Pi Computed To 10 Trillion Digits 414
An anonymous reader writes "A Japanese programmer that goes by the handle JA0HXV announced that he has computed Pi to 10 trillion digits. This breaks the previous world record of 5 trillion digits. Computation began in October of 2010 and finished yesterday after multiple hard disk problems, he said. Details in English are not fully available yet, but the Japanese page gives further details. JA0HXV has held computation records for Pi in the past."
What Does This Mean? (Score:5, Insightful)
Is there any practical application to this sort of thing, either having the number itself, or whatever method this guy used to arrive at it? Or is this a thumb gazing exercise?
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a message from god shows up in binary once you get to 20 trillion digits.
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Re:What Does This Mean? (Score:5, Interesting)
If you memorize up to the first zero in pi, you can navigate the circumference of the universe in a perfect circle and when you get to the end of the circle (based on the digits of pi you memorized) you'll be off by less than the width of a human hair.
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If you're off by nearly the width of a human hair, it's not a perfect circle now, is it? Sheesh.
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If you're off by nearly the width of a human hair, it's not a perfect circle now, is it? Sheesh.
You can navigate in a perfect circle, but when you reach the end of the perfect circle there will be a little left over because the number you were using for pi to calculate the circumference was off.
However, don't let me interrupt what must be a satisfying eye roll for you. I'm glad to see cowards on Slashdot have remained as polite as ever.
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People think in binary here. It's either perfect or not. In your case, it is not.
Re:What Does This Mean? (Score:5, Funny)
How irrational of me.
Re:What Does This Mean? (Score:4, Funny)
How irrational of me.
Get real.
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Well if they search long enough. They will find the collected work of shakespear hiding in pi.
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You mean if they search along the circumference of the universe for Shakespeare? What a strange notion. Or perhaps you replied to the wrong post.
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You mean like this [nersc.gov]?
There is no DEADBEEF [nersc.gov] in the first 4 billion digits of pi. but there is a DEADBABE [nersc.gov].
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To put numbers on that.
pi ~= 3.14159265358979323846264338327950
The first zero in pi appears 33 digits in. Memorising digits up to this first zero gives an error of less than 10^(-32). The radius of the known universe is 4.6 * 10^10, light years, and since a li
Re:What Does This Mean? (Score:4, Informative)
Roughly how many digits is that?
No need to google it... here you go: 3.14159265358979323846264338327950
Re:What Does This Mean? (Score:4, Interesting)
If you look at a naive theoretical model for a computer, then you would predict that certain classes of algorithms would be most efficient for calculating digits of pi. (These algorithms use huge FFTs in order to do bignum arithmetic.) Several world records were broken using this technique. However, as the problem size grew, the FFTs started to become impractical, as the communication overhead started to dominate, and eventually algorithms that didn't have such a communication overhead became favoured. Better models of computational efficiency were arrived at, and new records were broken. We now understand time/space trade-offs better.
However, your loaf of bread won't be cheaper because of this, nor will the number of homeless on the street decrease.
That is only true for measuring circles (Score:3)
There is a lot more to Pi than calculating circle sizes. There are open mathematical questions about Pi.
For example, is Pi a normal number? (A normal number is one in which all digits appear with the same frequency in every base). And if this product turns out to be true for the at least the first 10 trillion digits, it can be a great random number generator.
Re:What Does This Mean? (Score:5, Funny)
Re:What Does This Mean? (Score:5, Funny)
I believe that the correct term is "mathsturbation"
Given that Pi never ends, could we also call it "onanonanonanonanism"?
Re:What Does This Mean? (Score:4, Informative)
AFAIK, we still have no conclusive answer to the question whether Pi has finite or infinite digits.
No.
http://en.wikipedia.org/wiki/Proof_that_pi_is_irrational [wikipedia.org]
There's five different approaches. There are more, mostly closely related cousins.
http://en.wikipedia.org/wiki/Irrational_number [wikipedia.org]
rational = terminates (your "finite") or repeats (your "infinte"). Which doesn't matter because pi is irrational as per numerous different proofs and all irrational numbers are infinite in length.
If this is some sort of "holy book" "intelligent design" thing where the bible says pi is actually 3, then I can't help you there...
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No, you only need about 50 decimal places to have an accurate enough approximation to calculate the circumference of the entire universe with less than 1 planck length of error.
