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Pi: It Just Keeps On Going 323

dominic7 sent us a link on the National Post about a new record for "knowing" Pi. Using the ol' distributed approach, a math major in Canada has found the quadrillionth binary digit of pi. It's a zero.
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Pi: It Just Keeps On Going

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  • The official web page of PiHex, the group that originally made this shocking announcement (incidentally it was in early September), is here:

    http://www.cecm.sfu.ca/projects/pihex/ [cecm.sfu.ca]
  • Nice!

    It means that if you do: ./compute_pi > /dev/dsp, sooner or later you will ear Behetoven's fifth, last Madonna's song etc... (well, maybe not at the right speed)

    Or if you stream the PI digits to the framebuffer, you (or your grand-grand-grand-children) will see a digital representation of Da Vinci's gioconda.

    I wonder if this wold be accepted as 'prior art' in a patent or copyright lawsuit

    ;-)

  • Oh, that's way too complicated for lawmen to comprehend. You'd do better legislating for Pi to be 355/133, which not only is easier to type, but it also has had its share of signature space here on Slashdot.

  • and this helps me why? Why cant get get some decent articles on /. nowadays? what happened?

    Maybe doesn't. So what? It's a cool hack, just what /. is all about.

    This reminds me of way back when Steve Wozniak wrote a program for the Apple ][ (8 bit processor, 4.xx Mhz, 64K (!) of RAM, no fan) that calculated pi to some huge number of decimal places. The program would churn for a week and then print out pages of numbers. Cool hack!

  • by Masem ( 1171 ) on Friday November 03, 2000 @06:29AM (#653148)
    Ok, let's throw away all the synchotrons, super-colliders, et al. Shoot down the hubble, kill SETI, and stop looking into space.

    Seriously, there *are* fundamental basic studies that need to continue that are several steps down from public use but if funded right, may lead to something big. Understanding what the next smallest division of matter is may lead to improved energy sources, new materials, etc, as an example.

    But there are studies that are also mostly curiosity issues - finding the nth digit of pi where n is anything larger than 100 is a good example. It is necessary to know pi to decent accurracy for "large" fp calculations (large in decimal places), and in most scientific calculations, pi is multipled or divided into a measument value, which will probably, by our current standards, no more accurate than 10 to 12 digits of accuracy , which means that any digit beyond the 12th of Pi is lost in measurement error.

    The only thing, based on what I've read on pi, that interests mathemations is trying to determine if pi is completely irrational (can't be expressed as a fraction of two integers) -- if there's any point where the digits in pi repeat ad infinitum, pi becomes rational, and most of the current foundation of advanced number theory will have to be rewritten. Seems silly, sure, but what happens if SETI returns a definite signal? It's like the question that 'Contact' raises, if we don't look for it, we may be missing something.

    So while multi-billion dollar budgets shouldn't be spent researching the nth digit of pi, there should be a small but dedicated effort to continue that search. And by going to distributed cycle systems like SETI@home (I do believe there was one for pi), it becomes trival to maintain such a project.

  • 22/7 is only an estimation of pi. The calculated result is 3.14285714.....

    pi is 3.1415926....

    As you can see it deviates at the third decimal place.

    But then again I did use Microsoft's calculator :)

  • As any eighth grader knows, pi is 22/7
  • 'The case is perfectly simple. If we pass this bill which establishes a new and correct value for pi , the author offers to our state without cost the use of his discovery and its free publication in our school text books, while everyone else must pay him a royalty.'"

    My God, this guy was a century ahead of one-click.

    The scary thing is, the USPTO would probably let him get away with it today...

  • in hindsight, i thought the same thing about the length. nice gag, though. good job.
  • This is probably the most computationally expensive random single digit number generated ever.

    It's worse than that, since it was in binary representation. It was the most expensive coin toss in history.

    Of course, it's a so-called "coin toss" that comes up the same every time, but still...

