its possible, but not definate, because pi's digits aernt random, so theres no surety that the combination will be present in an infiniate given number of digits

luca-deltodesco wrote:

its possible, but not definate, because pi's digits aernt random, so theres no surety that the combination will be present in an infiniate given number of digits

no but they doesnt repeat and start over from 14159 (or at least noone has seen any kind of pattern in it as far as i know), so it must be an irrational order all the way...and since there are an infinite amount of numbers.....:p

Kurre, as luca pointed out, you make the assumption that pi's digits are random.  That does have to be the case.

For example, there doesn't have to be a 1/10th chance that the next digit will be 8.  There could be a 1/100th chance, and it would still be irrational.  Right now, we are finding that there are long strings of digits where 9 is completely absent.  We are trying to find out if at one point it will drop out all together.

luca-deltodesco wrote:

infinate amount of numbers doesnt mean infinate amount of combinations, take for example

0.1111111111111111111....111112

i.e. infinate 1's then a 2, infinate numbers, no pattern, but you can only get a combination involving 1's, or 1's with a 2 on the end

But luca, that doesn't make any sense. If there was an infinite amount of 1's, then they wouldn't stop and suddenly end with a 2, because then the 1's must be finite.

Interesting question.
It may be extended for another numbers, such as e, phi, sqrt(2), ect.
Last month I read about this theme.
I'll post a link with information.

Such numbers are called normal.
Here is it: (I'm not explaining because the explanations are there):
http://en.wikipedia.org/wiki/Normal_number

I am of the belief that there are patterns of digits of long lengths that won't exist in pi.
It is just a guess, but an analogy is that if time went on forever, you could not do everything you wanted to do so you have to pick and choose.

John E. Franklin wrote:

if time went on forever, you could not do everything you wanted to do so you have to pick and choose.

If time went on forever, there will always be time to do at least one more thing. If there is always time to do at least one more thing, there would be no reason to have to pick and choose since you would have time to do everything.

Patrick wrote:

Well, you're assuming pi doesn't have an exact value, but it does - as far as I've understood. It is EXACTLY:

where P is the perimeter of a circle and d is its diameter. So just because we can't seem to find a pattern, it doesn't have to mean the digits are random. Or am I totally off track?

I don't think anyone is claiming Pi does not have an exact value. It is just an exact value that cannot be shown with a ratio of two integers.

Ricky wrote:

"Random" has a meaning implied behind it which I think many have not heard of.

If I have 5 marbles in a bag, each a different color, and I have only a 10% chance of pulling out the blue marble, then the action of pulling out marbles is not a random one.

When we say random, we mean that the chances of all events happening are equal.

Now I believe statistically speaking, the number of digits in pi do not appear an equal number of times.  It's been a while, I'll have to see if I can find that again.  Thus, the digits in pi are not equal.

Now we only know a finite number of the digits.  So many this is only because we are looking at a subset of the digits that they aren't equal.  But when we've calculated it to over 50,000 places, thats normally enough to get a pretty good picture.

I think the important thing to remember is that since Pi has an infinite number of decimal places without a recognizable pattern, it does not matter if 1 appears more often than 5, since they will both appear an infinite number of times. The same goes for 09821346598712985170279561278934560 and 98435019823450928834087 both of which should appear an infinite number of times. Pi has been calculated to millions of decimal places, but that is still just a drop in the bucket of the infinite number of decimal places the irrational number contains.