typodupeerror

## A Much Bigger Piece Of Pi729

Punk_Rock_Johnny points to an AP story on Pi-obsessed Professor Yasumasa Kanada. A snippet from the story: "Kanada and a team of researchers set a new world record by calculating the value of pi to 1.24 trillion places, project team member Makoto Kudo said yesterday. The previous record, set by Kanada in 1999, was 206.158 billion places." Trillion! "
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## A Much Bigger Piece Of Pi

Why?
• #### Re:One simple question (Score:3, Funny)

Because pi is there. And they still have found only the tiniest fraction of the total of decimals of pi...

Nyh!
• #### Re:One simple question (Score:2, Insightful)

No matter how many decimals they calculate, that "tiny fraction" will always be just as tiny as always...
• #### Re:One simple question (Score:3, Funny)

Damn, if I could only compute e^(i*pi) with a trillion digits precision...
• #### Re:One simple question (Score:5, Informative)

on Saturday December 07, 2002 @11:47AM (#4832892)
Why?

Well, if you read the article, you would know why. Mapping out a very large number like that is useful for testing the accuracy of supercomputers. Also, the research process spins off lots of discoveries. Someone who mapped out pi to 1.24 trillion decimal places probably learned a couple neat tricks along the way.
• #### Well ... what is it? (Score:3, Funny)

on Saturday December 07, 2002 @10:00AM (#4832392)
How about we see this bad boy!? I'd sure like to paste it into my "info.txt" file for future referance. It could come in handy sometime.
• #### Re:Well ... what is it? (Score:2, Interesting)

So if I did my math correctly:
1240000000000 characters * 8 bits/character = 9920000000000 bytes

9920000000000 bytes/ 1024000 = 9687500 MB

9687500 MB = 9.6875 TB

Thats a pretty darn big info.txt file!

I think I'll just use the 32 byte version for my SIG. :-)

3.14
• #### Re:Well ... what is it? (Score:3, Interesting)

Why waste all that space? You can write any number from 0 to 255 in 1 byte, any number from 0 to 65355 in 2 bytes, and 0 to 4.2billion in 4 bytes.

Anyone care to do the math about how much space you need (uncompressed)? (I cant cause I'm dumb)

P.S. Does Pi compress very well?
• #### Re:Well ... what is it? (Score:3, Informative)

He was calculating the size of a text file containing pi, and for that, he was correct. Actually, by its nature, pi should not compress very well, if at all. The numbers in pi have no pattern (I forget the proof, but there is one) so most compression algorithms wouldn't be able to do much with it.
• #### Re:Well ... what is it? (Score:5, Insightful)

on Saturday December 07, 2002 @12:12PM (#4833010) Journal
Pi, like everything else, compresses down to one bit, given the correct decompression algorithm. (It is generally nonsense to talk about how well something compresses without specifying something about the algorithm you mean to use.)

Usually, "X compresses down to one bit for a correct algorithm" is a snarky answer, but in this case, it actually makes sense. Generally one has to define those algorithms as a table, where "X" is what the decompression function returns for "1", which definately feels like cheating. In this case, though, one can provide a finite algorithm to compute as many digits of pi as you please, so it makes sense.

In fact, we compress pi down to one or two bytes, with a mathematically defined decompression sequence you can use if you want, all the time. In fact, I've done it three times in this post already, where two different two byte sequences stood in for the infinite series that is that number. Can you find them?
• #### Information theory (Score:5, Informative)

on Saturday December 07, 2002 @02:21PM (#4833700)
You, Sir, despite your low member number, would get an F- for information theory at the university I was tought and now teach.

There is nothing that compresses to one bit. There is such thing as a most efficient way of encoding any message. Counted in bits. and no, not just one bit. One bit would just contain enough information to say "Pi" or "Not Pi". "Not Pi" would according to my intuition not be an acceptable answer, you also have to say "What kind of 'Not Pi'". And that takes bits. You forgot that your algorithm is supposed to possibly generate all possible messages, or else it's "not fair".