  • Yeah, it's right there at digit 2440. It reads 666.

    And yes, an infinite stream of random numbers is probably an excellent place to look for a message from God. No matter what message you are looking for.
    --

  • No. The first trancendental number proven to be so was specifically constructed to be easy to prove to be trancendental. The number is the sum of the infinite series (10^-1! + 10^-2! + 10^-3!... = 0.11000100000000000000001...). The digits in this number are most definitely *not* random, but the number is trancendental.

  • Actually, pi=2.0

    Draw a line segment of length 2.0

    Connect the ends with a semicircular arc

    The length of the arc is 2pi/2=pi

    Now instead make two semicircular arcs of half the radius, and align them so they span the line segment. Picture of all this here [maine.edu].

    The length of the arcs sums to pi again

    Repeat with four semicircles of 0.25 radius, and so on

    The semicircles converge to the line segment, so the arc length=pi converges to the line segment length=2.0

    Thus, pi=2.0

  • Whats the point? I can't imagine the benefits of knowing Pi to that level of accuracy outway the time required to do any real computational work with it. Can you imagine trying to even add two quadrilion bit numbers?

    I seriously hope this guy does other things to earn his keep besides calculate PI.

    Granted, I'm not math freak, but can anyone else out there think of reasons to know PI this deep?

    Captain_Frisk
  • This is all I remember:

    3.14159,
    2653589,
    7923284,
    626 and a whole lot more!

    It's a rhyme.
  • Throwing vast amounts of computing power to something as obscure yet elegant as computing pi to a bazillion places just oozes with the essence of nerdness. To find the quadrillienth binary digit is even more so. As such, it is indeed wonderful news for nerds. Bravo!
  • Here's the link to the Nasa site [nasa.gov] with the formula for computing an arbitrary hex digit of Pi.
  • by bloodSausage ( 98859 ) on Friday November 03, 2000 @07:37AM (#653161)
    All for naught, really.

    Sorry, couldn't resist.
  • No, you can have a 0 after the decimal and still have more numbers left to go.
    Take 77/25. It comes out to 3.08.

  • I thought it had already been proven that pi was irrational, by some greek bloke.
  • Pi is believed to be effectively random, so anything could be found if you use enough digits.

    Yeah, but what if you go down the digits far enough and it stops being "random" :)

  • ...of what you're saying? Everything that ever has been or will be done is encoded in Pi. The same holds true for e, sqrt(2), etc. There is nothing new under the sun.

    This sounds rather like the Mind of God(tm). Do we now need to worship Pi? Will prayer be reduced to chanting "three point one four one five nine two six five three five eight nine..."?

    b&
  • by ka9dgx ( 72702 ) on Friday November 03, 2000 @06:33AM (#653166) Homepage Journal
    Actually, they didn't settle on just one value of pi, they had many... including 3.2. Here's the requisite hyperlink. [cs.unb.ca]
    Mike Warot, Hoosier
  • If you need it in more places than that, then go here [pithemovie.com].
  • by nharmon ( 97591 ) on Friday November 03, 2000 @06:34AM (#653168)

    Well, according to this [nasa.gov], the farthest object we can see is about 1 billion light years away. Now, there are 5,865,696,000,000 miles in a light year.

    So we'll say that the farthest object we can see is five sextillion, eight hundred sixty-five quintillion, six hundred ninety-six quadrillion miles away.

    Now, at 56 digits, we're going to say that it can calculate to a precision of 10^-56.

    10^-56 * 5865696000000000000000 = 5.865696*10^-35

    So, a decimel at 10^-56 will represent a unit on this scale of 5.865696*10^-35 miles.

    Now, there are 63,660 inches in a mile, so...

    (5.865696*10^-35)*63660=3.7341020736*10^-30

    So, a decimel at 10^-56 will represent a unit on this scale of 3.7341020736*10^-30 inches.

    Now, the estimated size of a proton is 0.22 trillionth of an inch. That is twenty two hundred quadrillionths.

