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Pi Calculated To Record 2.5 Trillion Digits432

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."
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Pi Calculated To Record 2.5 Trillion Digits

• No one needs more than 50 digits (Score:5, Informative)

by Anonymous Coward on Wednesday August 19, 2009 @10:49PM (#29128463)

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

• Re:No pattern = a very good thing (Score:2, Informative)

on Wednesday August 19, 2009 @11:18PM (#29128681)

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.

• Re:Congratulations! (Score:5, Informative)

on Wednesday August 19, 2009 @11:29PM (#29128737)

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.

• Re:Question about Pi and circles. . . (Score:5, Informative)

on Thursday August 20, 2009 @12:09AM (#29129027) Journal

Pi was shown to be irrational in 1768 and transcendental in 1882, finally putting to rest the ancient problem of "squaring the circle".

• Re:Question about Pi and circles. . . (Score:3, Informative)

on Thursday August 20, 2009 @12:09AM (#29129031)
Sorry, slashdot took the pi symbol out of my link. Just search for "proof that pi is irrational" at wikipedia.
• Re:Question about Pi and circles. . . (Score:5, Informative)

on Thursday August 20, 2009 @12:12AM (#29129049)

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 [wikipedia.org]

Proofs of the irrationality of pi can be found on wikipedia : proof [wikipedia.org]

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 [wikipedia.org]

• Re:Well... (Score:3, Informative)

on Thursday August 20, 2009 @12:18AM (#29129097) Journal
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...
• Re:I've got an even more simple pattern (Score:2, Informative)

on Thursday August 20, 2009 @12:27AM (#29129161) Homepage

Actually, the program itself is a perfectly fine way of representing pi. See: computable numbers [wikipedia.org]. Note that almost all [wikipedia.org] real numbers are not computable, so it is a non-trivial property.

It also takes an infinite amount of time to write out the decimal expansion of 1/9, but that can be written very concisely as a rational number. Also note that pi is irrational [wikipedia.org] so its decimal expansion is infinite in all bases [wikipedia.org].

• Re:To all those who think pi may have a pattern (Score:2, Informative)

by Anonymous Coward on Thursday August 20, 2009 @01:40AM (#29129573)

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.

• Re:Question about Pi and circles. . . (Score:5, Informative)

<yttriumox@gmail . c om> on Thursday August 20, 2009 @02:21AM (#29129763) Homepage Journal

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.

• Re:Well... (Score:5, Informative)

on Thursday August 20, 2009 @02:38AM (#29129841) Journal
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.
• Re:No pattern in base 10 (Score:3, Informative)

<calum@callingthetune.co.uk> on Thursday August 20, 2009 @03:21AM (#29130037) Homepage
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.
• Re:Congratulations! (Score:2, Informative)

on Thursday August 20, 2009 @04:49AM (#29130459)
Pi is irrational which means that the decimal expansion never repeats or terminates! Case closed.
• Re:I've got an even more simple pattern (Score:3, Informative)

on Thursday August 20, 2009 @05:16AM (#29130605)

Wikipedia has pretty good article(s) on everything PI - how to calculate it in different ways, history, and all those quirks you don't even imagine to think about, before you read about them :-)

• Re:Well... (Score:5, Informative)

on Thursday August 20, 2009 @05:34AM (#29130683) Journal

There are, however, irrational--indeed, transcendental--numbers that follow a discernible decimal pattern, like the Liouville constant [wikipedia.org].

• Re:Well... (Score:4, Informative)

on Thursday August 20, 2009 @05:53AM (#29130759)

0.123456789012345678901234567890... = 1234567890 / 9999999999

Any recurring decimal can trivially be written as a fraction.

• Re:Well... (Score:3, Informative)

on Thursday August 20, 2009 @07:46AM (#29131225)

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 [wikipedia.org].

• 12345678910 (Score:3, Informative)

on Thursday August 20, 2009 @09:13AM (#29131863) Homepage
I expect that the number he meant to post was

0.123456789101112131415161718192021....

• Re:Question about Pi and circles. . . (Score:3, Informative)

on Thursday August 20, 2009 @05:02PM (#29139075)

rational numbers are those that can be expressed as p/q where p and q are prime integers.

Under your definition of "rational", 4/5 (0.8) is an irrational number. In order for a number to be rational, p and q need only be integers. Whether they are prime is irrelevant.

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