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Pi: It Just Keeps On Going
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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The official web page of PiHex, the group that originally made this shocking announcement (incidentally it was in early September), is here: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/
kugano
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
Ciao
----
FB
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.
In Soviet Russia, Jesus asks: "What Would You Do?"
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!
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.
"Pinky, you've left the lens cap of your mind on again." - P&TB
"I can see my house from here!" - ST:
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
"That's the sort of blinkered, philistine pig ignorance I've come to expect from you non-creative garbage."-Monty Python
As any eighth grader knows, pi is 22/7
My other sig is extremely clever...
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.
Slashdot, come for the goatse, stay for the trolls.
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...
Accountability on the heads of the powerful.
Power in the hands of the accountable.
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.
--
Pokéthulhu
Gotta catch you all!
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.
"Bite me, it's fun!" - Crowe T. Robot
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.
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
Sometimes I've believed as many as six impossible things before breakfast.
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!
Can we get a "-1 Wrong" moderation option?
Here's the link to the Nasa site with the formula for computing an arbitrary hex digit of Pi.
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.
Do really dense people warp space more than others?
I thought it had already been proven that pi was irrational, by some greek bloke.
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&
All but God can prove this sentence true.
Actually, they didn't settle on just one value of pi, they had many... including 3.2. Here's the requisite hyperlink.
Mike Warot, Hoosier
If you need it in more places than that, then go here.
"Ancillary does not mean you get to rule the world." --U.S. Circuit Judge Harry Edwards, speaking to the FCC's lawyer
Well, according to this, 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?
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)
Build Your Own PVR/HTPC news, reviews, &
Wow.. a zero, who would have guessed ;-)
I plan to plan / Dutch course in The Hague
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.
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....
Acting stupid isn't much fun when there's someone around who knows better
The purpose of this is that they are hoping that some time, some where, pi will start to repeat. So all those ideas that pi is irrational would be wrong. And we could finally write an exact value of pi.
I am a bad speler. Please ignore speling meestakes in me poast.
Actually that should be:
....
3.14159,
2653589,
7923284,
^^^
323
6264338327950288
(if I remeber correctly)
Johan V.
Dang! Why did it have to be a zero? That totally blows my Universal Theory of Everything! Twenty years of scribbling notes in my basement, all to waste.
If only it had been a three. Then I could have at least been left with a Theory of Something...
Read a good book lately?
Read a good book lately?
...is the the sextillionth bit of pi will be a one!
After all, I have a 50-50 chance of being right... ;)
All about me
If your trolling good one. If not, get a clue. Read Infinity and the Mind by Rucker and realize what you just said is TOTALLY FALSE.
...and failed miserably.
Think about it.. Your circles won't be able to close. All that money into marketing "Pi is 3" will leave you with tires with flat parts (Think, ca-chunk,ca-chunk,ca-chunk), coins which can stand on a point, and open-top airplanes at 36,000 feet.
As far as e, e is around 2.78 and change. And, e raised to the pi times i power is -1.
Don't try to screw with the universe, dude. It screws back harder.
I used to be someone else. Now I'm someone better.
Real life is underrated.
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.
----
---- I made the Kessel Run in under 11 parsecs.
Trancendentals are numbers which are not the root of any polynomial with *integer* coefficients.
(Note that by definition, polynomials have only finitely many terms. The infinite-term version of a polynomial is a power series.)
While it is supposed that pi is "normal", I'm not sure it has been proven. This releates closely to Kolmogorov complexity. Check Google for more (I weep for Mathworld...)
"It's overkill, of course. But you can never have too much overkill." - Anonymous Slashdot Coward
355/113
I aim to misbehave.
How many digits in base pi would you need to express decimal 1.
Someone you trust is one of us.
Here's my question. Pi is infinite, right? 2 is contained in pi. So is 2347134 if you look hard enough. And so is 1271828777271891727176172. But is any number contained in Pi if you mine deep enough? Is e contained in pi?
--
One more drink, and I'll move on. --Dave Matthews Band
Incorrect... the chance that there will be about half 0s and half 1s is quite good.
Quite good? Try probability 1. Such numbers are called "normal numbers", and have measure 1 in [0,1]. Moreover, the "completely normal numbers" (numbers which are normal with respect to every basis) also have measure 1 in [0,1]. Interestingly enough, no one has yet proved the complete normality of a single number! The number .12345678910111213141516... can be shown to be normal base 10, but I don't think it's normal in other bases. No one has yet produced a proof that e or pi or sqrt(2) are normal in any base.
Disclaimer: the above is based on my somewhat fuzzy recollections of material I read years ago. Sprinkle liberally with IIRCs.
To within half a percent, pi seconds is a nanocentury. -- Tom Duff
See a description of some cool formulas for doing so.
:)
www.HearMySoulSpeak.com
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
Am I incorrect in remembering somewhere else that the same book described some large circular vessel as being 10 cubits across and 30 cubits around the rim, thereby setting pi to exactly 3? I can't quite remember where in the book it was, though. Damn lossy cerebral data compression...