    Size of Proton = .00000000000000022 inches

    Size of Known Universe * 10^-56 = .0000000000000000000000000000037341020736

    So, 56 digits of pi, as you can see,... is TOO accurate.

  • One of my favorite quotes is "The numbers in Pi pass every test for randomness," which is interesting since it can be calculated. Is that true for all trancendental numbers?
  • hmmm... You've never known a math major, have you? Or a Canadian math major at that, huh? You probably wouldn't understand till you get to know one.


    luckman

  • You're very wrong. When Bell Labs invented the Laser in the early 60's, they didn't know it would be used to play music in the 80's. Or that it would ring up prices in a grocery store.
  • ... his Math Prof. still made him "show his work"
    (or took points off)
  • Wow.. a zero, who would have guessed ;-)
  • by Anonymous Coward
    yeah, and stuff like that gets modded up ? Moderation really sucks here.
  • (Or in deep pie?)
    Carl Sagan said that there is a secret code buried
    deep in the digits of pi, placed there by the
    Builders of the Universe.

  • by Red Moose ( 31712 ) on Friday November 03, 2000 @05:40AM (#653176)
    This is like, a change moment in mankind's science.......a paradigm shift; it will change the world as we know it. Suddenly, computers will be faster, people will stop needlessly shooting each other, and McDonald's will serve Egg & Bacon McMuffin's *all* day....
  • by radja ( 58949 ) on Friday November 03, 2000 @05:41AM (#653179) Homepage
    only about 1 in 10 people...

    //rdj
  • actually, from what i've heard, the digits of pi pass all statistical tests for "randmoness" (whatever that means). The problem is, nothing is truly random, except possibly brownian motion (
    I have my doubts about that). The digits of pi, while not truly random, are pretty damn close.
    ----
  • Further research shows that pi is actually finite at about the 500trillionth decimal place. It's all zeros after that, he just didn't notice.

    :)

  • Sure, we could. We could also just code it as:

    c/d, where we now c is a circumfrence and d is it's diameter.

    The point of the Berry paradox was not to say we should encode PI in words, it was just to demonstrate there are algorithmic ways to express very complex messages. Saying "The smallest number not describable in less than 100 words" is the result of some algorithm to express large numbers in small ways. Essentially, it is just an example.

    Woz
  • by Pfhreakaz0id ( 82141 ) on Friday November 03, 2000 @06:42AM (#653197)
    I had $50 on "1"!
    ---
  • Ah, but what's interesting is that ALL THREE DIGITS they have looked at are zeros!

    This means that they have the Improbability Drive!

  • And I'll legislate for PI to be 8E+16 ^ (1/34), which is a close approximation, although as another irrational, not very useful.
  • by donutello ( 88309 ) on Friday November 03, 2000 @10:18AM (#653209) Homepage
    Pi has been proven [seanet.com] to be irrational. You can't perform this exercise hoping to find a sequence because you never will.
  • by Greyfox ( 87712 ) on Friday November 03, 2000 @06:47AM (#653213) Homepage Journal
    Take checksums of all the metallica MP3s and start a distributed project to search pi for them. Since pi is both infinite and random, they've gotta be in there somewhere. Once you know where they are in pi, you can compress the songs to however many bits are needed to express the first and last positions in pi. Since we can calculate pi starting at an arbitrary location, playing the song would just be a matter of piping bytes in from your calculation program (given the start and end locations) to your MP3 player.

    In other news, the RIAA gets a restraining order against PI.

  • by Nagash ( 6945 ) on Friday November 03, 2000 @10:56AM (#653215) Homepage
    So the conclusion is that there are no numbers that cannot be described in a hundred words.

    Counterexample:

    There is a number that is greater than zero, but less than two, which,

    when taking the set of Natural numbers to not include zero is less
    than or equal to evey other number in the set. It is also the
    identity element in the group that defines multiplication, which means
    it is its own inverse. Often, it denotes the boolean value true and
    finishing ahead of anyone else in a competition. Prime numbers are
    divisible only by themselves and the number in question. It can be
    drawn in a single stroke and is also known as the loneliest number.


