# Pi enthusiast calculates it to ten trillion digits

##### October 20, 2011 by Bob Yirka report

(PhysOrg.com) -- Shigeru Kondo is a seriously committed guy. Ever since discovering he had an interest in calculating pi (aka π) back in his college days, he’s been following the results achieved by others using massive supercomputers. Now, in his late 50's, with some help from Northwestern University grad school student Alexander Yee, he’s succeeded in calculating pi to ten trillion digits; on a home built PC yet.

Pi, the mathematical constant that describes the ratio of a circle’s circumference to its diameter, is generally rounded off to just two places, bringing it to 3.14. Believed to have been first described by Archimedes way back in the 3rd century BC, the ratio is used in all sorts of mathematical computations, not the least of which is in figuring out the area of a circle. But because pi is an irrational number, it’s value cannot be written as an fraction which means when written as a decimal approximation, it’s numbers go on infinitely, and perhaps more importantly, never repeat.

For hundreds of years, pi has held fascination for mathematicians, scientists, philosophers and even regular run of the mill people. Why this is so is hard to say, and so too is the seemingly endless progression of people that have set before themselves the task of calculating its digits. In spite of that, it’s possible that none has ever been so obsessed as Kondo. He’s spent the better part of a year with the singular task of finding the ten trillionth digit, and of course all those past the five trillionth and one digit leading up to the ten trillionth, since he found the five trillionth digit just last year.

Finding the value of pi to 10 trillion digits requires performing a lot of calculations (using software written by Yee), so many in fact, that Kondo had to add a lot more hard drive space than you’d find on your average PC. Forty eight terabytes to be exact. So intense was the computation that the computer alone caused the temperature in the room to hold steady at 104° F.

Also, it’s not as easy to keep a custom built super-sized PC going full steam ahead twenty four hours day for months on end, as it might seem. Hard drive failures and the threat of power disruption from the earthquake in Japan back in March threatened the project many times. And of course there was that power bill itself which ran to something close to \$400 a month as the computer ground away.

But in the end, it was Kondo’s persistence that paid off. For his efforts he will be forever known (in the annals of science, and probably the Guinness Book of World Records) as the man who calculated the ten trillionth digit of . It’s 5.

Explore further: Supercomputers crack sixty-trillionth binary digit of Pi-squared

10/21/2011: The story has been updated.

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##### NameIsNotNick
5 / 5 (4) Oct 20, 2011
"Its 5"
No it's not, it's 4. Better run that calculation again!
##### NameIsNotNick
5 / 5 (4) Oct 20, 2011
No, wait. You're right. It's 5.
##### Jaeherys
3.5 / 5 (8) Oct 20, 2011
What's the point of calculating to the nth digit of pi? I don't understood peoples obsessions with pi.
##### NameIsNotNick
5 / 5 (2) Oct 20, 2011
What's the point of calculating to the nth digit of pi? I don't understood peoples obsessions with pi.

I suppose it's a hobby. It would be interesting if the sequence did eventually repeat... Why pi? because it's a very important irrational constant.
##### Jaeherys
5 / 5 (1) Oct 20, 2011
Yea supposing it's a hobby is a good enough reason for me. It seems like a waste of time to me but there's nothing wrong about doing it so why not; it's better than watching TV (unless it's the discovery channel :P).
##### Isaacsname
5 / 5 (1) Oct 20, 2011
That is a big pi ..o,O

I wonder if he managed to find anything like Feynman's points ?

##### VitalStatistic63
not rated yet Oct 20, 2011
Is anyone game to call him on it and say he's wrong, it's not 5? With proof?
##### antialias_physorg
5 / 5 (7) Oct 20, 2011
What's the point of calculating to the nth digit of pi?

Statistical analyses of the digits (and subsequences) in pi might be interesting. Is there a 'bias' to math (which might hint at an artificial universe)? If you want to go all strange one might even look at unusual clusters of digits (i.e. 'hidden messages' like in "Contact").