Pi would not compress at all, given it's an infinitely long number. (To be precise, it's length would be reduced from inf to inf/(alphabet entropy) which is still inf, although a "smaller" inf). If you are content with a finite number of digits, its length would be reduced by about a little more than three bits per decimal (because log2(10)=3.???) with any decent entropy encoder. You could try to reduce this further by taking two decimal digits at once, but unfortunately it would not work, as not only are Pi's digits uniformly distributed from 0 to 9, pairs of digits are also distributed uniformly from 0-99, so you would remain with 6.???? bits (log2(100)) per decimal digits pair.

Another approach you might take, if you want infinite precision (silly on a finite machine), or more generally random precision, is to write a code in a predetermined programming language, in this case a series developement, or whatever the number thorists use nowadays to calculate pi, and decide that the "decompression algorithm" is a compiler (that is perfectly legal, as any finite message can be passed that way, eg "#include <iostream> int main(){cout << "The message";}").

My idea is that the c compression algorithm would be beat by a perl compression. Maybe try in BrainFuck, it might beat perl, but BF sucks at multiplications.

Anyway, the most optimal compression for pi is probably saying "Pi" by itself. Any decent geek knows at least one way to calculate that/ find it on project gutenberg/whatever. But don't ever think that you could compress it to two bytes or less : you gotta be sure that I will not understand "the string of decimal digits a.k.a. Pi, do write it in numbers when decompressing", not just "mu turned over", "Pi the string" or "Private investigator". This certainty takes bytes.

Another example is : "you cannot encode '3 4 8 15 3.141592653 78 54' as '3 4 8 15 pi 78 54', because that would increase the number of symbols in the alphabet, and all the other symbols would have to contain more bits as a result, so the compressed message length would suffer- hope there are a lot of 'pi' in the compresed message".

I must leave now, gotta go bowling with friends. Start your flames, I can see blatant holes in my reasonments. Hope you get the point. Mailing a link to the message to my signal theory professor (formally one of my bosses), so I will suffer if I told bullshit.
• #### Re:Information theory (Score:5, Informative)

on Saturday December 07, 2002 @03:08PM (#4833928) Journal
A compression function is a mapping from input to output. A decompression function maps from all possible outputs of the compression function, back to all possible inputs (though there may be some illegal input to the decompression function). As long as decode(code(x)) = x for any x in the domain, it's a "compression" function, even if possibly a really bad one. There's an infinite number of such functions but most of them are terribly uninteresting. For instance, a particular 'code' might repeat x twice and one of its corresponding 'decode's might cut the input in half again; it meets the definition but we'd never be interested in that.

Different functions perform better or worse in different domains, which is why we have "zip", "gzip", "bz2", "shl" or whatever the lossless audio encoder is, and all kinds of other compressions.

It is trivial to define a function that maps one bit to pi, even if pi is defined as some infinite sequence, instead of a finite symbol representing the infinite concept. You just do it.

Where all numbers are in binary:

decompress(x) = { (the infinite binary encode of pi) if x == 1
what gunzip would do if x != 1 }

Perfectly permissible since "1" isn't a legit gunzip file.

compress(x) = { 1 if x == (the infinite binary encoding of pi)
what gzip would do if x != pi }

For your choice of binary encodings of real numbers that makes sense in this domain.

You seem to have neglected that strings have length, and that just because a given thing compresses down to one bit, does not mean that all things the compression scheme produces will be one bit. In fact, that's impossible for obvious reasons.

There's a perfectly well defined mapping that exists. Of course you can't implement this directly since x can be infinite in this case, and would thence take an infinite amount of time to check if x is pi for the compression case, but it's the same kinda thing as "you can't implement a Turing Machine because you can't have an infinite tape." The function itself, like Turing Machines, is perfectly well defined.

There's nothing unrealistic about this, either; the same principles underly the proof that no compression algorithm can compress all input. You forget that there is no "one true representation" of anything; we can define symbols to mean whatever the hell we want.