Bugrit! Millenium hand and shrimp!
I had $50 on "1"!
---
DO NOT DISTURB THE SE
This means that they have the Improbability Drive!
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
Computer Game Could Hold Key To Internet Security: The key to solving one of the most vexing and profound problems of modern mathematics could lie in a most unusual place: Minesweeper, a simple computer game on millions of computers that rivals solitaire as an office time-waster.
The math problem, called the ``P versus NP conjecture,'' asks why some questions are so difficult to answer with computers. It is considered so important that in May the Clay Mathematics Institute in Cambridge offered a $1 million prize for a solution. Proving the conjecture false would mean that modern encryption technology, the foundation of electronic commerce, would be open to easy attack. Here's the link.
There's always sufficient, but not always at the right place nor for the right folks.
Actually....
if you look at what computer science really is, it is just applied mathematics.
Now, things like this are really cool because even if the resulsts are basically useless, the process behind achieving these resulsts helps develop new ways to think, so this DOES help
Jeremy
If you take the distance from our sun to Alpha Centari as the radius for a circle, and use only the first digit of 2 to calculate the diameter of that circle, the result will be *exact*.
Amazing, they guy was actually going to give them his "invention" for "free", and then *charge* other schools for using it! Hey! Unicorns exist, and I'll give you the privilage of printing that as fact for *free*, but I'll charge other schools. Better get in while you can!
It's 10 PM. Do you know if you're un-American?
So what are all the digits out to that 0? Is there somewhere where I can go look at all of them and scroll through the whole number pi? (All pages and pages of it) I just want to know what the 35,434,927th digit is.
Elp
"You keep using that word, I do not think it means what you think it means..." Inigo Montoya
And I'll legislate for PI to be 8E+16 ^ (1/34), which is a close approximation, although as another irrational, not very useful.
No, the conclusion is that there is no smallest number that cannot be described in less than 100 words.
"It's overkill, of course. But you can never have too much overkill." - Anonymous Slashdot Coward
They can't be. If they were, then there exist integers p and q such that pi = p/q, and pi is rational. However, pi has been proven not to be rational, so not all the rest of the numbers are 0.
I aim to misbehave.
Pi has been proven to be irrational. You can't perform this exercise hoping to find a sequence because you never will.
Mmmm.. Donuts
No way man, I encrypt my drive...
"It's overkill, of course. But you can never have too much overkill." - Anonymous Slashdot Coward
When you're talking about finding numbers in it, you should obviously limit yourself to finite strings of digits. It's obvious that you'll never find 1.7 sinde of Pi. It's also evident that you won't find an infinite string of 1s and an infinite string of 2s at the same time.
Apart from that, it is known that Pi does not terminate and is indeed transcendental.
In other news, the RIAA gets a restraining order against PI.
I'm trying to teach myself to set people on fire with my mind... Is it hot in here?
My computer was one of the computer inolved in the project. It was called PiHex. It is a formula called BPP which is based on Bellard's (sp?) formula. It represents Pi as a sequence. It only solves the one bit of Pi that you're solving for. When I read the document on it that came with PiHex, I didn't understand the math, I should read it again, last time I checked it was up on the PiHex site. The e-mail from Colin Percvil said that now that he had reached his goal, he was done.
The strange thing is I was talking to someone about this project today. I had a K6 at the time, and I was having errors from the latest version of the program, as were other people with K6's. I sent him the regester output when it crashed (I was running winblows at the time, yeah) and he replied and told me what the error was: the fpu was overheating the processor. I was impressed. The early versions of the program required you to e-mail him to get and send back work units. Later versions of the program connected to a server to send and recieve work units. IIRC he said that now he is concentrating on finding pi acuratly with a more standard aproach.
There are exactly 42,935,718 letter sized sheets in a square mile.
Counterexample:
I think you meant to say there is no number we can't describe in less than 100 words. =)
Woz
The value of Pi Rules.. OK
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.
Like e ^ (pi * i), which is equal to -1.
I memorized 50 digits when I was in high school and still remember them. FWIW, it is easy to memorize the first 20 digits in Japanese because it reads like a sad poem when you say them out aloud. The rough translation of this poem is "One body, one world, life is meaningless. No medicine for my illness, I recite the scripture."
Download Mazes and Puzzles from www.puz.com
please stop this now!!! this is a loop computation problem planted by aliens. this is how they entice you to use up all your resources to satisfy your little curiosity like computing the next digit of PI... speaking of resources, what are we thinking of next to burn up energy? something more exotic like continuous fireworks on nuclear explosions??? i mean all these machines are going to be hooked up to the net, then we require them to be up 24x7 to burn fossil fuel, and then the facility they are housed need to have AC to be on 24x7 or the computer would heat up and burn...it's clear we have created a situation where the production of energy will soon be majorly used "just to keep things running"...and this requirement will keep on going up. It's no longer a simple demand where energy is ONLY BE USED when you need it!!! like turn up the thermostat now when I'm cold...or I'm going to start my car now because I need to go somewhere... The net is like, I'm going to start my car now to go somewhere and when I get there, I'll leave it on running because my car needs to be running 24x7!!! Think about it people! think think think unabomber
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.