Ther might also be some value for crypto-algorithms based on transcendental numbers like pi or e.
##### Jaeherys
not rated yet Oct 20, 2011
@antialias
Now *those* are some interesting points! Could it also be possible there are a finite number of digits of pi? I know it is supposed to be infinite but nonetheless is it even possible?

If it somehow did turn out to be finite what would that mean for math?
##### LVT
2.1 / 5 (12) Oct 20, 2011
If the Planck distance has anything to it then pi has a limit to it's NEEDED accuracy.
##### F111F
2.1 / 5 (7) Oct 20, 2011
Pi repeats every 10 trillion numbers...go ahead, prove me wrong... LOL.
##### CHollman82
1.4 / 5 (11) Oct 20, 2011
What's the point of calculating to the nth digit of pi? I don't understood peoples obsessions with pi.

It's an enigma, people doubt that it actually doesn't end or repeat...
##### antialias_physorg
5 / 5 (9) Oct 20, 2011
Could it also be possible there are a finite number of digits of pi?

Pi has been proven to be transcendental by the Lindeman-Weierstrass theorem (no, don't ask me how. I just went to the wikipedia entry and didn't take the time to go through the math - and doubt I'd get very far if I tried).

All transcendental numbers are irrational - which means they cannot be expressed as a ratio of a/b (where a and b are integers). Any number with finite digits is rational (as well as some with infinite digits). Pi, being an irrational number, therefore must have an infinite number of digits.

One interesting aspect:
It is not entirely known whether the distribution of digits (in differing number systems) of pi is normal (i.e. whether all digits occur with the same frequency or not). For base 2 this does seem to be the case.
##### El_Nose
5 / 5 (6) Oct 20, 2011

-- this story is a few days old -- try slashdot.com sometime where this was addressed -- i am basically repeating their answer.

It helps set benchmarks for super computers. You calculate all of and including the nth digit of pi, then when the next generation of supercomputers comes out that can do this calculation in a few days they run the test to verify that everything seems to be in order.
##### tjwied
4.5 / 5 (2) Oct 20, 2011
Why pi? Good question, we should be concerned with tau! Tau = 2pi! Pi just represents a proportion of an irrational constant. it's as arbitrary for us to use pi (in the form 3.14...) as it would be for us to use tau (6.28...).
##### LVT
1 / 5 (3) Oct 20, 2011
I'd have thought using "slice" i.e. pi/4 would be more useful as it comes in the range 0..1

So 8slice*r = circumference

##### SincerelyTwo
not rated yet Oct 20, 2011
Is anyone game to call him on it and say he's wrong, it's not 5? With proof?

He just gave you the proof by exhaustion ... not exactly my favorite method, if I had a favorite method, but yeah. :)
##### Parsec
3.7 / 5 (3) Oct 20, 2011
If the Planck distance has anything to it then pi has a limit to it's NEEDED accuracy.

These 2 concepts have nothing to do with each other.
##### sherriffwoody
not rated yet Oct 20, 2011
There are some students in china who did a similar calculation on pi some months ago. They managed to calculate pi, on a home computer - modified a little of course - in 40-50 hours (I'd have to relocate the article to get an accurate timframe), to 5 trillion places. Sounds like their algorithm or machine was a lot faster than this guys.
##### albenza
1 / 5 (2) Oct 20, 2011
Seems like a waste of good calculating power. I mean, when will anyone, ever, have a need to know? (Keyword here is "NEED").

Hope he is happy with the result though. (Now use that power on something productive. :)
##### VitalStatistic63
not rated yet Oct 20, 2011
There are some students in china who did a similar calculation on pi some months ago. They managed to calculate pi, on a home computer - modified a little of course - in 40-50 hours (I'd have to relocate the article to get an accurate timframe), to 5 trillion places. Sounds like their algorithm or machine was a lot faster than this guys.

Not necessarily. I have had a passing interest in pi since high school. The formula given to us then was

pi/2 = (2n/2n-1 x 2n/2n 1) ... (for n=1:infinity)
so = (2/1 x 2/3) x (4/3 x 4/5) x (...)

