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Pi inside pi inside pi ..by Edi
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#1
Jan1513, 07:47 AM

P: 176

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
Jan1513, 08:08 AM

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



#3
Jan1513, 08:32 AM

P: 907

There can only be countably many nonterminating 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 nonterminating decimal expansions, it is certain that not all of them appear. 


#4
Jan1513, 02:14 PM

P: 150

Pi inside pi inside pi ..



#5
Jan1513, 02:19 PM

P: 7

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
Jan1513, 02:24 PM

P: 907




#7
Jan1513, 03:11 PM

P: 824

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



#8
Jan1513, 06:21 PM

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


#9
Jan1613, 10:32 AM

P: 886

You are looking for a number n such that 10^n*pipi is an integer. Call this integer q.
Then (10^n1)*pi = q pi = q/(10^n1) 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
Jan1613, 11:45 AM

P: 907




#11
Jan1613, 06:34 PM

P: 886

you know what I meant.



#12
Jan1713, 02:42 AM

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#13
Jan1713, 07:24 AM

P: 907

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



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