Cute :)
The length of the curve formed by your semi-circles always equals pi for any subdivision.
You might as well just define pi = 2.
-josh
Yeah, but you would need a *really* steady hand...
"I don't need a compass to tell me which way the wind shines." - Mr. Furious, Mystery Men
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.
Colin Percival
Author, PiHex
Tarsnap: Online backups for the truly paranoid
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.
Tarsnap: Online backups for the truly paranoid
Wow, they must have a hell of a lot of storage space to be able to even save that entire number to some storage medium.
1,000,000,000,000,000 bits
=125,000,000,000,000 bytes
=122,070,312,500 kilobytes
=119,209,289 megabytes
=116415 gigabytes
=113 terabytes
Yes - over 113 terabytes just to save the number itself - I can't even imagine how difficult it would be to -process- it.
--
--
grep "xercist"
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.
It's the season for Pumpkin Pi! I think I'll go have a slice now, with whipped topping.
--- Speaking only for myself,
Does anybody that's read the book Contact by CS remember the end? How come we're not doing this? I feel lied to!
Where's the beef?
"Blame Canada! Blame Canada! They're not even a real country anyway ..."
- South Park: the Movie
Don't worry. I'm from the damn place!
I don't have a fancy sig like you all do, so if you have a problem with that, you can go fsck yourself! ^_^
calculated pi to the quadrillionth-1 decimal ? And could he say quadrillion-1 without saying "quadrillion-1" ? It would seem a mouthfull, "I calculated pi to the 9 (tridrillion ?) ... 999 decimal today "
...
* Testing your shining new home supercomputer by computing a few billion digits and comparing them to a known solution.
Lucky Guess.
He had 50/50 chance!
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.
42, everyone knows it ends up really being 42... somehow
I seek not only to follow in the footsteps of the men of old, I seek the things they sought.
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 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...
DO NOT LEAVE IT IS NOT REAL
Store it in quantum memory. One "quantum bit" is enough, all you need is the damn right method to measure it!
Fight hunger. Filet a politician and send him to a 3rd world country of your choice.
Proof, dammit, proof.
And don't show me *a* proof. *Hard* proof.
Victorian-era scientists could "prove" frogs came from rain, after all.
Stating on Slashdot that I like cheese since 1997.
about the quadrillionth binary digit of pi? If you're looking at binary digits, it should at least have been some power of 2.
If my Aunt Had Balls, She'd Be My Uncle ! Mods: Don't mark this as a Troll. It's just bad humor !
,Collect the whole set !
- Save The Whales
Success is not the result of spontaneous combustion, you must set yourself on fire.
How's THAT for prior art? This pi thing is better than a roomful of monkeys.
Revenge is a dish best served cold -- grits should be served hot!
So it may be a waste of time, unless you want to really check things :).
. html#HEXPI
h tml
m l
http://www.nas.nasa.gov/Pubs/NASnews/97/05/math
Also search for:
Bailey-Borwein-Plouffe
http://www.mathsoft.com/asolve/plouffe/plouffe.
http://members.wri.com/victor/articles/pi/pi.ht
1/7 = 0.(142857)*
^^
7 being the first natural number which inverse produces a composite periodic sequence, thus making an infinite sequence of 42's possible, and there they are -- in the very first interesting rational number we can find!!
It's GOT to mean something!!
Thus log(-1)'s imaginary number is PI
it follows the rule
For x0 Then
ln(x)=PI*i+ln|x|
after all, trig functions are simply complex exponentials.
Well I once memorized it to 100 places, but I guess the rule of 7 applies.
Miles??? Inches??? What is your deal? After 4 years of college those units don't mean anything to me.
The asertion that any infinite number must have any imaginable number in it is completely false.
And here's a simple counterexample: I can think of an infinite chain of numbers that doesn't have the number "2" in it. Now this chain won't have the number "42" in it, which is certainly an imaginable number. Therefore, your premise is wrong.
-------------
The following sentence is true.
The following sentence is true. The preceding sentence was false.
Unfortunately, many of the distributed projects on the Internet are similarly useless. The RSA challenges at distributed.net are particularly useless given that the money wasted to power the computers participating FAR exceeds the prize money. No new advancements are being made, aside from the programmers possibly learning more about optimization for a particular CPU (but even this could be done without dragging thousands of computers into it).
When my spare processor time can be used to help find a cure for cancer, replenish the O-zone, or clean polluted waters, let me know.
that's pretty incredible, now will they have to prove it? I'd like to see a printout of that, but that would be one big file :P
-motardo
The guy says this is an example of what can be achieved when the idle processing power of networked computers is brought to bear on "complex" problems. Calculating the digits of Pi is hardly a complex problem.