If you write up a quick program or spreadsheet with this formula you can readily see that each extra digit of precision takes significantly longer than the previous one.

There are a few methods that I know of to calculate pi and probably many more I don't know, so theirs is probably way more efficient than mine. But I'll bet it still runs like molasses when you get up to the trillionth digit.
##### antialias_physorg
1 / 5 (1) Oct 20, 2011
Seems like a waste of good calculating power. I mean, when will anyone, ever, have a need to know? (Keyword here is "NEED").

Hope he is happy with the result though. (Now use that power on something productive. :)

...says the man whose CPU sits 99% idle most of the time.
##### Silverhill
2 / 5 (1) Oct 20, 2011
antialias:
If you want to go all strange one might even look at unusual clusters of digits (i.e. 'hidden messages' like in "Contact").
If the digits of pi (or any irrational number) are truly random, then *any* "diagram" will eventually be discernible in one string or another. "Messages" will also exist, encoded in ASCII (and EBCDIC, and base64, and ROT13, and all other encodings). Moreover, all manner of things (FTL ship designs, future stock-market tips, etc.) will occur innumerable times in the stream of digits.
Now all we need is God's Own Computer to evaluate the digits, and to search the strings for accidental (or deliberate?!) meanings....
##### YummyFur
1 / 5 (2) Oct 20, 2011
5.

nice.
##### gwrede
2 / 5 (4) Oct 20, 2011
Seems like a waste of good calculating power. I mean, when will anyone, ever, have a need to know? (Keyword here is "NEED").

Hope he is happy with the result though. (Now use that power on something productive. :)
What is a waste of computing power is using computers for gossip or porn.
##### RayInLv
not rated yet Oct 20, 2011
So he calculated it. 10 Trillion Digits... At 10cpi That takes 1 Trillion inches to display. That's only 15,782,828.282828.... Miles of characters or roughly 330 round Trips to the Moon.

Big number..... But that other number is 10^-35th quite a bit smaller.
##### sherriffwoody
not rated yet Oct 20, 2011
Not necessarily. I have had a passing interest in pi since high school. The formula given to us then was

pi/2 = (2n/2n-1 x 2n/2n 1) ... (for n=1:infinity)
so = (2/1 x 2/3) x (4/3 x 4/5) x (...)

If you write up a quick program or spreadsheet with this formula you can readily see that each extra digit of precision takes significantly longer than the previous one.

There are a few methods that I know of to calculate pi and probably many more I don't know, so theirs is probably way more efficient than mine. But I'll bet it still runs like molasses when you get up to the trillionth digit.

I relise this, I've written a program to calculate pi to n myself and the difference on my laptop between 5000 decimal places and 10000 decimal places is larger double. But a few days to five trillion compared to months and months to get 10 trillion?
##### Grizzled
1 / 5 (1) Oct 20, 2011
Pi repeats every 10 trillion numbers...go ahead, prove me wrong... LOL.

PROVE you wrong??? Hmm, you may be interested to know that you HAVE been proved wrong ... just about the time of Archimedes at least. Probably even earlier. Time to catch up man :-)
##### Grizzled
1 / 5 (1) Oct 20, 2011
Looking through some of the posts here, it looks like there is a bit of confusion over the nature of pi (as well as "e"and a lot of others).

Those numbers are not only irrational (meaning they can't be represented as n/m fraction for any integer n and m values), they are also transcendental, meaning that they cannot be the root of any algebraic equation (polinomial).

The last statement is a LOT stronger than the first - all transcendental numbers are of course irrational. The reverse isn't true.
##### Grizzled
1 / 5 (1) Oct 20, 2011
Is anyone game to call him on it and say he's wrong, it's not 5? With proof?

Nah. Not after you added the last two words in your challenge. You see, you can't have a proof of something that isn't so.
##### altino
not rated yet Oct 20, 2011
From infinity is born infinity.
When infinity is taken out of infinity,
only infinity is left over.
##### Grizzled
1 / 5 (2) Oct 20, 2011
And finally, to answer several posters who asked "What the heck for?" - Someone else already mentioned supercomputers. And this is true.

