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Pi Calculated To Record 2.5 Trillion Digits
Joshua writes "Researchers from Japan have calculated Pi to over 2.5 trillion decimals using the T2K Open Supercomputer (which is currently ranked 47th in the world according to a June, 2009 report from Top500.org). This new number more than doubles the previous record of about 1.2 trillion decimals set in 2002 by another Japanese research team. Unfortunately, there still seems to be no pattern."
A nice little article on why it's useless to know pi to more than 50 digits in this universe.
http://everything2.com/title/Too%2520small%2520a%2520Universe%2520to%2520memorize%2520Pi
We know without a doubt that it never repeats - if it did it would be a rational number, it has been proven to be an irrational number, moreso it is transcendental. We also know the exact pattern, take the taylor series of sin about pi/4, you get an elegant and simple series solution for pi.
That is not the point. The point is and exercise in computing, everything we do in computing involves rational numbers only (floats) and there is substantial error involved with this. It is computationally difficult to deal with large numbers, hence any method to do this more effectively is a gain for science.
Pi was shown to be irrational in 1768 and transcendental in 1882, finally putting to rest the ancient problem of "squaring the circle".
I believe you are confusing rational numbers and real numbers. rational numbers are those that can be expressed as p/q where p and q are prime integers. The existence of real numbers that are not rational follows from cantor's diagonal argument : http://en.wikipedia.org/wiki/Cantor's_diagonal_argument
Proofs of the irrationality of pi can be found on wikipedia : proof
The sqr root of a negative is not defined in the real set but only in the complex set. http://en.wikipedia.org/wiki/Complex_numbers
Better ways to represent that.... \[4\cdot\sum_{n=0}^{\infty}\left(\frac{\left(-1\right)^{n}}{2\cdot n+1}\right)=\pi\] was trying for a more elegant representation, but I'm going to first have to figure out how to make slashdot accept mathml...
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Not necessarily. We can't really know about anything smaller than the Planck length, so in practical terms your paradox probably fails. The universe may be discrete on those scales.
Mod parent up - AC or not... I had to scroll a LONG way before seeing this argument and was going to post it myself if no-one else had. There's a lot of "weird" points about the universe that just don't seem to make sense. Posts such as the GP saying, "Clearly this definition of reality is flawed: stop using it." (with regard to travelling through an infinite number of points in a finite time) are all well and good, but don't go anywhere towards explaining WHY this definition is flawed. By defining the universe as discrete rather than continuous, it is no longer flawed, as with many other oddities and apparent paradoxes.
This would also potentially have an interesting effect on Pi in that if the number itself is truly irrational, then it's also wrong for every case we're using it - we actually should HAVE TO round it off somewhere to be correct when using it in models of the physical universe.
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The f1r5t p0st is right. Just b/c we haven't found one yet doesn't mean there isn't one. However, the fact that Johann Lambert proved it in 1768...does.
but have you considered the following argument: shut up.
There are, however, irrational--indeed, transcendental--numbers that follow a discernible decimal pattern, like the Liouville constant.
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0.123456789012345678901234567890... = 1234567890 / 9999999999
Any recurring decimal can trivially be written as a fraction.