(This assumes gzip is defined for infinite input, which IIRC it is, since it's a stream-based compressor; conceptually, there's no reason that gunzip won't perfectly happily run forever on an infinite input, giving perfectly well-defined output, as long as the machine in question has infinite memory.)

Pi would not compress at all, given it's an infinitely long number.

Trivially wrong anyhow, even with your misunderstandings. The people in the article who generated over a trillion digits of pi did not pull them out of their ass; there's a mathematical procedure that produces the digits of pi, as many as you have time to compute. Realistically, that means that pi is compressed as the Turing Machine that spits these digits out, and this Turing Machine is fed to the Universal Turing Machine, which "decrypts" (normally we wouldn't use that word, but a UTM fits into the definition of a decryption function, mapping input to output) the output into the string of numbers. The Pi TM is finite, the output is not. Again, you can't run in finite time, but conceptually, the TM represents all of Pi, given enough time. (It "limits" to it, if you like, as time goes to infinity.)

(The corresponding encryption routine for UTM as a decryption routine is much, much tougher, beyond human capability to perform optimally, and often at all; many interesting things about that have been proven.)

A friend of mine has toyed with a theory of "computable" numbers, lying somewhere between the reals and the rationals. A "computable" number is one where there exists a Turing Machine that will output it, as time goes to infinity. Since there are fewer TMs then real numbers, it's clearly smaller then the set of reals, yet equally clearly, it's larger then the rationals, since it includes things like Pi, e, and, most interestingly, any number we could ever conceivably communicate to each other in such a way that we could construct it. That's the most interesting part of it; it's not the full reals, yet you can't point to a real number or reference one that is not in this "computable" set. Not directly germane, but perhaps interesting to anybody following the posts this deeply.

Anyway, the most optimal compression for pi is probably saying "Pi" by itself.

Ironically, you further demonstrate a decompression algorithm ("simplifying an expression into its decimal equivalent according to the corpus of human mathematical knowlege") that decompresses the sixteen-bit phrase "Pi" into the infinite decimal sequence.

My idea is that the c compression algorithm would be beat by a perl compression.

And what is that supposed to mean, anyhow? Algorithms exist independently of their implementation in a given language!

Your understanding of information theory is skin deep; you recall some of the results but you do not understand the deeper logic. I'm not an expert but I'm pretty confident that this post is accurate enough for Slashdot. (I'd be a bit more careful with definitions and domain specifications for a class assignment, but this isn't, and it's long enough.) The exactly compressions techniques you learned are just a special case that happens to be useful in the real world, not the be-all end-all of compression.
• #### I dunno about you, but... (Score:5, Interesting)

<hilleh AT email DOT com> on Saturday December 07, 2002 @10:00AM (#4832395) Homepage
How come I can see this making a kick-ass distributed computing project? Pi@Home, here we come!
• #### Re:I dunno about you, but... (Score:2)

Pie@Home, mmmmm......
• #### Re:I dunno about you, but... (Score:5, Funny)

on Saturday December 07, 2002 @12:38PM (#4833143) Homepage
The Mac version of this program could be called Apple Pi.
• #### OK, now this is overkill (Score:2)

I think I read somewhere that to draw a circle to circumscrible the known universe with a an error of +/- the width of a proton, you only need to know Pi to about 20 places. What practical purpose is there to know pi to 1.whatever trillion places. Unless, of course, you're Count Duckula, in which case it's a party trick.
• #### Re:OK, now this is overkill (Score:4, Insightful)

<nathaniel.tagg@gma[ ]com ['il.' in gap]> on Saturday December 07, 2002 @10:14AM (#4832461) Homepage
Hmm..

size of the proton: ~ 1 fm = 10^-15 m
age of the universe: ~15 Gyr
speed of expansion ~ c = 3 x 10^8 m/s

gives:

So you need about 40 places for this. Of course, you might want to calculated it to the Plank scale, so maybe tack on a few more.. say 100 for safety. Yes, a trillion digits does seem a bit like overkill.
• #### Re:OK, now this is overkill (Score:2)

Well I guess the problem is statistical round-off error (i.e. as the number of values multiplied together increases, the error also is going up, so you have to round down as it is no longer accurate to that number of places). What I was taught:

When multiplying a*b = c, the place of c is the lesser place value of a OR b MINUS one.