Stop to think for a moment - suppose you've designed and built the latest and greatest ... how do you know it works? Not just works but works correctly? Even when pushed to the exremes of its capabilities?

Well, one way to try it is to desing (using it) an all-new thermonuclear reactor and see if it runs as expected...or not. A much cheaper alternative to examining a multi-kilometer crater might be checking how well it calculates the tenths (or hundredth) digit of pi.

Don't you agree?
##### altino
1 / 5 (3) Oct 20, 2011
Pi does not equal 3.141592...

Al = (14 ROOT 2) ÷ 4
= 3.1464466.....

:)

##### Humpty
1 / 5 (5) Oct 20, 2011
I just calculated it to the 11 trillionth number.
##### _etabeta_
1 / 5 (3) Oct 20, 2011
What a tremendous waste of time, money and effort.
##### Grizzled
1 / 5 (2) Oct 20, 2011
I just calculated it to the 11 trillionth number.

And what do the previous 1 trillion say? Just curious. You know, even if you limit yourself to 16 bits (how's that for antiquity?) you can still pack about 3 characters per two digits if you omit some less popular ones.

That makes it roughly 1.5 trillion characters you have just discovered. Wow. No, on second thoughts it's WOW!!! Do tell us - what does all that wisdom say?
##### LongPurple
not rated yet Oct 21, 2011
@ antialias
"If you want to go all strange one might even look at unusual clusters of digits (i.e. 'hidden messages' like in "Contact").

I'm wondering if there was any search for something like those pages upon pages of 1's and 0's in "Contact". I assume no pattern recognition was part of the project, just straight calculation.
##### plasticpower
not rated yet Oct 21, 2011
...You calculate all of and including the nth digit of pi, then when the next generation of supercomputers comes out that can do this calculation in a few days they run the test to verify that everything seems to be in order.

Thank you. That actually makes a lot of sense.
##### spaceagesoup
5 / 5 (2) Oct 21, 2011
How is it a tremendous waste of time and energy? Most people in the world couldn't even tell you what the pi relationship is, let alone contribute anything to its interesting and relevant mathematics.

The pi ratio is a powerful and prevalent natural institution. The better we understand it, the more we (probably) will find uses in the physical world around us.

And working on pi is a damn site better than all the non-contributors who whinge daily on this site, or the scores of others whose more intellectual pursuits amount to nuking their microwave dinners, flicking on the TV and screaming at the kids.
##### antialias_physorg
5 / 5 (2) Oct 21, 2011
If the digits of pi (or any irrational number) are truly random, then *any* "diagram" will eventually be discernible in one string or another.

Yes, but one can determine how likely it is that some sequence occurs.

Example: The sequence 9999 is to be expected to occur once within the first 10000 digits of pi (in base 10). but if it occurs 50 times in the frst 10000 digits instead of just once then the statistics are skewed to the point where there is only a very small likelyhood that this is a random fluke (though that likelyhood never reaches zero. We must always expect some false positives). If some 'complex message' (e.g. an inordinately long sequence of zeroes and ones) occurs way earlier than expected then we should take a look.

Though I really don't expect any such message to be in there.
##### Ricochet
not rated yet Oct 21, 2011
I would think any kind of pattern-matching software would take much longer to trudge through all those numbers to find anything at all.
##### antialias_physorg
not rated yet Oct 21, 2011
I would think any kind of pattern-matching software would take much longer to trudge through all those numbers to find anything at all.

Depends on what kind of patterns you're looking for. Simply looking for consecutive numbers that are 'unlikely' is pretty easy to do and would only take a couple of hours. Though depending on where you set your threshold for 'unlikely' and how many types of patterns you're looking for the amount of time needed will scale up.

E.g. a simple check for long swathes of unlikely ones and zeroes would take a couple of minutes.