    I think you meant to say there is no number we can't describe in less than 100 words. =)

    Woz
  • It's not very telling though. There are 3 components to the speed of calculation. The raw machine speed, improved algorythms, and alogrythms which converge in a non-linear fashion, eg if you give it twice as much CPU time, you get 4 times as many digits. Without seperating these components, you can't tell why it's getting faster.
  • Actually, couldn't we just encode PI as follows:

    PI is the ratio of the circumference of a circle to its diameter.

    I just encoded PI in 65 characters or 13 words.

  • by Wiggin ( 97119 ) on Friday November 03, 2000 @06:57AM (#653224)
    Yeah, but you would need a *really* steady hand...
  • I tried submitting this when it was news and it got rejected (2000-09-11 12:24:13 The quadrillionth bit of Pi is zero (articles,science) (rejected)).

    I guess things have to get into a major newspaper before they are considered newsworthy.

    BTW, the original announcement is here [cecm.sfu.ca].

    Colin Percival
    Author, PiHex
  • by cperciva ( 102828 ) on Friday November 03, 2000 @11:43AM (#653226) Homepage
    Well, I'm not in the US, I'm in Canada, so you can trust me ;)

    Seriously though, if you want to check up on me, I can send you all of the intermediate results (partial sums of the sequence), and you can 1. verify that they add up to the result I gave, and 2. take partial sums at random and verify that they are correct.

    A complete triple-check of the results would only take 600,000 cpu hours, actaully, so you could even do that if you like.
  • Something strange happens between the 127th and 327th decimal. It's the name of G_d or something like that. All subsequent digits have got to be leftover resonating turbulence.
  • I don't think you get the point. If you can predict the order of ones and zeroes, based on the preceeding numbers, you have shown that Pi is not a random stream of numbers. It's predictable. That was what I was told at school the whole point of calculating pi to huge numbers of decimal places was - to see if there was a pattern.

    There are loads of uses for these algorithms, but you are all evidently too stupid to comprehend them, so I won't bother.
  • It's fair to say that yes, we don't need to know what the gazillionth digit of pi is (like a lot of the hecklers around here are doing), but it is actually a pretty interesting accomplishment.

    I took part in the earlier phase of the project, that found the trillionth digit, and was impressed by the fact that the person behind it, Colin Percival, was only 16 or so at the time. That wasn't so long ago -- I doubt he's even 20 by now. This may not be earth-shattering knowledge, but I'm impressed by the fact that someone so young is doing something so impressive.

    It reminds me of a large-scale version of the mathimatical riddles that Paul Erdos is said to have constantly posed -- check out The Man Who Only Loved Numbers [fatbrain.com] some time, it's a really good book. This kid may be on track to be the same caliber of mathematician. Who knows, the next puzzle he solves might not be trivial -- maybe he'll prove or disprove the P vs NP conjecture & break or affirm modern cryptographic systems. Maybe he'll find the real proof to Fermat's last theorem. I look forward to finding out...



  • by Pru ( 201238 ) on Friday November 03, 2000 @05:41AM (#653262)
    All you need to draw a circle around the entire visable universe that devieates from perfect circularity by only the width of one proton. IS 56 DIGITS OF PI.

    But Pi does give us a good benchmark for computing sometimes.
  • {HUMOR}

    Since PI is actually defined as the ratio of the circumference of a circle to its diameter this value changes with the geometry. Now I will not deny that finding the quadrillionth digit of this ratio in Euclidian/Plane/2-D Geometry can be a bit tricky. However, finding the quadrillionth digit of this ratio in "Taxi-Cab" geometry is quite simple -- it's 0. In fact this ratio is exactly 4!!! For that matter if they were working in 1-D the value of this ratio is exactly 2!!! Maybe they were working in "Taxi-Cab" geometry?????