Makes me want to go rent that movie Pi! Great flick. Twisted, dark and intense. Certainly not a romance.
F******* LOUDER! I CAN'T HEAR YOU! --Ozzy Osbourne
The math major (he, she) could have said any digit at all. How would anyone else know?
--
it's = "it is"; its = possessive. E.g., it's flapping its wings.
Sorry to be anal, but e is closer to 2.72 minus some change. (e = 2.718281828459045...)
Nope, it's just assumed since it just goes on and on and on...
This is trying to disprove the assumtion.
I am a bad speler. Please ignore speling meestakes in me poast.
Or you could say "three metric tons of pi", which I'm sure would give anyone a huge tummy ache. ;)
Pi was proved to be irrational in 1770. A later, simpler, proof can be found here.
Something that isn't known about pi is whether or not it is "normal". That is, whether all finite digit sequences of a given length appear with the same frequency in the long run. Based on the tiny initial segment of pi that has been computed (just a few billion digits) pi "seems" to be normal, but initial segments can be misleading.
> So the conclusion is that there are no numbers that cannot be described in a hundred words.
> Counterexample
<BR><Pedantry></BR>
<BR>Of course, what you actually gave was an <EM>example</EM>.</BR>
<BR></Pedantry></BR>
The transcendental number e is the most powerful force in the universe. It is content to work behind the scenes.
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.
Or could we get to a certain number of digits and thats it?
yea but they changed it to pi95 then pi98
and now they call it piME.
Paying taxes to buy civilization is like paying a hooker to buy love.
Sorry for the inconvenience?
People replying to my sig annoy me. That's why I change it all the time.
... hmm... as I seem to recall no one really knows the questions, the mice kinda lost it...
Have you read the book?
Bjarne
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 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."
--
A feeling of having made the same mistake before: Deja Foobar
err, it's irrational, so it's not quite a ratio...
Ratios can be irrational. Ratios of integers can not.
Bantam Dominique roosters crow a four-note song. Once you've heard it as "Happy BIRTHday" you can't NOT hear it that way
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.
Sheesh, evil *and* a jerk. -- Jade
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?
--
The gift of death metal does not smile on the good looking.
Sorry -- I couldn't help myself... to any more pi. <gr&d>
"Three point one four one five nine! If you know that, you're doing fine!"
Hey, happy birthday! :) I didn't mean to criticize you about a typo. Just wanted to set the record straight about the number's value, that's all. Ah, I'm such an INTP. :)
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)
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?
If I choose to give, instead of my phone number, the place that it first appears in PI, is it likely that it will have more digits than the numer itself or less?
Headline:
Greg Lyons Successfully Calculates Quadrillionth Binary Digit of Pi
by Matt Provinsano
Some math major (Colin Percival) broke a record for calculating the quadrillionth binary digit of pi. It is zero. He calculated it by using spare processing power of thousands of computers on the Internet. He used an algorithm that was developed by NASA and some of his math professors at Simon Fraser University.
This development proves conclusively that the same calculation done mentally by Greg Lyons months ago was correct.
"After I heard about That Guy's [Percival's] original record of calculating the 5 trillionth bit of pi, I knew I could do it better and faster," said Lyons, who classifies himself as an inquisitive computer hacker with interests in mathematics, music, and walnuts. "I decided right then and there that I would be the first to calculate the quadrillionth bit. After calculating mentally for several seconds, which is a really long time for me, I arrived at the answer of zero."
"I think Percival deserves some credit, having coordinated so many computers to calculate the answer, but I do believe my calculation was completed first," said Lyons. "I'm not bitter, though. I haven't met Percival, but I'm sure we have a relationship of mutual respect."
Lyons' calculation is not likely to be officially recognized, however, while Percival will get all the glory for this accomplishment. Officials reportedly did not accept Lyons' calculation for the record books simply because he did not show his work. According to Lyons' high school math teachers, this has always been his biggest weakness.
"Greg never showed any work on his Calculus tests," said Miss Koykar, a former math teacher at Winnebago High School, whose first name is actually Miss. "He nearly always got the right answer, but our policy is that if you don't write down the work, you must have copied the answer from someone else. Therefore, the answer is counted as wrong. If it wasn't for that, he would have often been the only student in class to correctly answer certain questions."
Lyons' wife also attempted the calculation mentally. She actually finished faster than her husband, but her answer was off by just one. "I guess I just rushed a little too much. I'm just too competitive," she explained.
Percival, the officials who keep the record books, and Conan O'Brien were not available for comment.
Force the hapless target system to calculate pi to some obscenely high decimal place.
- White Knight of the Order of Mihoshi Enthusiasts
So the Maclaurin series for tan^-1(x) is the following;
tan^-1(x) = x - x^3/3 + x^5/5 - x^7/7 ....
so using pi/4 = tan^-1(4) gives:
pi = 4[1 - 1/2 + 1/5 -1/7 + ...]