So no matter what, to be accurate/not cheat, you are slowly losing granularity as you churn out the calculations.

If there is a God, I hope that he DOES have Pi out to some ludicrous number of digits. I don't want to see the round off error of those calculations ;)
• #### Re:OK, now this is overkill (Score:4, Informative)

on Saturday December 07, 2002 @11:22AM (#4832784)
Hrm.. Well, as one of my Computer Science teachers once told me (in a discrete math class).. Mathemeticians do things because it interests them. The fact that it often has no practical application is why they are often cold, bitter and broke. :)
• #### If Pi were made into a classic video game... (Score:3, Funny)

on Saturday December 07, 2002 @10:02AM (#4832402) Homepage
We would have either found the end by now or discovered a pattern.

heh.
• #### How? (Score:2, Interesting)

Just how is Pi calculated? Are there any free apps available for Linux that I could look at to see how it is done?

• #### How To Calculate Pi (Score:3, Interesting)

You can calculate Pi by doing:

(1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ..) x 4

Obviously the more iterations you do, the closer you will be to the 'true' value of Pi.
• #### Re:How? (Score:3, Informative)

You could always just do it with Good ol' Calculus [aol.com].
• #### Re:How? (Score:3, Funny)

Here's a program written in BrainF*ck to calculate pi: http://www.people.fas.harvard.edu/~jafowler/pi/pi. b [harvard.edu]

Here's the analysis of the program [harvard.edu], and a link to what the Turing-inspired BrainF*ck [catseye.mb.ca] programming language is about.

• #### The 1.24th trillion digit of pi is .. (Score:5, Funny)

on Saturday December 07, 2002 @10:04AM (#4832411) Homepage
The number Six!
• #### OMG! That's 4+2 !!!!! (Score:5, Funny)

by Anonymous Coward on Saturday December 07, 2002 @10:13AM (#4832457)
42 really is the answer to life, the universe, and everything!!!
• #### Re:The 1.24th trillion digit of pi is .. (Score:2, Funny)

Bert: My favorite number is 6.
Ernie: Bert, nobody's favorite number is 6!

• #### math question about pi (Score:3, Interesting)

on Saturday December 07, 2002 @10:04AM (#4832412)
Does the problem that pi can't be expressed in decimal notation extend to other base systems? For example, if you tried to write pi out in binary or hex would you encounter the same problem? Is there a special base system (other than base pi) which can describe pi in a finite number of digits?
• #### Re:math question about pi (Score:5, Funny)

on Saturday December 07, 2002 @10:06AM (#4832419)
You can write Pi as 1 (base Pi).

• #### Re:math question about pi (Score:3, Funny)

He said other then base Pi.

You can write it as 0.5 (base 2Pi)
• #### Re:math question about pi (Score:5, Informative)

on Saturday December 07, 2002 @10:38AM (#4832568)
Nope. Do you write the number 2 as '1' in binary (base 2)?
sorry, but in base pi, pi would be written as 10.

(fyi, i made the same mistake back in the day also)

• #### Re:math question about pi (Score:4, Informative)

on Saturday December 07, 2002 @10:07AM (#4832424)
No - pi is irrational... as far as I know this would be the case for base-n where n is of course an integer.
• #### Re:math question about pi (Score:2, Interesting)

No - pi is irrational

Okay, I've heard this many times, and I don't doubt it's true. But are there any simple elegant proofs of this (like the one for proving that the square root of 2 is irrational), or are the proofs very involved, or are there no proofs at all except "well, nobody has found the end yet"?