This is just a "because we can" exercise. (Also, supposedly, to determine if PI is actually infinite or whether it contains a repeating pattern after you get to a certain point)
Re:What Does This Mean? (Score:5, Informative)
(Also, supposedly, to determine if PI is actually infinite or whether it contains a repeating pattern after you get to a certain point)
What? There's a mathematical proof that pi is irrational (in fact, transcendental). Specifically, if it were not, -1 would be irrational (in fact, transcendental) thanks to the Lindemann-Weierstrass theorem [wikipedia.org] and the fact that e^(pi*i) = -1. The digits cannot simply start repeating after a while (in particular, they cannot eventually just become 0, as happens with, for instance, 1/2 = 0.5000... .
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Any 1st year calculus student should know both that it's been proven that Pi is irrational and does NOT repeat, but should be able to do that proof on their own.
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pi is irrational (not the ratio of two numbers)
pi is transcendental (not the solution to an algebraic formula)
pi might not be normal - the distribution of digits might not be balanced and even ...it looks like it is but it has not been proven to to be...
Pi is *exactly* 1 (Score:3)
Pi is exactly 1, if your numbering system uses base pi.
Re:What Does This Mean? (Score:5, Informative)
The only practical application I've ever heard of for projects like this is as an integrity check on new supercomputers. They compute the first X digits of pi and then compare it to a known result which someone computed and verified earlier.
On a completely separate note, it's "pi", not "Pi". The Greek letter used is lowercase, and the standard English version is similarly lowercase.
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Which if you think about it is really strange for pi to not be a proper noun.
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Indeed. The symbol indicating the ratio between a circle's diameter and its circumference (pi) means something totally different in math when upper-cased. There it's used to express the product of the terms of a series. Given that, upper-casing it (except when it's the start of a sentence) really would change the meaning hugely.
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No more stranger than one, two three, four, five, fi or e.
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It depends how it's done. Many record holders develop new algorithmic or implementation techniques in the process, and that's actually very useful.
The calculation was commissioned (Score:3)
The calculation was commissioned by an anonymous group known as Occu-Pi.
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I can guarantee that this isn't the case. Some of us are excessive and use it to sixteen significant figures or so. Seriously, if we're doing calculations we're using C or Fortran. What type of float do you know that stores so many digits? I just do what I think most people do and fill up the number of bits in the float I'm using - and even that's more than needed.
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There are floating format mathematical libraries which support arbitrary precision, but that said I can't see a use for trillions of digits of pi in engineering or science. You can't even write it down given the cost of toner these days. It might be useful as a cryptographic key of course.
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You're talking to astronomers - if you saw any codes we've written you'd know full well that most of us can't program for toffee :) What's pretty much standard is to use the float size built into your compiler. Some people redefine them in the headers of their codes and then just ignore it. I dread to think how much numerical noise has been touted as a result over the history of astronomy, only to vanish when looked at a bit more closely at the cost of only a few hundred man-hours and CPU time. Thankfully n
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Even then, this has no practical consequence whatsoever. If you want to compute the circumference of the galaxy, to accuracy such that your answer is off by less than a nanometer, you still need only ~100 digits of pi.
So yes, in principle you could need more than 10 digits, allthough in practice it's pretty unlikely (it wouldn't matter unless you knew the -radius- with that high precision).
But raising the bar from 5 trillion digits, to 10 trillion ?
Irrelevant in the real world. (possibly there's math-applic
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Even then, this has no practical consequence whatsoever. If you want to compute the circumference of the galaxy, to accuracy such that your answer is off by less than a nanometer, you still need only ~100 digits of pi.
That assumes we know the radius of the galaxy to within a nanometer, which, ummm...we don't. Best estimates are more like "rounded to the nearest million light years".
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Even then, this has no practical consequence whatsoever. If you want to compute the circumference of the galaxy, to accuracy such that your answer is off by less than a nanometer, you still need only ~100 digits of pi.
... and a measurement of its radius to within a nanometer ;-)
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True, no one will need to know pi to more than 640x1024 digits.
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I imaging that it has applications in astronomy. When you want to precisely compute something over the distance of light years, you may want more than just 10 digits for Pi.
As a professional astronomer I can guarantee that distance scale measurements are a little bit less precise than one part over 10^13. Even for most precise measurements, e.g. gravitational waves experiment, 16 digit suffices!