    {/HUMOR}

    This message has been formatted for the humor impaired.

  • You overlooked the other important factor! These people had time to do it.

    Tomura: Hey Kanada, whadda want to do tonight while backups are running?

    Kanada: I dunno, why don't we see if we can run off pi to 536,870,898 places

    Tomura: Works for me.

    Looking at that chart [netcom.com] I can't help but wonder if this was all these guys ever did. And now Tamura, replaced by Takahashi, is on a street corner holding up a sign "Will calculate Pi to 1,073,740,800 places for food."


    --

  • err, it's irrational, so it's not quite a ratio...

    Ratios can be irrational. Ratios of integers can not.
  • by Black Parrot ( 19622 ) on Friday November 03, 2000 @05:42AM (#653271)
    Vote for me, and I'll set e=2.0, pi=3.0, and extrapolate the rest of the number line from there.

    I recognize that that won't fix everything, but at least it will bring two of the worst freaks of nature into line with what the citizens expect from their number system.
  • Egg and Bacon McMuffin's? Personally I like apple or hair pi.
  • Maybe the current political climate in the U.S.A. has increased my already sky-high levels of cynicism, but exactly how do we know that he actually calculated that the billionth-millionth-squillionth (whatever) binary digit of Pi is a zero? He might just have guessed! After all, he's got a pretty good chance of guessing right and what are you going to do, prove him wrong?

    --
  • SETI@Home. Or that new one for decoding genes or whatever. What's more important, knowing yet another binary digit in pi or knowing whether or not intelligent life exists outside of earth, or what genes turn off cancer?

    J
  • My bad. You are correct. None-the-less, it was fun to write.

    Anyway, I still think I have a counter-argument.

    The conjecture is that there is no number that cannot be described in 100 words. While that was not the conclusion of the Berry paradox (there is no conclusion of the paradox - it's just a paradox), I think I can construct a contradition.

    Let's say there are Num words in a natural language L. Since the number of words in a language is finite, an absolute upper bound of sentences that are 100 words long is Num ^ 100. This number is finite. Thus, there is a number that cannot be decsribed in 100 words. Bear in mind most of the sentences formed will be non-sensical, but this is an upper-bound.

    Now, this is not really a proof, but it's the intuition behind one. This falls apart when the language is infinite, however, if it's countably infinite, we can always start using real numbers and there is bound to be one we can't describe, since that set is uncountably infinite.

    This would be an interesting problem to look into...

    Woz (with thanks to R. Kitto)
  • by stx23 ( 14942 ) on Friday November 03, 2000 @05:43AM (#653282) Homepage Journal
    A binary digit of Pi is zero? What a surprise.
    I'll predict that of the next quadrillion binary digits, approx. 50% will be zero, and approx. 50% will be one.
    Right, where's my slashdot story?
  • Yep. I was blatantly wrong. It was wishful thinking on my part after seeing the 10.10110111 part.
    <p>
    Damn, I wish it had been true.
    --
    Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.
  • Yeah, sure, group theory and physics, but that was in the past, and times have changed. Science is dead, haven't you heard? killed sixty years ago by the secrecy of the Manhattan Project. Literature is dead, too, kidnapped and murdered by the Disney Corporation and the Sonny Bono (that jackass!) Copyright Act, all so a disgusting cartoon rat might continue to generate profits.

    slashdot is a site devoted to hacking but the Digital Millenium (thousand-year-Reich) Copyright Act has made non-corporate computer programming a jailable felony; look at a MS Word document that you yourself wrote with a hex editor, and it's off to Miniluv for you.

    Non-human psuedo-intelligent entities with indefinite and potentially endless life spans control society these days, and you have no right these days to disobey them, or even to complain [panix.com]. These entities are known as "corporations." Shut up, keep your head down, and work. Stockholders demand your labor; for just so long as your labor continues to increase their wealth, you'll be allowed to continue to eat.