• #### Re:math question about pi (Score:5, Informative)

on Saturday December 07, 2002 @10:14AM (#4832464)
Pi is worse than irrational - it's trascendental. Merely irrational numbers can be expressed as simple expressions with finite numbers of terms, but transcendentals require an infinite number of terms.
• #### Re:math question about pi (Score:2, Interesting)

Well, at least pi is a computable number - other interesting ones, like Chaitin's Omega [wolfram.com], aren't, at least not ahead of time. In fact, if I recall correctly, it is even (provably) possible to construct Turing machines for which no single digit of Omega can be computed at all, but I'm not really sure about this anymore.
• #### Re:math question about pi (Score:2)

No. Conversion to any other base does not make Pi become non-irrational. The base does not make any magic transformation occur that changes Pi from an irrational number to a rational number. It's just not possible.

A Much Bigger Piece Of Pi

Doesn't matter, I still want seconds. With ice cream!
• #### Why? (Score:2)

How could this ever be useful? I mean that as an honest question, what could anyone, ever, use this for?
• #### How to calculate PI yourself (Score:5, Funny)

on Saturday December 07, 2002 @10:06AM (#4832422)
One way to calculate for yourself the value of pi is to drop a lot of toothpicks onto a large piece of paper that has lines drawn on it!

Here's how it works. You'll need several boxes of toothpicks. Get a large piece of chart paper, and draw parallel lines on it, from one side to the other. The lines should be separated by a distance just slightly larger than the length of a toothpick.

From a height of about one metre, drop a measured number of toothpicks onto the chart paper, so that they all fall randomly somewhere on the paper. Count how many toothpicks are touching a line (or would be, if they weren't resting on another toothpick).

Repeat this process as many times as you can. Lots of people can do it at once. All that's important is that, each time you drop some toothpicks, you write down how many you dropped, and how many of those ended up touching a line. When you're done, find a total for each quantity.

You now have all the numbers you need to calculate Pi:

c ... toothpick length (in mm) <BR>
a ... line separation (in mm) <BR>
N ... total number of toothpicks dropped <BR>
M ... total number of intersections <BR>
(c must be less than a) <BR>

Now here's the formula you need to calculate Pi:

PI = 2cN / aM
Fill them in the formula, and work out your own value of Pi!
• #### Re:How to calculate PI yourself (Score:2)

Informative? come on now...!
• #### Re:How to calculate PI yourself (Score:5, Funny)

on Saturday December 07, 2002 @10:20AM (#4832485)
One way to calculate for yourself the value of pi is to drop a lot of toothpicks onto a large piece of paper that has lines drawn on it!

You are toothpicks seller, aren't you?
• #### Re:How to calculate PI yourself (Score:2)

Of course, you could also write a program that just printed out "3.141592654" and then just started generating random numbers...

Run the program, and impress your friends. Tell them you wrote a simulation of the toothpick technique described on slashdot... just don't release the source.
• #### It's called Buffon's Needle (Score:4, Informative)

on Saturday December 07, 2002 @11:58AM (#4832928) Homepage Journal
You could at least give credit where due ;)

Here's one of the nicer [angelfire.com] sites I've seen that has a java applet to simulate this.

• #### I like this quote: (Score:2)

Figuring out pi to much more than about 1,000 decimal places serves little purpose in math or engineering

And in 100 years it'll be:

Figuring out pi to much more than about 100,000 decimal places serves little purpose in math or engineering
• #### Faking it ... (Score:3, Funny)

by Anonymous Coward on Saturday December 07, 2002 @10:07AM (#4832428)
How to fake it:
int main()
{
cout << 3.1415926535897932384626433832795;

for(int i=0; i<1000000000000; i++)
cout << rand();

return 0;
}
• #### Signature of God? (Score:5, Interesting)

on Saturday December 07, 2002 @10:10AM (#4832438) Homepage Journal

In the book version of Contact by Carl Sagan, but skipped in the Jodie Foster movie, was the notion that the aliens had discovered proof that the universe was created by a higher intelligence. A God or society of Gods far higher and more advanced than the aliens. The whole point of dragging Human-kind to that remote beach to talk with daddy was to tell Human-kind that it was time for them to look for God's signature on this universe.