Re:What Does This Mean? (Score:5, Informative)
The radius of the part of the universe visible to us is about 46 billion light years [wikimedia.org] or about 4*10^26 meters. The planck length, assumed to be the shortest length there is, is about 1.6*10^-35 meters. That is, the radius of the known universe is 2.7*10^61 planck lengths. Thus with just 62 digits of pi you are as accurate as the laws of physics allow. In practice you'll never need even that. Indeed, you'll not even measure cosmic distances to the meter (27 digits), or even to the kilometer (24 digits). Even measuring to the light year (12 digits) is probably impossible for objects that far out.
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You'll never need more than 10 significant figures
Do you work at the CERN?
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The primary reason for this is to confirm the never-ending nature of pi,
Or find a cycle in the digits, a pattern that repeats itself (like 27/11 = 2.454545...).
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The never-ending nature of pi is well-confirmed by mathematical proof. It is proved to be irrational (which already implies the never-ending nature) and even transcendental. What might be a motivation is checking the normality, i.e. the assumption that there's no pattern in the digits of pi. Normality has AFAIK not yet been proved.
Re:What Does This Mean? (Score:4, Funny)
I can calculate any digit of pi in binary off the top of my head with 50% accuracy.
Why not (Score:2)
would just using =Right(Pi, 1) be quicker?
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would just using =Right(Pi, 1) be quicker?
There is an overflow risk. Try Right(Pi,1,10000000000000) instead.
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Ham Radio Callsign (Score:3, Insightful)
Kind of obvious to me, being one. Here is his info:
http://hamcall.net/call/JA0HXV [hamcall.net]
And although I'm not first, let me congratulate Shigeru on a job well done! Oh, and to the idiot complaining of all the wasted CO2, please turn in your geek/nerd card now: computing Pi (and e and...) is NEVER a waste! :P
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Re:Ham Radio Callsign (Score:4, Interesting)
Yes, there are. Modern radio systems are meant to be good enough to be reliable. Ham radio systems are the art of the possible. Most hams these days are experimenters who enjoy trying odd things. I've seen voice powered radios, I've seen radio systems designed to communicate via lunar reflections, I've seen radio systems designed to pick up spacecraft in deep space.
Some hams like to study radio wave propagation. Again, this is the art of the possible, not the engineering of the certain. Bouncing signals off of thunderstorms, sporadic E layer reflectors or meteor trails are all in this category. Occasionally, they stumble across something that works surprisingly well.
Some still tinker with modulation methods. Hams were playing with spread spectrum radios in the mid 1980s --long before the engineers sat down to work on the so-called wireless standards. Today, work continues with all sorts of forward error correction codes and modulation techniques.
So, yes, there still is a ham radio. Yes, there still are a more than a few slobs who like to do nothing better than listen to themselves talk on short-wave. But there is still a vibrant core that continues to study all sorts of forgotten alleys in the technology.
Quantum Computing? (Score:2)
Supposedly, this ran for nearly a year -- imagine how fast someone can come to the same result if he/she was dealing in qubits.
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Quantum computing is about algorithmic efficiency, not speed. So calculating pi will be a whole lot slower until you find and implement an quantum algorithm that is more efficient than classical solutions.
Contact (Score:3)
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The big question is, does it turn out to contain the plans for a teleporting device?
Undoubtedly it does, embedded somewhere in the sequence.
Also the text of every novel that will ever be written.
Just got to figure out what the encoding is. And figure out where the relevant substring starts.
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No, the Teleporting device plans came by radio singnal (along with a few prime numbers and the TV broadcast of Hitler at the 36 olympics.
The first message that was found in pi was a circle drawn in 1's and zeros in base eleven.
This was in the book anyway, I think they left the whole pi thing out of the movie.
Even better (Score:3)
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This reminds me of a scifi (short) story I read too many years ago - I forget the title or author - I think pi was also being calculated to the Nth and some some magic number was reached and the universe started to unravel. The stars started blinking off, etc.
Wonderful stuff. I read so many short stories in my youth, I can't remember many, what I do remember though is the slightly-musty smell of the books in a library and immediately having to go to the toilette for a nice bowel movement... olfactory tri
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This reminds me of a scifi (short) story I read too many years ago - I forget the title or author - I think pi was also being calculated to the Nth and some some magic number was reached and the universe started to unravel. The stars started blinking off, etc.
Do you mean Clarke's "The Nine Billion Names of God?" [wikipedia.org]
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Sounds to me like you're thinking of Aurthur C. Clarke's The Nine Billion Names Of God [wikipedia.org].
What's the message? (Score:2)
Isn't that one of the plot ideas in the book (which the movie was based on) "Contact"?
Scientist travels across interstellar space to meet super-advanced aliens and asks:
"Do you believe in God?"
