Talking about Pi

[rov1200]

If you take the digits 0 - 9 of Pi over a long stretch do they eventually settle out almost 1/10th of the total for each. For example if you toss a coin 1000 times it should be close to 500 heads.

3.1415926535897932384626433832795028841971693
9937510

582097494459230781640628620899862803482534211
70679

821480865132823066470938446095505822317253594
08128

481117450284102701938521105559644622948954930
38196

442881097566593344612847564823378678316527120
19091

456485669234603486104543266482133936072602491
41273

724587006606315588174881520920962829254091715
36436

789259036001133053054882046652138414695194151
16094

330572703657595919530921861173819326117931051
18548

074462379962749567351885752724891227938183011
94912

983367336244065664308602139494639522473719070
21798

609437027705392171762931767523846748184676694
05132

000568127145263560827785771342757789609173637
17872

146844090122495343014654958537105079227968925
89235

420199561121290219608640344181598136297747713
09960

518707211349999998372978049951059731732816096
31859

502445945534690830264252230825334468503526193
11881

710100031378387528865875332083814206171776691
47303

598253490428755468731159562863882353787593751
95778

185778053217122680661300192787661119590921642
01989

[factor-fiction]

Well, i have just checked the first 10 million digits and teh results are:
in first 10,000,000 digits of pi
0 - 999440
1 - 999333
2 - 1000306
3 - 999965
4 - 1001093
5 -1000466
6 -999337
7 1000206
8 999814
9 1000040

[rov1200]

That was quick factor30. What got me thinking about this question was the sometimes long sequences of the same number. Even with the 1000 numbers above there was a sequence of 6 nines. I'm sure there must be sequences greater than this.

[mibn2cweus]

That looks to me like factor 30 listed the occurrences of each digit 0-9 in the first 10000000 digits of pi. Looks like a fairly random distribution to me.

[mibn2cweus]

The string 666666666 occurs at position 45,681,781 counting from the first digit after the decimal point. The 3. is not counted.

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

[squarebear]

Pi goes on for an infinite number of digits, so there will be an infinite number of each digit.

[beso]

Pi has been calculated to 2.7 trillion decimal places.

However any of the digits of Pi can be determined without calculating those that come before the digit being calculated.

A 256 binary digit sequence including the two quadrillionth bit has recently been calculated using spare capacity in the Yahoo search engine.

It took 23 days to calculate and over 500 years of CPU time.

http://www.newscienti...yahoos-computers.html

http://arxiv.org/abs/1008.3171

[mike11111]

I think your post should be merged with this one.
http://www.theanswerb...g/Question945711.html

[rov1200]

I can't agree that factor30 results appear random. A regression towards the figure of 1,000,000 appears to happen spread over a 10 million sequence. Possibly over a longer sequence there could even be a better fit.

Statistics seems to operate at two levels. Random events such as tossing the coin eventually adhere to a non random outcome when taken over a long period of time.

[beso]

Rubbish. Unless there is some bias in the coin, tosses do not adhere to non-random outcomes as the nuber of tosses increases.

Random does not mean they are all the same. Well understood theory predicts the probability of various outcomes ranges. The probability of all possible outcomes being of absolutely equal frequency is very small even for a truly random distribution. I have no doubt the figures posted for Pi by factor30 fall into a very high probability range of frequencies.

[factor-fiction]

Sorry rov- you've lost me there. I think people are just using the term 'random' in slightly different ways. I think we all agree that based on as you increase the number of decimal places analysed, each digit's share gets closer to 10%. In my data after 10 billion digits the least frequent digit (1) occured 9.993% of the time and the most frequent digit (4) occured 10.011% of the time. This small variation from an equal distribution (10%) is probably just as close as you'd get if you rolled a 10 sided dice 10 billion times.

However I think I read somewhere that if you examine 3 digit strings, 000 appears more than any 111 or 222 or...or 999.

[mibn2cweus]

Seems like back when I played those heads or tails games I always fared best when I let my opponent make most of the predictions . . . I loath guessing.