As any artist, the creator signed the creation. Where? Deep into the insignificant but irrefutably valid digits of several of the fundamental mathematical constants such as pi and e.

The main character finds one of the signatures at the end of the book: if calculating digits of pi in base 11, after a few million or billion places, a 500x500 digit span is almost entirely zeros. If the span was rendered as a square of pixels, the non-zero digits drew a perfect circle inscribed in the square. A circle in a square. The key concept defining pi, in the digits of pi itself. The whole way the universe works is affected by that constant, so any such 'design' in it has, if you pardon the pun, a transcendental import.

Why base 11? It's left to the reader to decide, but I expect Sagan wrote it because it is considered one of the possible designs of the universe, one of the string theories is based on an 11-dimensional all-inclusive physics model. As the alien explains to the main character, it wouldn't be base 10, because what's the likelihood that the creator also happened to have ten fingers?

• #### Re:Signature of God? (Score:2)

When I was in college, I wrote a distibuted computing project that drew detailed plot of the Mandelbrot Beetle [geocities.com]. I fantasized that if I could zoom in on JUST the right spot, I'd see "God was here" as if in graffiti. Wouldn't that just be kick ass?
• #### Re:Signature of God? (Score:5, Insightful)

on Saturday December 07, 2002 @10:30AM (#4832532) Homepage
Well, it seems pi is normal, which means any finite sequence appears somewhere along the expansion of the number. So trivially, that image of a circle is in there somewhere, as is an image of a triangle, the source to Linux 4.0, an image of Bush playing with G.I. Joe dolls on his desk and so on.

• #### Re:Signature of God? (Score:2)

Of course. Though in terms of probabilities, the chances of a few million digits with equal distribution, followed by a square image of a quarter million digits with very limited distribution, followed by billions more digits with equal distribution... we're talking about a big "whoa."

I also find it funny in that it's the skeptics and agnostics who are then brought to the argument, "for without faith, He is nothing." Sure, even the circle-in-square is possibly coincidence, and sure, you could go out to the digits at 11^(-800) and find a similar stretch with a triangle, just based on the statistics. A religious God needs plausible deniability, or so says traditional theology.

• #### I love this Quote (Score:5, Funny)

on Saturday December 07, 2002 @10:10AM (#4832439) Homepage
I love this quote:
Among the most puzzling mysteries: Mathematicians are pretty sure, but still cannot prove conclusively, that the numbers following 3.141592 occur randomly.

"I don't think we're any closer to answering this question than the Greeks were 2,500 years ago," Borwein said.

Um, you have 1.24 trillion digits of pi. I think you can begin a statisticall analisys now.
• #### You don't understand maths, then (Score:2)

mathematicians are pretty sure, but still cannot prove conclusively

In the best case, statistical analysis could come up with something like "there is a 99% probability that the numbers occur randomly". That's not a proof, that's just quantifying "pretty sure".
• #### Accuracy? (Score:2)

How do they check such a calculation for accuracy?

I'm not trolling, I'm just not mathematician enough to just know.
• #### Re:Accuracy? (Score:3, Informative)

How do they check the accuracy? Easy!

See:

http://www.math.hmc.edu/funfacts/ffiles/20010.5. sh tml

You can figure out what any digit of pi is, without bothering with any of the preceding digits.

This only does base16, however I remember seeing one that was for base10 as well. When in doubt, google.
• #### Irrational (pi != 22/7) (Score:2, Troll)

Some people here seem to bee a little uninformed. pi has been proved irrational and trancedental (duh).
• #### I'll be impressed when he memorizes it... (Score:2)

This story reminds me of conversation we had in High School at the computer club about guys memorizing pi up to the 10 thousandth decimal. At which point, one of the less cool geeks, who happened to pronounce DOS, dose, chimmed in enthousiastically, "I once hear of a guy who memorized 30,000 numbers!"

