminating decimal expansions found in consecutive digits in the decimal expansion of pi -- the one starting at the first digit, the one starting at the second digit, the one starting at the third digit, etc.

Since there are uncountably many non-terminating decimal expansions, it is certain that not all of them appear.

4. Jan 15, 2013

Is there any proof that every (finite) number combination is in pi?

5. Jan 15, 2013

### telecomguy

The string 31415926 occurs at position 50,366,472 counting from the first digit after the decimal point.

http://www.angio.net/pi/bigpi.cgi

6. Jan 15, 2013

### jbriggs444

It is not known whether pi is normal in base 10.

7. Jan 15, 2013

$\pi$ is not periodic. If it were it would be in $\mathbb{Q}$ which it isn't.

8. Jan 15, 2013

### HallsofIvy

Interesting but does not answer the question which was about the entire countable string. On the other hand, Edi seems to be under the impression that we could have entire string, then additional digits which is not possible.

Edi, it is NOT known whether "every number combination is in pi" is true or not.

9. Jan 16, 2013

### Khashishi

You are looking for a number n such that 10^n*pi-pi is an integer. Call this integer q.
Then (10^n-1)*pi = q
pi = q/(10^n-1)
To find such an n, pi would have to be a rational number, which is isn't.
So, no, pi cannot repeat or contain itself.

10. Jan 16, 2013

### jbriggs444

As has been pointed out, n=0, q=0 satisfies this criterion. Pi contains itself -- in a trivial sense.

Yes
pi = 0/0 ?

11. Jan 16, 2013

### Khashishi

you know what I meant.

12. Jan 17, 2013

### CompuChip

Happy?

13. Jan 17, 2013

### jbriggs444

Well, I could be even more picky and take n = 0.1200175... and q = 1.

14. Jan 17, 2013