To which they reply "Yes".
(A little surprised) "Why?"
"We have proof"
(Very surprised) "Proof?! What is it!"
"If you calculate Pi to the n-th digit you will find a message..."
Since I didn't read the book, I'm not sure this is how the exchange went, nor do I know what the "message" was. But it makes a good story! (I th
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Wen calculating pie in a given number base (I forget which base), there was an abnormally long string of zeros and ones. The length of this string was the product of two prime numbers.
Arrange the zeros and ones into a two-dimensional matrix with one prime's units on the X axis, and the other prime's units on the Y axis.
The result was a "picture" of a circle.
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Can we have xkcd [xkcd.com] now?
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Anyway how would you determine, when looking at an infinitely long string of "random" numbers, what is a "message"?
And I suppose people are thinking it's going to be something in a current language... But I'm thinking some DNA-like thing instead.
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Good question.
I suppose you'll find this article interesting :
http://en.wikipedia.org/wiki/Normal_number [wikipedia.org]
We're not sure pi is normal.
So it is believed that the complete works of Shakespeare in Klingon are hidden in pi, but you'll probably need a whole library to describe its location.
Re:What's the message? (Score:5, Informative)
To decipher the math-speak on that page for the less mathematically inclined, here's my explanation of what a normal number is, geared towards a programmer.
Say you generated a number by randomly picking digits 0-9. After generating 100 digits, you'd expect close to 10 of them to be "7" (1/10). After generating 1000 digits, you'd expect about 100 to be "7" (1/10 again), but you'd expect only about 10 copies of the string "57" (10/1000 = 1/100), since there are 100 possible two-digit strings ("00", "01", ..." 99") and there are about 1000 length-2 substrings in a string of 1000 digits (999, to be precise). In general, for such a string of length N, we'd expect about 1/10th of the digits to be "7" and 1/100th = 1/10^2 of the substrings to be "57". If we made N very large we would also expect these estimates to get closer and closer to the truth.
You might get some strange abberations by random number generation. For instance, with astronomical bad luck you might generate 0 each time, and then your estimated fraction of "5"'s would be completely wrong. Still, the above properties are pretty good measures of how "well mixed" the digits of a number are, and they're taken (with mild generalizations) as the defining conditions of a normal number.
Specifically, for a given number x, imagine writing out its (infinitely many) digits in base b. Pick a substring of length m that you're interested in--say an encoding of Shakespeare's complete works in the original Klingon. In the first N digits, we would like to require the fraction of substrings matching our given string to be 1/b^m in analogy with the above (1/10^2 came about from b=10, m=2). That's too much to ask, so instead specify a small tolerance above and below 1/b^m. The key condition for normality is that if we look at the first N digits where N is larger than some number (which depends on the tolerances, the substring we picked, and x itself), the actual fraction of matching substrings will be within our tolerances of 1/b^m. A normal number is one where you can perform this operation in any base, with any substring, and with any tolerances.
If pi were normal, there would have to be at least one (indeed, infinitely many) occurrence of a given encoding of Shakespeare's works, since otherwise for N large enough the number of matching substrings would be near 0, and we could specify our tolerances to be between, say, 1/2 * 1/b^m and 3/2 * 1/b^m, which is strictly greater than the fraction of matches for N large enough since that fraction tends to 0, so it can't be within these bounds.
It's not too surprising that proving the normality of a number is much harder than believing it. Essentially, any number whose decimal digits appear "quite random" feels normal.
Now that is a key! (Score:2)
Talk about the best one time pad set ever.
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A one time pad that can generated perfectly by anyone using simple maths and published techniques? Try worst pad set ever, by telling your adversary the pad is found in the first 10 trillion digits of pi, you just reduced the search space to at worst log2(10*10^12) 45 bits.
Sagemath.org can do many digits (Score:2)
The sagemath.org open source computation engine has a 2 line benchmark that computes Pi to 5 million digits.
It took my Atom desktop computer about 15 minutes. I watched it with Top. It sucked up 99 to 100% of the CPU and strangely only 200 Mb out of 2 Gig of RAM.
Also, it didn't use the Linux swap at all. It kind of got me puzzling that my Ubuntu Linux might be missing some performance optimizations.
What to do with it? Resume studying mathematics. Make a pretty good symmetric encryption gadget with a CD of
Computers get faster and faster (Score:2)
So the record will be broken over and over and over again...
Thanks for the answers (so far) (Score:2)
Thanks for the answers to some of my questions. I didn't read the book, but might if it recommended (and if it's an e-book).