Since this converges to slowly you can use the following identity to get more accuracy with less iterations:
pi/4 = tan^-1(1/2) + tan^-1(1/3)
This was obtained from my Calculus 5/E book by Howard Anton, Wiley publishing... This is one of my better text books, if your looking for a Calculus book for Uni, fully recommend...
Hope that helped,
Brad
-Karl
[root@kgutwin
msdos.sys: fsav (linux) virus (17518-87)
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. 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
Well yes, of course they go over the edge, but that's where the trans-dimensional physics and the peculiarities of 23rd dimensional horfnoggler diets come into play.
All kings is mostly rapscallions. -Mark Twain, The Adventures of Huckleberry Finn
No, the conclusion is that there is no smallest number that cannot be described in less than 100 words.
Without a smallest one, I believe the set of numbers is empty. Is that not true?
--
Anyway, for a truly random numbers, the chance that there will be about half 0s and half 1s is quite good.
--
Preventive War is like committing suicide for fear of death. - Otto Von Bismarck
to go before we reach the circle-within-a-circle huh? (Carl Sagan 'contact' for all you illiterates)
on a different note, i'm in calc II right now and we're doing all sorts of things with infinite series and whatnot, so i'm wondering if there's someone out there who'll explain to me in lamen's terms what the hell divergent and convergent series mean? maybe i'm not trying hard enough but it just seems to me that a limit approaching something, and converging on something, and all the rest just seems to go round and round and make little sense. BTW, i have a big test next week so i'll appreciate any help in understanding these infinite series (esp. power, taylor series).
------ Poo-tee-weet?
nono, Ford and Arthur hit upon a foolproof method for extracting the Question from Arthur's subconcious... it was "What do you get when you multiply six by nine?"
To calculate PI you use a series such as Maclaurin, noting that:
pi/4 = tan^-1(4)
So the Maclaurin series for tan^-1(x) is the following;
tan^-1(x) = x - x^3/3 + x^5/5 - x^7/7
so using pi/4 = tan^-1(4) gives:
pi = 4[1 - 1/2 + 1/5 -1/7 +
Since this converges to slowly you can use the following identity to get more accuracy with less iterations:
pi/4 = tan^-1(1/2) + tan^-1(1/3)
This was obtained from my Calculus 5/E book by Howard Anton, Wiley publishing... This is one of my better text books, if your looking for a Calculus book for Uni, fully recommend...
Hope that helped,
Brad
So the conclusion is that there are no numbers that cannot be described in a hundred words.
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Why do you have to be so fucking condescending???
In 3 dimensions, that's a sphere.
The *next* digit is a seven
Phear my l33t homepage.
No we don't. We put circles on 2d objects in our 3d space. A 3d circle is called a sphere.
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.
Also FatPhil on SoylentNews, id 863
You're the numbnuts; that was obviously a joke.
--
Find free books.
Of PI what if the the rest of numbers PI in pie are 0. I really doubt though but it would be fun to find out. We may have the next distributed problem contest find out the next digit in PI. I did not get to read the article the site has been slashdotted.
you had more than one 3.141592653589...? Would you have multiple pi/pis/pies/pii?
this is a left handed sig
I just figured out Pi to the googleplex digit in base 36 math! it's a "Y". Go ahead, prove me wrong!
Please, for the love of God and all that is holy, use the metric system for such stuff...
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Not if they've only found a zero...it is exactly the same as before!
perl -e 'print $i=pack(c5, (41*2), sqrt(7056), (unpack(c,H)-2), oct(115), 10);'
If they publish the details of their calculation (algorithms, hardware, etc), in theory one could look at what they did and say, "yeah, that should be okay".
Of course, if the processor or hardware bugged out for some random reason (Intel Pentium FDIV error comes to mind) there really would be no way to check without running the whole thing again... and even then there is still a 25% of repeating the error if the hardware spits out random numbers at some point.
-rt-
-rt-
** Evil Canadians are taking over the world. Learn about the conspiracy
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.
ManicHawk - Just because you're manic doesn't mean the walls aren't bouncy
What would that digit be on a first gen Pentium?
this is a left handed sig
And if you take the digit placements (2 and 6), the difference from 0 (the first) and 2 is 2, and the difference from 2 and 6 is 4. If you invert them you get 42. Coincidence?
The twelfth letter of "Who gives a fsck?" is a "c".
There is no such "SET". Set theory creates sets by applying axiomatised procedures to known sets (the axioms include a starting point too). You cannot describe the above class of numbers using set theory. Therefore all bets are off when it comes to applying traditional set operations to that class. (such as taking the least element)
Search for "Zermalo Frankel Set Theory" for more info.
