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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."
These researchers are now in possession of the most useless piece of information in science.
3.14 was very useful. 3.1415? Even more so. But after that it's diminishing returns, baby. 2.5 trillion digits? Good heavens. Of course it never repeats - we kind of knew that already.
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Otherwise how would you calculate it? The "pattern" is it matches the stream of digits produced by a simple algorithm!
Researchers will find that Pi begins to repeat after 2,500,000,000,001 digits.
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
Of course there's a pattern. I mean, otherwise, I wouldn't be able to match it with 3.[0-9]{1,}
I fail to see how not understanding the word "seems" is insightful.
I've constructed a perfect circle, with a circumference of 1 meter. It's the diameter I'm having trouble with.
Of course there's a pattern, even a simple and elegant one. It's equal to:
4 * (1 -1/3 + 1/5 -1/7 +1/9 -1/11 +1/13 -1/15 etc., etc., etc.)
Just because the pattern doesn't come out pretty in a decimal representation doesn't mean it's not elegant or not a pattern.
To travel from one point to another, an object must pass through all the points in between. There are an infinite number of points "in between," thus to move at all, an object must travel through an infinite number of points in a finite time. Clearly this definition of reality is flawed: stop using it.
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I heard somewhere it's equal to the circumference of a circle divided by it's diameter...
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I always found the Basel problem to be the most elegant converging series involving pi (being the square root of six times the sum of the reciprocals of the squares), probably because there are so many (elegant) proofs of this (pdf), because it's so simple to understand yet not so simple to prove on a cursory inspection, and because it's the specific case that generalized to one of the most important unsolved problems in mathematics.
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.
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
00000001 110000000
00001110 001110000
00110000 000001100
01000000 000000010
01000000 000000010
01000000 000000010
00110000 000001100
00001110 001110000
00000001 110000000
About two trillin digits down the line, in base 2, scientists discovered a curious pattern... is it purely random, or perhaps a message from the Creators?
There's a good argument that the choice of pi = (circumference / diameter) was unfortunate; it should have been (circumference / radius). In the light of modern mathematics it seems clear that the radius is more "fundamental" than the diameter; choosing pi = (circumference / radius) = 6.28... gives a number of nice things like:
A = (1/2)pi r^2, just as E = (1/2)m v^2 or d = (1/2)a t^2, and for the same reason.
In general, in the current convention, 2pi seems to show up a lot more than pi, e.g. there are 2pi radians in a circle, sin(x) has period 2pi, etc. All these would become simply pi with the (circumference / radius) convention
Wait, we can record a ridiculous amount of data (2.5 trillion digits!) just by calculating pi?
Best.
Compression Algorithm.
Evar!
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.
It's a great way to test the performance of these supercomputers, to ensure that their calculations are correct. The calculation of pi to additional decimal places beyond what was previously known is never done with just a single method--otherwise, it is impossible to verify the additional digits. It is always done with two different algorithms to ensure that the result is valid. There are many rapidly converging algorithms (e.g., variations on AM-GM methods can be quadratically convergent or better; BBP-type digit extraction methods; and of course, classic Ramanujan series-type methods). However, computing pi to so many decimal places has much less to do with the chosen algorithm than it has to do with the memory- and computing time-efficient implementations of such algorithms in massively parallel architectures. Thus these calculations serve as very good tests for the robustness of supercomputers. The result is also verifiable to previously known digits, and even beyond the previous record, it is possible to perform statistical analyses to determine whether there are any significant deviations in the distribution of digit frequencies.
So, in summary, it is hardly a useless computation. Not that you're going to get an explanation like this from your usual news sources, which generally do not write for technical audiences.
Also note that distributed computing resources such as Folding@home, or even the Great Internet Mersenne Prime Search don't bother with calculating pi, as the purpose of these projects is to make new discovers in their respective fields of interest.
There are, however, irrational--indeed, transcendental--numbers that follow a discernible decimal pattern, like the Liouville constant.
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