Likewise, never heard of "normal" numbers before (like I said, I'm not a mathematician). So thinks for the info.
Uh, is there any way to check this person's answer (short of duplicating the entire calculation)? Like I heard there's a way of confirming If a number is prime that's easier than figuring out what's the next prime number.
Mistake (Score:4, Funny)
It looks to me like there is a mistake in the 34,518,296,721th digit. Could you repeat and compare please?
Actually calculated 10 billion digits (Score:2)
The guy is using short scale [wikipedia.org]. :)
This being Slashdot, you could have written 10^13, that being unambiguous.
Call me back when someone actually computes 10 trillion (10^19) decimals of Pi
Is there a prize (Score:2)
Is there a prize for memorizing, and then reciting all 10 trillion digits?
Tau, not Pi! (Score:4, Informative)
That's all well and good, but what about digits of tau [tauday.com]?
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how do they verify that it isn't random numbers
They actually verify the formula, method and hardware used, and if it is actually feasible within a reasonable time.
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I think there are formulas for calculating the nth digit without knowing the previous ones. Assuming this is so, you can get a probabilistic proof very easily: just pick 100 random digits, compute their values, and check against the claim. (It may require some computational power to do this, but it should still be plenty tractable.) If they all match, you've got solid evidence it is correct.
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So I'm sort of right and sort of wrong. There are digit-extraction methods for pi [wikipedia.org], but according to wikipedia, they work in O(n^2) time (for the n'th digit). But it also looks like there's an algorithm to compute up to the nth digit in time O(n log(n) log(log(n))).
Which means that asymptotically, if the storage requirements of the second alogrithm [wikipedia.org] don't preclude its use in those cases, there's some N for which it's actually faster to compute all of the first N digits than just do the N'th digit directly.
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No we couldn't, that would be double u as w is vv. And due to the Romans not having a u, they would use v instead hence double u looking more like double v.
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You would be assuming that Slashcode can handle displaying a Greek letter. I'm not going to try, but that's probably a ropey assumption to make...
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Thank you for wasting the earths resources (electricity, etc..) to make the world a better place!
Aren't you wasting those resources by reading such a story in the first place?
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70 billion instructions per second.
10 trillion (10,000 billion) instructions in 143 seconds (just over two minutes).
Somehow I have the feeling that the calculation of one more digit of pi involves a bit more than one processor instruction. The instructions to store the result to hard disk will require more than that already. If the calculation and storage of a single number, including all overhead, amounts to just 1,000 processor instructions, then it would be one month on your icore7 already. And I would
Re:Electricity usage (Score:5, Insightful)
Probably not nearly as much as other useless endeavors, such as playing computer games, updating facebook status, or watching super bowl. And reading slashdot, of course.
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I am curious to know how much electricity was wasted on this apparently useless endeavour.
I think you're just suffering pi nos envy. He's obviously got way more pi nos than you do.
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Yeah but my circumference is larger because I rounded up
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let me keep alive a bit of usenet history:
On Tue, 22 Jul 1986 06:33:45 +1000, Calum T. Dalek, chairentity wrote
> In article eugene@ames.UUCP (Eugene Miya) writes:
> > We have just received a letter from Japan that a newer record for
> > computation of digits of Pi was accomplished. Previously David Bailey
> > here at Ames did a 30 million digit computation on the Cray-2.
> > The new computation was done on an older Hitachi 810 supercomputer
> > using extended storage. The new record is 33 million digits.
> > Dave replied, "This means war!"
>
> I think NASA should pay more attention to launching rockets and less attention
> to calculating the next million digits of pi.
> --
> Greg
> gjk%a@lanl.arpa and greg@harvard.harvard.edu
I think Los Alamos should pay more attention to developing high tech methods
of mass destruction and less attention to flaming NASA in net.math.
Hugs and kisses,
Calum
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... and when it gets sore from doing that, then you fill in the time by calculating the digits of pi ...
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Yes, like reading about it on slashdot and complaining that he's wasting time :)
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You can calculate any particular digit of pi(in base 16) without calculating all the preceding digits to verify they are correct.
Pi = SUM(k=0 to infinity) 16^(-k) [ 4/(8k+1) - 2/(8k+4) - 1/(8k+5) - 1/(8k+6) ].
Hopefully that won't get mangled.
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>All that CO2 for nothing!
All those digits were calculated with Occupy San Fran bicycle-powered laptops [france24.com], you insensitive clod!
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