FatPhil
Also FatPhil on SoylentNews, id 863
The interesting thing about this calculation is that it did *not* give all the digits up to the quadrillionth digit. The algorithm used really computes only the Nth binary digit. The algorithm is based on a formula for Pi that was found using one of the "10 algorithms of the 20th century". This algorithm (sorry I can't think of the exact name at the moment) is used to find relations between real numbers. They used it to find a relation between Pi and certain fast-to-compute numbers.
Good one. a - b is zero, so you can't divide that out of the equation.
This guy's making a name for himself. I hope some good samaritan keeps him away from synagogues and power drills.
The author of the essay you're linking to at teleport.com (John T. Boatwright) has been making a fool of himself for a long time on USENET. My favorite idea of his was when he claimed through Biblical analysis that God specifically prophesized ICBM technology. It's on his web page somewhere.
Circles are impossible in any number of dimensions other than 2.
Alrighty math cadets!!
PI is random and this has been supposedly *proven* right? Ok simple test, taken any two given digets in the series and you should be able to find everything from 00 up to 99 right? ? WELL GUESS WHAT?!!! I GOT A VISION FROM GOD TODAY AND HE DIDNT PUT IN ANY 00's. Guess why? TO FUCK WITH MATH PEOPLE WHO TRY TO UnDERSTAND HIS MIND. IT PISSES HIM OFF Ya'LL KNOW. Besides if there is no remainer afer ya do'it twice, how does ya'all reckon one could go on? It means you found the last number dumbass. SIMPLE DIVISION from 11th grade advanced math class.
...
Ok pundits, I suppose you went and cheated instead of doing PI by hand? Well guess what? They're calcs are all wrong, you have to calc it yourself. Second of all--if you still get those pesky 00's yourself then do this: make a fraction
then a sphere is just a special name to save us from having to write: "the three demensional circle"
Humans are slow, innaccurate, and brilliant; computers are fast, acurrate, and dumb; together they are unbeatable
So pi doesn't have to contain itself, although it does contain approximations of itself. You will find a 3, 3.14, 3.142, 3.1416, etc....
roni
I think its about time PI was dropped and we started studying Eulers constant in as much detail as we know little about it and is as if not more important. This isnt e by the way its lim n->00 (1+1/2+....+1/n - log n)
Oh, I'm sure there'll be an option. But then, I'm the type that considers goatse.cx tricks to be the lowest form of trolling, so I wouldn't particularly care.
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So how does one go about verifying this? Wouldn't they have to reproduce it? Since Pi is non-repeating, non-terminating, how else could you do it? IF you had to verify it, couldn't you just go one digit more and thus steal the thunder of anyone?
http://www.popularculturegaming.com -- my blog about the culture of videogame players
Well, I can die a happy man now.
------------
CitizenC
I remember a math site on here that proved formulas such as 0=1. It was in someone's sig. If anyone knows of it can you post or email. I believe it was called "Math Tricks That Will Stump High School Teachers" or something to that effect
i have misplaced my signature.
This story, SOMETHING ELSE TO THINK OF regarding the P vs, NP problem is more important than the Pi story by the degree of n. I advise you all to review it. Also, if you're inclined to put in the time, you could win $1,000,000.
DAILY ROTATION
It is written in the Bible that Pi equals 3.147. Anyone who claims otherwise is under the influence of Satan. This is from Laws 2:22.3
And lo saith the LORD, the ratio of the breadth of the circle to its circumference is inversely three leagues and one hundred two score and seven inches. And the people of Israel were well pleased by this.
There is my proof. See that you obey the commands of the LORD.
Sincerely,
Bob Jones III
-Legion
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.
----
ADVENTURERS! - ANTIHERO FOR HIRE - CARDMASTER CONFLICT
I'll give you the right answer here. A convergent sequence is an infinite list of numbers that gets arbitrarily closer together, ie 1/n, this gets as close as you want it to to zero. Similairly with the digits of pie, if you create a sequence with the first term being 3, second 3.1, 3.14,.... and keep going you get a converging sequence towards pie. Can I recommend Spivaks book, "Calculus", by Publish or Perish. This has got everything being discussed re this message, the transcendental nature of pie and e, ifninite sums, the construction of the number line, etc. a couple of the other answers are wrong, they discuss summable sequences, which are an entirely different thing. They must be convergent, yes, but they also must converge to zero and converge quickly enough (1/n is not summable, but it does converege to zero). This is really off topic though, but if you want more help, I'd be more than willing if you emailed me.
Ok it is just a little strange when they spend all this time calculating pi. I mean Pi is Pi and it will never end so why try. You already know enough to figure out everything you ever wanted to know. QUICK where is my Geometry teacher she would die to see this, lol.
--Nick D.
inick@netacs.net
http://www.inick.net
http://www.lavoixceline.com
It's not normally my inclination to try to re-allocate other people's efforts. After all, as much as the world needs biomedical engineers, 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.