    Yours WDK - WKiernan@concentric.net

  • Noone's calculated a quadrillion bits of pi[1].
    He's (organised a distributed computation of) the quadrillionth bit of pi. Without calculating the previous bits. That's why the algorithm is so clever. You can look for any digit and don't need to work out the previous ones.

    FatPhil

    [1] I have, actually. They're all 1s. I'm not telling you which bit positions they are in, however.

  • Ignore me. Also ignore the other times I've said that. I thought I saw a clever pattern in e and I turned out to be totally wrong.

    I've asked for a (-1, Misinformative) moderation before, and now I wish it would be used on me. Thank you.
    --
    Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.
  • Its seems strange to want to know the value of Pi down to some tiny decimal place, but it does have its uses, primarily in the field of space navigation. The accuracy allows trajectories and orbits to be calculated with a very small degree of error - a minor slip of a few millionths of a degree at the beginning of a spaceflight can mean the difference between a spacecraft reaching its destination and completely missing it. The effect of this sort of error is exaggerated most clearly over the astronomical distances between our planet and everywhere else in the solar system etc.
  • That's what I thought. I saw the headline and had to rack my brain to work out _how old_ the story was.
    Congratulations, anyway.
    /. is not a perfect medium.

    FatPhil
  • by Kotetsu ( 135021 ) on Friday November 03, 2000 @05:46AM (#653331) Homepage
    Yes. Pi has been proven to be a trancendental number, that is a number which cannot be expressed as a root of a finite polynomial equation. Trancendental numbers have been proven as a class to be non-terminating and non-repeating.
  • well, being an infinatly long number, probability would say that yes, all the universe's secrets are somehow encoded into pi somewhere in the sequence.
    So, that would mean DeCSS is hidden in pi as well! Wait till the mpaa sues!

    --
  • He said nothing of the order, only about the relative frequency (over a largeish number of samples) of the two digits.

    I haven't actually verified their frequency, but I'd be all set to believe them pretty equal.
  • Any number with a finite representation (like the examples you gave), you will find in Pi. However, you won't find "e", as its representation is infinite too. If you think about it, you'll see why.
  • by roryi ( 84742 )

    Waaaaaaaay back in the day, the techs at UCal would run a calculation of Pi for a couple of weeks on any new kit, just to give it a rudimentary burn-in test.

    Once, we had an interconnected series of three PDP-15s [With shared single 1/2" tape spools - the first incarnation of what would becoming DEC's famed VAX Galaxy clustering technology] that was hooked up to a huge auto-fed Adler high-speed line printer.

    We set up our standard "Calculate Pi" test routine and left the hardware guys to power on all the peripherals. Us software techs then left to attend a conferance for a week...

    When we got back we discovered that the door to the computer would no longer open... Upon investiagtion, we found that the damn HW geeks had turn the lineprinter on too, and it'd been set to echo all terminal output! It'd got through three metric tons of paper, spewing nothing but Pi!

    Pity I didn't have a camera...

  • it would be a shame if there weren't just a few people who devoted their lives to figuring out where all my socks go after I put them in the washer.

    I saw/heard in a science show/book (i forget where, it was during a period where I was gobbling up these facts) that your socks end up going up over the side of the washer bin and then fall down inside. I forget hwat happens after.
    ----
  • Honestly, I would have liked to, but oddly enough, the prevelant material concerning distances in the stellar and micronic fields were in english measures,... and converting would have only obscured the outcome.
  • They must be making some great insights into Brownian motion - I've never heard of anybody achieving an improbability of 1:8 with one of those things! Next thing you know, lightning will strike Pennsylvania TWICE!
    --
    Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.
  • Actually, one US state (I believe it was Indiana) was one vote away from legislating that pi = 4.0
  • I beg to differ.

    e in binary
    10.10110111011110111110111111011111110111111110...

    and e is quite definitely irrational. However, Pi is what's called a "normal" number, and that means that it acts fairly random. Not completely, though - I believe it's been proven that there can't be 43 of the same digit in a row in pi. That lack of a pattern could be considered a pattern.
    --
    Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.

