# DailyDirt: Pi Math

### from the *urls-we-dig-up* dept

National Pie Day is not actually March 14th (although it really should be, if only to make it more memorable). But here's to the number, not the delicious dessert.
- Does pi contain every set of finite number sequences? The answer to that question may not be known, but the first trillion or so digits of pi appear to be statistically random -- with 0-9 appearing with even distributed frequency. [url]
- It's possible to calculate the nth digit of pi without calculating every previous digit. So the gazillionth digit of pi can be verified, if you really need to know it. [url]
- If you're thinking about coming up with a new way to calculate pi, you can check your work for the first several trillion digits. Beyond about 10 trillion digits, you're into record breaking territory, and you'll need to adopt some other strategies. [url]

Filed Under: calculations, irrational, math, numbers, pi

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Anonymous Coward,15 Feb 2013 @ 4:27am## Re: Re: Pi

it is far from random as you correctly stated because you can calculate it, but once you do that calculation you find the distribution of any number position to have a random distribution.

and as it meets the definition of a random distribution, given a string long enough all possible sequence combinations of any length will occur, 100% of the time.

and infinitely long random distribution of numbers IS LONG ENOUGH.

even a small number like 100 million random numbers give a 100% chance of getting 1 to 5 length string matches.

and 100 million is TINY, compared to 10000000 trillion which is tiny (equally tiny) compared to infinity.

you could put a digit on every cell in your body (approx. 50 million million) or 50 trillion cells and you would not even come close to finding that length sequence of numbers in an infinite sequence of random (distributed) numbers.

if fact the set of sequences of random number that would occur in an infinite set of random numbers is itself infinite.

so the probability of any sequence of any length is 100% that it will occur and infinite number of time within that infinite sequence. (of randomly distributed decimal numbers).

The length of the string of randomly distributed decimal numbers to ensure 100% chance of a sequence of ANY size can be calculated.

That calculation does not equal infinity, with a finite sequence length it's a finite number of randomly distributed numbers.

you could probably write a random number generator and have it generate a 100 digit number of random distribution.

very good odds you will have in it 10 1's

make it 1000 and you will have close to 100 1's

if it is a random distribution with 10 1's on your 100 digit number one of those 10 1's will be followed by the random number 2

so with a 100 length distribution you can expect 10 1's and 1 followed by 2 occurring on one occasion.

therefore with a 100 length distribution you have an almost 100% chance of getting the sequence '12' or any other 2 length sequence.

for 3 digits match, you are going to need all the 2 digit sequences to have occurred at least 10 times (to cover 0 to 9) so you are going to need 1000 random numbers to ensure 100% chance for a 3 digit match (of non-repeating random numbers).

to ensure 4 digits match, 10,000

with pi only calculated to 100 million places you can have 100% probability that a 0 to 5 length sequence will occur.

so if you need 100 million to ensure 5 length sequence, you would need 10 times that value for your 5 length to occur assuming a random number between 0 and 9 fall as the next number, now if it's only 10 times bigger there is a possibility of a number repeating, so if you make the size 100 times larger, your 5 sequence will occur 100 time within that sequence, out of that 100 time there is 100% chance the next digit will be a 0 to 9 digit.

so you can clearly see that you do not need a string of infinite length of distributed numbers to find any length finite size string match with 100% probability you just need an exponentially larger initial number.

No where even close to infinite

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