That said, some projects just scream out, "I have lots of energy and resources but I couldn't figure out anything useful to do with them." The web, for example. And possibly pi digit identification. So wouldn't it be nice to start a project to help herd people with that kind of muscle into projects they and everyone else would find more useful? Far be it from me to suggest a particular project that should have been diverted (for all I know this pi thing involved new frontiers in computational methods). But I'm sure there are lots of projects out there, in many fields, that haven't gotten done because nobody had both the interest and the resources.
I'd consider hosting such a project's web pages myself, I'm sure they would be extremely low-volume.
> 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.
1 reply beneath your current threshold.
As with most of these inane 42 facts: yes.
--
Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.
Win dain a lotica, en vai tu ri silota
If you take the distance from our sun to the nearest star, Alpha Centauri, as the radius for a circle, and use the first 50 digits of Pi to calculate the circumference of that circle, the result will be accurate to within *1 meter*.
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.
Win dain a lotica, en vai tu ri silota
I wouldn't think you'd need more than a hundred or so digits for that, even over solar-system distances.
Great games
take a look at what's called "p-adic numbers". that's pretty much what you are looking for...
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.
Win dain a lotica, en vai tu ri silota
The wording of the article isn't very precise. Did this he just calculate the quadrillionth binary digit, or did he compute all the digits up to and including the quadrillionth digit? The former would be interesting, the latter would be useful.
Slashdot monitor for your Mozilla sidebar or Active Desktop.
Aw, didn't anyone find the field of naughts and ones forming a perfect circle in base eleven yet?
"People are stupid."
There's much more information about this project on its home page at SFU. The guy behind it also has a page there.
M
GROGGS: alive and well and living in
..
Ok pundits of my previous post,...which was PURE and purposeful none sense. I
have been messing with PI for a few here, just somehow inspired myself..
Anyway if any math inclined person reads this please answer this --
have you seen this before, or did i just find it myself :
"PI cannot be represented by a fraction (integer over integer) beyond
the 314th digit accuracy place." [aside from bullshit like dividing by multiples of 10]
This is probably the most computationally expensive random single digit number generated ever.
Okay, so there might be plenty of numbers that cannot be described in a hundred words, but neither of them is the smallest one?
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Ahhh, this brings back memories of that cheasy Star Trek episode where the spirit of Jack the Ripper took over the Enerprize's computer. To buy some time, either Kirk or Spock ( I forget which) ordered the ship's computer to calculate the complete value of pie down to the last decimal to keep it occupied so they could come up with a plan and regroup. That REALLY pissed the spirit off!
I wonder what ASCI White could do if they let it crunch the equation for a while.- ---------------------
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"And may your days be long upon the earth."
That being that this is fun and interesting. Setting up the project, and watch it churn out the result must have been immensely satisfying. I once remember this math nut that I went to high school with. He had memorized pi to a thousand decimal places, and we'd see if we could trick him by changing a digit or so. Of course, he would be able to spot the error every time. This facination with a number that is in virtually every physical aspect of our lives is not surprising. Although, I wonder if we were to give 'e' a different name that it might have as much popularity.
If you take the second and the sixth decimal places, you get 42. Surely a more profound and significant result.
It may be true that a greater degree of accuracy than usual is required for spaceflight, but a quadrillion places? I really, really doubt that that type of precision has any practical use in spaceflight, given the current precision of the manufacturing methods used.
My own record for knowing pi is 3.14159265358979. This much is forever logged in long term memory. I was on a quest in 7th grade when my math teacher told me he would give me an A if I could recite from memory the first 100 digits of pi. At the time I thought it was a good Idea. Now, 11 years later, I wish I could take it all back.
Both proofs are not rigerous enough for the mathmatitions who have idle computers. They both SEEM to demonstrate that pi is MOST LIKELY irrational, but there is a SLIGHT CHANCE that it rationalizes itself. Personally, I think they passed the point where you just say "okay, you're right" a long time ago...
I am a bad speler. Please ignore speling meestakes in me poast.
I once made a proof using infinity-math and integration that all numbers tends to approch 0 as the time evolves, i.e.:
forall c in R: c->0 for t->infty
This is certainly usefull since maths, baking, accounting, etc. is uniquely bound to end as a 0.
The 0 in the end of the PI confirms this theory.
Dr. Ø, degree in chaotic maths, spoiling it in the webbiz
Eih bennek, eih blavek
There are often stories about someone calculating pi to some new nth degree of accuracy. I would really like to know, how do they calculate this? Anyone can give me pointers to some explanations?
;)
And note, I want just an overview - I'm not interested in checking the answer
Doesn't "The smallest number not describable in less than 100 words" fall under the category of the "busy beaver problem"? The Busy Beaver problem is this: "Find p(n), where n is a number of states, and p(n) is the most productive Turing machine of n states. Productive means that it will output a large number of '1's on a tape, and then terminate. It cannot enter an endless loop. If I recall correctly, this problem was prooven to be unsolvable by computers.
My other first post is car post.
In other news: Larry Ellison still not dead.