  • > Its seems strange to want to know the value of Pi down to some tiny decimal place, but it does have its uses, primarily in the field of space navigation

    No at all. We are talking about the quadrillionth binary digit alone (ie: without the preceeding ones).

    Pi digits are interesting (I'd say fascinating) in a few ways:
    * For the exploration value.
    * For the algorithmic challenge. Going further in Pi basically mean doing better algorithm. And I don't talk about micro-optimisation, I talk about radically different ways of doing things. Discovering that getting the nth binary of Pi was easier than getting every preceeding one, have been a major breakthrougt.
    * At a theorical level, the idea is knowing things about number-universe (don't know how it is said in english), which are numbers that include everything (ie: numbers typed by infinite monkeys).
    * Lastly, exploring numbers may give us insight about what reality is really is, and what may be hidden behind.

    It is definitely not to get increased precision.

    Cheers,

    --fred

    Btw, you should try to see 'Pi', the movie. Pretty good one.
  • e is not normal - there's not much encoded in e. Ever wondered about that strange quasi-pattern at the beginning of e in base 10? It's an artifact from the real pattern that shows up in bases that are a power of 2. e in binary is this:
    10.10110111011110111110111111011111110111111110. ..
    --
    Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.
  • Coincidence?

    As with most of these inane 42 facts: yes.
    --
    Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.

  • Uh, right. We live in 3 dimensions. We've got circles. I think I just proved you wrong.

    --
    Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.
  • e isn't popular because it isn't a normal number. If you look at it in binary, the 1's and 0's form a pattern, as I've noted in other comments. I'm not sure, but I believe this pattern could show up in a more obfuscated way in base 10. The whole reason we look for digits of pi is that we don't know what they're going to be, while it took me about 30 seconds to determine that the quadrillionth binary digit of e is 1. (Nothing unexpected. The number of 1's in e approaches 100% as you take more decimal places.)
    --
    Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.
  • by marnanel ( 98063 ) <slashdotNO@SPAMmarnanel.org> on Friday November 03, 2000 @05:54AM (#653392) Homepage Journal

    There's much more information about this project on its home page [cecm.sfu.ca] at SFU. The guy behind it [cecm.sfu.ca] also has a page there.

    M

  • by lpontiac ( 173839 ) on Friday November 03, 2000 @05:55AM (#653400)
    If you take the second and the sixth decimal places, you get 42. Surely a more profound and significant result.
  • In general, all the approaches for specific finding digits within transcendental (non-rational, radix patternless) numbers require discovery in order, from the greatest significant digit down. You can't find out the 50th digit without finding the 49th first and refining the result.

    So yes, the guy has worked from finding it to be a little more than 3.0, to finding the next quadrillion fractional binary digits.

  • A while ago, I got interested in various ways of calculating Pi and saw some of the discoveries made by simon plouffe (this guy memorized the first 5000 places of pi), especially the one he found that allows him to calculate the n-th hexadecimal place of pi without having to get the n-1 places first : this is called digit extraction ,and was kind of unexpected before it was discovered !
    There is also a nice little formula from Ramanujan that is an exact sum from 0 to +infinity of Pi
    At rank 0, it's got 6 places correct, and it adds 8 correct places each time you increment it (cool eh !)
    A couple of Pi links :
    Plouffe algorithm [mathsoft.com]
    Ramanujan's formula [caltech.edu]
  • There are sites out there, where you can download not just one digit, not just two digits, but 30,000,000 (from here [cecm.sfu.ca]) and even 4,200,000,000 (from here [super-computing.org])!

    Or, as one Tolkein character might say...

    Precioussssssss Pi!!!! Givessss meee digitssssssss of Pi!!!!!! Gollum!

