Can a mathematician show that: In the number [math] \pi [/math] there will never be a repetition of the numeral 1 one thousand times in a consecutive fashion?
What is the largest repetition, found to date, in [math] \pi [/math]?
Is the statistical analysis of [math] \pi [/math] in terms of repetition a glimpse into a random number generator?
This is [math] \pi [/math] as it walks in 10 dimensions.
>>8008603
and some more walking [math]\pi [/math]
The first 1000 digits of [math]\pi [/math] contain ample double consecutive digits (marked yellow), and a few triples (marked green). The presence of the sextuple (marked red) in such a small sample is an intriguing anomaly. For comparison, τ (2π) contains a run of 7 nines (marked purple) near the same point.
>>8008608
>keep it going to a trillion places
>it forms a perfect wireframe representation of costanza.jpg
>>8008591
>Can a mathematician show that: In the number π there will never be a repetition of the numeral 1 one thousand times in a consecutive fashion?
Probably not, because there does exist such a sequence in pi.
>>8008644
Where does it exist?
>>8008652
in this number
0.1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
>>8008652
I don't know, but probably it does, somewhere.
>>8008663
>The digits of π have no apparent pattern and have passed tests for statistical randomness, including tests for normality; a number of infinite length is called normal when all possible sequences of digits (of any given length) appear equally often.
>>8008664
That explanation is a bit misleading, this gives more info
>https://en.wikipedia.org/wiki/Normal_number
t. phd in wikipedia math
>>8008664
>>8008670
So [math]\pi [/math] is a special number that is infinitely long and will never have [math]\pi [/math] within itself?
I have searched through [math]\pi [/math] and found the sequence 31415926 three times in the 200 million digits of [math]\pi [/math].
>The string 31415926 occurs at position 50366472.
>The string 31415926 occurs at position 143343711.
>The string 31415926 occurs at position 157060182.
>>8008737
If pi contains pi within itself then
(10^n)pi - pi = x
where n and x are some integer
but then we have
pi(10^n-1) = x
pi = x/(10^n-1)
But this would mean pi is rational. By contradiction, pi cannot contain itself.
>>8008591
couple things
1) The answer to your question is "yes" if pi is "normal" as that other poster said, so read a little on normal numbers.
2) Looking at pi only in base 10 is probably not the best choice. Try binary, which is generally a lot more useful than base 10.
>>8008862
Fuck, I missed the word "not" in OP's post. The answer is "no" if pi is normal.
>>8008640
plz do this
>>8008635
>For comparison, τ (2π) contains a run of 7 nines (marked purple) near the same point.
But that's not really surprising since 2 x "......99999999...." is always going to have a bunch of 999999s in it.
FYI, the mathematical term for "1111111...." is
REPUNIT
Now you know a new word.
>>8010359
Thanks, I never knew.
>>8008591
Pi is transcendental, and goes on infinitely
You can find any sequence you like in the digits of pi
>>8010780
>Pi is transcendental, and goes on infinitely
So is 0.101001000100001...
but that obviously doesn't contain every finite sequence.
>>8010788
What he probably meant was the walk of pi in base 10 in 2 dimensions.
http://functions.wolfram.com/Constants/Pi/visualizations/2/ShowAll.html