--
A feeling of having made the same mistake before: Deja Foobar
Original announce of the algorithm
A page with a lot of info/links
Colin Percival pageThe real info about the PiHex project (Probably in the natinal post article too, but I can't access it)
Cheers,
--fred
1 reply beneath your current threshold.
And I guessed it three years ago. Shouldn't I be able to file that with the USPTO or something?
---------------------------- DevNull - a discernible void in the province of Saskatchewan
Oh, ok, well... my wife wanted a three, but it's OK.
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
Ramanujan's formula
"The obvious mathematical breakthrough would be development of an easy way to factor large prime numbers." Bill Gates,
Just add a few digit, up to 40, for example, and you will never notice any measurable error even with the most complex differential equations.
Actually, calculating the Xth decimal place for transcendental numbers is partially usefull when considering the nature of randomness and what we mean by. On the face of it the distribution of the digits 0-9 appears to be random in PI (and trancendaental numbers). OTOH the quadrillionth DP might be a bit excessive ;)
IIRC modern interpretations of randomness are tightly linked with information - which is of interest to /. ers ;)
Or, as one Tolkein character might say...
Precioussssssss Pi!!!! Givessss meee digitssssssss of Pi!!!!!! Gollum!
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
A message from God? (really)
For some people, this kind of thing is where science and religion meet. Imagine looking for a message from God in the digits. If she wanted to put a message somewhere for all of us to see, the digits of pi would be a great place.
'Scuse me, but part of science is *discovering* things that are not yet known to mankind. Now work with me for a little longer: how can you set a goal in the good ole engineering approach, if you are deep in uncharted territory? I think that if mankind never did pure scientific research, we would never have come out of our caves!
How to make a sig
without having an idea
Yah sorry should have put some backing on that one, and well should have even got the quote right...
"Only 47 decimal digits of pi would be sufficently precises to inscribe a circle around the visable universe that dosent deviate from perfect circularity by more then then the distance acrost one proton"
The Quote is from here
See this quote 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.
http://www.urbanlegends.com/le gal /pi_indiana.html
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.
Gamingmuseum.com: Give your 3D accelerator a rest.
can someone tell me the formula used to figure you Pi????
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.
--
Well, here's a simple way to remember it to 6 d.p.:
But beware the tactical misspelling at the end. :)
GROGGS: alive and well and living in
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....
if someone posted a quadrillion digits of pi to slashdot (must be a friggin karma whore) would slashdot collapse miserably? the guy'd have to be on a pretty fat pipe to post something that big, eh? christ, he'd have to be inside va linux on a terminal to connected to the machine and...
never mind ^^;;
--
Peace,
Lord Omlette
ICQ# 77863057
[o]_O
Why? Pi is believed to be effectively random, so anything could be found if you use enough digits. It's like finding clues to the author of Shakespear in his works - it could be that it was put there delibertly, but it's more likely the human mind finding patterns where there are none.
You know what that sounds good, but I dont even think it will be right... If you write out a very large number in binary their is very little chance that the zero's and ones's used will be anywhere near or even close to 50% each.
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.
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AAHHHHHH OH MY GOD WE'RE OFF COURSE BY A METER!!! - super intelligent microbes in their tiny spaceship
Someone you trust is one of us.
Wow. Wondered why the National Post and canada.com were down this a.m.. Now I know. I'm part of the online newspaper network that's currently enjoying the wonderful interest you folks are expressing in the National Post article. (Not posting the link to MY newspaper site tho!) Any hot tips I can pass along to the techies? I let 'em know... probably slamming IP's shut as we speak. I'd already suggested the that *nix was the way to go. (Heh-heh.) R.
Beta only seems to work for Google. Such a shame.
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
Come on, the quadrillionth binary digit of pi turns out to be a zero? I'd be much more impressed if it turned out to be, say, three.
Ok, what's the significance of knowing pi to this kind of accuracy? What actual use is pi to the quadrillionth accuracy?
Steve's Computer Service, Hobbs, NM
I could've sworned it would be eight.
Aside from idle curiosity, and the wow-aren't-we-clever factor, what use is this knowledge?
Much less than a meter, actually. The nearest star to our sun (I thought it was Proxima Centauri, not Alpha) is something like 4 light years away.
4 light years=3.7842e16 m
C=2*pi*r
so differential C with respect to pi=2*r*d(pi)
If we take d(pi) to be 1e-49 (50 total digits of precision), dC = 7.5684e-33 m. So 50 digits of pi gets you about 10^-32 meter of precision at 4 light years. For reference, a proton is about 2.4e-15 m across. Any calculation of pi beyond a few dozen digits is purely academic, but it's fun to see how far we can go.
Bugrit! Millenium hand and shrimp!
"There will never be a use for group theory"
Go ask your physicist friends whether they could do without group theory.
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
Sorry the page is in french, but the math language is universal, isn't it ?
Somme pretty cool formulas
"The obvious mathematical breakthrough would be development of an easy way to factor large prime numbers." Bill Gates,