  • My question for the future US pres, Mr. B. Parrot:

    You have stated earlier that you will rationalize both e and pi. but what will you do with i ?

    //rdj
  • by NME ( 36282 ) on Friday November 03, 2000 @06:13AM (#653422)
    http://www.wpdpi.com/facts.html

    http://www.exploratorium.edu/learning_studio/pi/ pi.html

    Found two. They disagree somewhat.

    -nme!
  • See this quote [go2net.com] for an old take on the uselessness of knowing pi to the 100th decimal place. Still, my mind occasionally reels at the implications of an irrational relationship between fundamental concepts such as the circumference of a circle and its diameter. But I'm easily reeled.
  • According to the Guinness Book of World Records, it was actually France that declared pi was de jure 4. Apparently egomania isn't even limited by the laws of the universe.
  • Do you have a link or reference that backs up that assertion?

  • No thanks, I like my Magnum, P.I. [imdb.com] just fine, thank you.

    --

  • by interiot ( 50685 ) on Friday November 03, 2000 @06:01AM (#653436) Homepage
    This page [netcom.com] gives a history of Pi calculations on computers.

    From '49 to '83, the calculated length gained an order of magnitude roughly every 10 years.

    From '83 to '97, one order of magnitude roughly every 5 years.

    From '97 on, an order of magnitude every 2 years.
    --

  • Sorry, don't take this as a flame, but I'm shure you have no idea of what you are talking about.
    There is NO pre-computable relation between the millionth digit of pi and the accuracy of any precalculation of trajectories of a spacecraft (and a million digits for pi is doable at home).

    Don't belive me?
    Then read something about calculating of errors and the physical meaning of 1E-1000 [insert favorite measure here] in light of quantum physics....
  • by Millennium ( 2451 ) on Friday November 03, 2000 @06:22AM (#653445) Homepage
    I'm impressed. It's been a long time indeed since someone has managed to trick me with a goatse.cx link. Disguising it as a part of Slashdot's own layout was a particularly nice touch.

    This said, I think it's time to introduce a (-1, "goatse.cx trick") category into moderation. This is really getting out of hand, and I think it's safe to say that the vast majority of people who've seen goatse.cx never want to see it again.
    ----------
  • by Nagash ( 6945 ) on Friday November 03, 2000 @07:22AM (#653449) Homepage
    PI is an interesting phenomenon (as well as a decent movie). It is a good example of the intution behind Kolmogorov/Chaitin complexity.

    For example, we can look at PI from the standpoint transmission through a channel, as envisioned by Claude Shannon (Communication Theory, which in turn, relates to Coding Theory). If we try to encode PI for transmission through a channel, we realize it never ends. This is a problem. However, the way the Kolmogorov/Chaitin method looks at it, they see a way to encode PI as an algorithm. Note the subtle difference. Now, the cool thing about this is that the algorithm for PI is pretty short, so encoding is easy.

    There is another example with the Berry paradox. Imagine the smallest number not describable in less than 100 words. But wait a sec - I just described it in less than 100 words!

    Both are good demonstrations that algorithmic complexity is quite interesting. I always use PI as an example because it is so well known. Just goes to show PI can be used for more than just eating up CPU time =)

    Woz
  • Once you know where they are in pi, you can compress the songs to however many bits are needed to express the first and last positions in pi

    I bet, that for most things you might want to find inside of pi, the offset number is longer than the data itself.


    ---
  • by WhiskeyJack ( 126722 ) on Friday November 03, 2000 @07:29AM (#653463)

    Cue the music, lads!

    o/~ Bye bye to one more mystery of pi,
    Some idjit found a digit in binary base. Why?
    So some good ol' boys in the computer lab cry,
    "Zero's the quadrillionth digit of pi!
    Zero's the quadrillionth digit of pi...." o/~

    -- WhiskeyJack

Those who can, do; those who can't, simulate.

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