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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.
Pointless mathematical dick-sizing. Problem is, this dick is so huge no vagina will ever make use of it.
...have they found the circle yet?
http://michaelsmith.id.au
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. In fact, an infinite number of them. My favourite is the one in the generalised continued fraction expansion of pi.
entropy happens
Since Pi is irrational, does that mean that a "perfect" circle cannot actually exist? If you don't understand my question, think about it like this. Let's say I want to construct a circle of radius R. To create a "perfect" circle, it seems like I would need a length of material to build the circle out of that was exactly 2*Pi*R, but since Pi is irrational, it seems that you could never actually get any length which is an exact multiple of Pi? If Pi really expands out infinitely, even a circle with a radius the size of a galaxy, or a cluster of galaxies, could never be *exactly* the right length?
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.
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.
Cryptography has nothing to do with a prime "not being a prime". It's to do with quick factorization of primes.
Besides, I don't see why pi having any sort of repeating pattern would disrupt any theorems. I honestly can't think of any theorem that requires such a thing. Irrational and transcendental yes, but no repeating decimal pattern?
Maybe you can enlighten me to such a theorem.
I heard somewhere it's equal to the circumference of a circle divided by it's diameter...
Free the Quark 3 from asymptotic confinement! Bring your charm! Don't get down! All colours and flavours welcome!
I'm glad there is more than one computer.
Ever stopped to think that throwing more computing power at a problem is about as productive as throwing more money at a problem or more man power? You can only do so much before an effort becomes either redundant or the return on investment is as dismal as the stock market has been this past year.
I don't honestly know what the practical value of knowing Pi to the 2.5 trillionth digit is but I'd like to think that there are enough resources in play that the fight for cancer isn't going to miss this one.
Dedicated Cthulhu Cultist since 4523 BC.
Ahhh! what is wrong with you geeks! Hand in your cards, all of you.
There is an extremely simple pattern to pi, just not in base10 decimal expansion. Its already been said but here we go:
pi = 4(1-1/3+1/5-1/7+1/9-1/11+...)
Mathematicians were all over this stuff years ago, try to think about what the implications of this are for precision in scientific computing.
While I think that the computing horsepower was misdirected (covered elsewhere), and the last trillion digits could have waited, this post is mostly here for me to be arrogantly dismissive and make dick / vagina jokes.
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.
FYI
The reason the Babylonians, and the Egyptians, and we use 360 degrees is this:
355/113 = 3.14159292035
pi `= 3.14159265359
A difference of 8.5x10-6%
Which makes 355/113 close enough to pi. 360 is close to 355 which is why we use 360 degrees for angles and time.
The pattern just isn't in base 10. It's in base e. Why does anyone expect to see a numerical pattern in an arbitrary number base like 10? Just because we have 10 fingers doesn't make it the "correct" base for anything.
having effectively zero size, your girlfriend must wish you were throwing a hotdog through the halway :P
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...
In God we trust,
everyone else we firewall!!
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
Because if there's a pattern in one base, there's a pattern in all bases. It's just maybe less obvious and easy to describe in some.
Wait, we can record a ridiculous amount of data (2.5 trillion digits!) just by calculating pi?
Best.
Compression Algorithm.
Evar!
There is no doubt pi is irrational, but your definition of irrational numbers is dead wrong. Try clicking the link to the definition of irrational numbers in your own link and study up a bit.
Sorry to burst your bubble, but being an irrational number does not not mean it can't have pattern. It just means that the decimal goes on forever without repeating (i.e. no repeating pattern).
Case in point: Champernowne's constant, an irrational number:
0.12345678910111213141516...
Note that for this irrational number the decimal goes on forever without repeating; however, there is a clear pattern.
Now a simple pattern for pi expressed in base 10 may never be found (such a pattern may not even exist), but your statement that it is "impossible" for an irrational number to have a pattern is simply untrue.
Ok so pi = 1.000000000... in base pi. That's a nice pattern. What does that pattern look like in base 10, even if it stands out a little less?
They better keep on going, 'cos what if the pattern is that the SECOND three trillion digits are the same as the FIRST three trillion digits, except like BACKWARDS! :O
Man, that'd be SO AWESOME.
Sam! If you will let me be,
I will try them.
You will see.
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.
Egads, I'm sorry to dump on you but I remember when posters on slashdot knew their calculus 101 and some really elementary facts about numbers. If pi had a repeating pattern, it would be a rational number. If it was a rational number, that pattern would appear in any number base, it's a simple property of numbers that has nothing to do with the base you express it in.
[FUCK BETA]
You mean the Creators are sending us a goatse?
Just because nobody has detected a pattern doesn't mean there is one.
What's the pattern in base e? Cos I'm not seeing it.
10.101002020002111....
The most dangerous drug
There are, however, irrational--indeed, transcendental--numbers that follow a discernible decimal pattern, like the Liouville constant.
Tomato wedge sperm darts that are Republican.
0.123456789012345678901234567890... = 1234567890 / 9999999999
Any recurring decimal can trivially be written as a fraction.
I'm surprised that nobody posted this yet.
"Unfortunanely, there seems to be no pattern yet", but what about secret messages?
In the example you give, perhaps you're thinking of Champernowne's number, 0.123456789101112....
This is an irrational number, and was the first number proven to be normal.
Slashdot: news for Apple. Stuff that Apple.
0.123456789101112131415161718192021....
http://www.geoffreylandis.com
Now if only God provided source code! Instead we get these damn executables...