You can bet your ass the room filled up with Louis Skolnick type laughter, along with ribbing along the lines of, "Once I hit 30,000 I stop counting..."

That was BEFORE we had beowulf cluster jokes!

• #### Pi info (Score:4, Informative)

on Saturday December 07, 2002 @10:16AM (#4832471) Homepage Journal
Dr. Math's Pi FAQ [mathforum.org]. Very informative.
• #### ummm timothy ... (Score:2)

"A trillion is more than a billion numbnuts ... "

(c) Austin Powers and MPAA and protected by the DMCA

• #### Hidden humor (Score:2)

I found it hilarious that the story "Professor breaks own record -- for thrill of pi" ended with a link named "Subscribe to the P-I".

And well it should! For it is from the Seattle Post-Intelligencer, whose logo is a globe with the initials "P-I". Someone should get those guys to put it on their top page.

Perhaps they held back since it also was posted exactly 61 years after the invasion of Perl Harbor. Oh well.

FWIW, I've been hoping desperately that they'd find some neat geometrical patterns in Pi. My guess is that the reason the mathematicians cannot prove that all those digits are random is that they aren't.. they are just using an extremely good hash algorithm to encrypt the darn thing.
• #### Is this really necessary? (Score:2)

I'm curious. These guys spent 5 years writing the software and then used some 400 hours of computer time on this supercomputer to calculate it. Is there really any advantage besides getting into Guiness to justify this expense? I'm not bashing it, I just don't know. Seems kind of wasteful to me, personally.
• #### Cartman (Score:2, Funny)

Cartman may be round, but even he had to say...

No... more... pie...

-Zaphod

• #### Any books on Pi? (Score:2)

Anyone have any recommendations for books on the current theories and the history of pi? I found comments like:

"Among the most puzzling mysteries: Mathematicians are pretty sure, but still cannot prove conclusively, that the numbers following 3.141592 occur randomly."

interesting and want to be able to read more indepth.
• #### Balancing costs and pure science (Score:2, Interesting)

In the New York Times article about this story, Kanada has a team of researchers who have been working on this for five years. This undertaking is very sizable in both expense and effort. But when should we end the pursuit of finding pi to the nth digit? If pi is infinite, does this mean the amount of resources needed to calculate pi as accurately as possible is also infinite?

So who sets the limits? Why didn't Kanada just let his computer algorithm run for another year or even just another few minutes to get an even more accurate number? Who decided 1.2 trillion digits was enough and why?

It's just intersting to note that the measurement objective reality is always hampered by subjective, practical matters. And it might also prove that it is impossible for man to ever know the universe---it's just too damn expensive! I'm sure someone out there has thought about this before.

• #### In other news (Score:5, Funny)

on Saturday December 07, 2002 @10:46AM (#4832608) Homepage Journal
Kanada and a team of researchers

"While we were looking through through the binary version of Pi, and one of our special forces noticed that hidden in from digit 12,166,133,883 onwards was a c source to DeCSS. Obviously these terrorists must be stopped!"

The case is not expected to hold up, as it is doubtful canada will be able to proove it has the computing power [mcgill.ca] to calculate Pi beyond 4 decimal places - and no confusion can occur.
• #### On sale now! (Score:3)

on Saturday December 07, 2002 @10:56AM (#4832653) Homepage Journal
Buy the complete six DVD set!

You'll need to insert all six one after the other next time you #include <math.h>
• #### Full text of article: (Score:5, Funny)

<<gro.kred> <ta> <kred>> on Saturday December 07, 2002 @11:04AM (#4832700) Homepage
3.14159265358979323846264338327950288...... ah, this is gonna take a while :-/
• #### For comparison... (Score:5, Interesting)

on Saturday December 07, 2002 @11:05AM (#4832701) Homepage Journal
A google only has 100 zeros, thus 100 places.

10^trillion is 1 followed by 1 trillions 0's... Assuming we are following the american system that would be equivalent to.

10^(10^12)

Okay... now.. let's get some interesting facts with this.

The absolutely smallest length measurable by quantum theory is the planck length which is approx 10^-34 m. Needless to say, if we have a diameter of an incredibly small perfect circle, we'll know it's circumference beyond what is possible by quantum theory (but since there are no perfect circles, and quantum theory adds probability, this doesn't mean anything really useful. :-P)

Now, since we know the smallest measurable... lets look at what the estimates for the size of the universe are. Recent estimates put it as 10 billion light years in radius source [nasa.gov]
Which works out to about... (assuming american notation on billion)

10^9 * 300,000,000 m/s* 365*24*3600 ~= 10^25 m

Okay... now if we were to measure the circumference to as accurate as allowed by quantum theory we'd have.

pi*2.10^25 ~= 6.28*10^26 10^27 with an accuracy of about 34 decimals...

So... to get perfect accuracy as allowed by quantum theory we would have at most 35 decimal places afterwards... therefore, we'd need pi with an accuracy of

~10^63...

We have pi with an accuracy of 10^(10^12) which is
63 : 10^12 ~= 1: 1.59x10^11
Way more accuracy then we really need. :-)

That's absolutely insane, but it is fun math.

Just some food for thought.
• #### Google nitpick (Score:3, Informative)

by Anonymous Coward

"Googol" - 10^100.

• #### Think about it more... (Score:4, Informative)

on Saturday December 07, 2002 @04:51PM (#4834395)
Dude, they measure it to 1.24 Trillion, not 10^(Trillion).Someone had pointed that out, but...

If you think about it, you could not have fitted the entire observable universe with enough paper to record (even if you write in very very very very small fonts) the number of decimals if you know PI to 10^(Trillion).

In fact the entire observable universe had about 10^120 atoms. So you are out of luck very soon. (You can imagine packing more atoms, but then the universe will become too dense and collapse on herself so fast you won't have time to expand to her current volume).

• #### Re:For comparison... (Score:4, Funny)

on Saturday December 07, 2002 @08:31PM (#4835222)
A google only has 100 zeros, thus 100 places

Employees:
More than 500.

And they're not zeros, they're somebodies and they do an damn fine job at making a search engine.
• #### Pi (Score:3, Funny)

on Saturday December 07, 2002 @11:11AM (#4832735)
is EXACTLY 3.

• #### PI = 3 (Score:3, Informative)

Only in Indiana [uwaterloo.ca]
• #### Bah - another incomplete article (Score:5, Funny)

on Saturday December 07, 2002 @11:14AM (#4832749)
I can't believe you report this and don't even include the value of Pi he calculated in the article!

I guess I'll have to wait for one of the page widening trolls to post it.
• #### woo (Score:3, Funny)

<nomadicworld AT gmail DOT com> on Saturday December 07, 2002 @11:26AM (#4832800) Homepage
Now I finally have the measurements needed to make my cookies PERFECTLY round.
• #### accuracy (Score:5, Funny)

on Saturday December 07, 2002 @12:05PM (#4832975)
> pi to 1.24 trillion places,

Wow! Imagine the improved accuracy this will bring to our everyday scientific calculations :)
• #### Reminds me of that commercial... (Score:4, Funny)

on Saturday December 07, 2002 @12:11PM (#4833004) Journal
There is a U.S. cable net commercial where the guy is sitting at his computer and all of a sudden a dialog box comes up and says "You've reached the end of the Internet, there are no more pages left to see." and the guy says "Woah, honey, come here..."

Imagine this program screaming along calculating a few more trillion places when all of a sudden it stops. Pi is NOT infinite after all.

Imagine the hiliarity that would ensue (oops, wrong web site...)

10 to the minus 6th power Movie = 1 Microfilm

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