##### Skultch
4 / 5 (1) Oct 21, 2011
If the Planck distance has anything to it then pi has a limit to it's NEEDED accuracy.

These 2 concepts have nothing to do with each other.

Why? The perfectness of a circle can be described as its level of detail; its resolution, no? How perfect can a circle be could also be related to the question: how small can objects be? Right? Or does geometry lose its meaning at sub-atomic volumes?
##### antialias_physorg
not rated yet Oct 21, 2011
Why?

One is an abstract notion (pi) and the other is a physical approximation (real circles).

There are many uses of pi which have nothing to do with circles ( e.g. in number theory, analysis, ... )

The 'needed' accuracy is a matter of what you want to do with it. For certain number crunching tasks the more digits you have the better.
##### Skultch
not rated yet Oct 21, 2011
Are you saying that since there can never be a "perfect" circle, the search for "how perfect can a circle be in reality" is a meaningless question or at least, a question that cannot be answered?
##### Ricochet
5 / 5 (1) Oct 21, 2011
I'd say drawing a perfect circle would be a matter of figuring out how many digits of pi must be used to represent the appropriate resolution of the medium.
##### YummyFur
1 / 5 (2) Oct 21, 2011
Hang on, if the sequence is random and non repeating then should we not eventually find Shakespeare's complete unabridged works including any obscure notes or shopping lists, somehow encoded in the string. Best of all there would be no exploiting of monkeys. I say we push on to at least one thousand trillion.
##### Deesky
5 / 5 (2) Oct 21, 2011
Are you saying that since there can never be a "perfect" circle, the search for "how perfect can a circle be in reality" is a meaningless question or at least, a question that cannot be answered?

I think you're too hung up on physical measurement of physically drawn circles. All circles are 'perfect', as is any other geometric shape as defined mathematically. There is no need to equate a mathematical concept with the physical world constrained by the limits of measurement.
##### antialias_physorg
not rated yet Oct 21, 2011
Hang on, if the sequence is random and non repeating then should we not eventually find Shakespeare's complete unabridged works including any obscure notes or shopping lists, somehow encoded in the string

Yes we would (if the numbers are truly random - something not yet proven!)...though the likelyhood that these types of lists/works of art occur at digit numbers far, far, FAR exceeding the number of atoms in the universe is extremely high.

Or conversely: Finding any one of these in a list of digits - with each atom in the universe used to store one digit - is incredibly unlikley.
##### Skultch
not rated yet Oct 21, 2011
Hypothetical: We observe a (relatively) stationary string of particles configured in the shape of a circle. Each particle is 1.616199(97)10^(neg)35 meters apart. Can we add particles to the circle and it is still a 'perfect' circle?

(weird; Pi is in the formula for Planck time, but not length hmmm)
##### Jeddy_Mctedder
1.7 / 5 (6) Oct 22, 2011
i would like to see the digits of pie mapped out as a mandlebrot fractal. and watch someone on acid watching them. that is what this has become. a long acid trip some people call mathematics, other people call pointless and ignore.
##### Lazernugget
not rated yet Oct 22, 2011
I just calculated it to the 11 trillionth number.

Really? How? You must have a lot of computer space. lol.
##### antialias_physorg
not rated yet Oct 22, 2011
Can we add particles to the circle and it is still a 'perfect' circle?

Circles are an abstract mathematical concept. It is the set of all points equidistant from a geometrical point. What does this have to do with particles?
##### Grizzled
1.8 / 5 (4) Oct 22, 2011
And yet another twist on the same subect of infinite sequence of non-repeting digits is that it is a certainty, not just a virtual certainty but a true certainty that at some X-trillionth digit there is a plain ASCII text which says: "Hi, I'm the pi number talking to you. Yes YOU. Don't believe me? Ok, check the Y-trillionth digit text." --- And, when you do, the text at that position says: "See? Told you so!"

How's that for predictive power?
##### S_Bilderback
1 / 5 (3) Oct 22, 2011
Numerically, in base pi it's a rational number ... but then the rest of the universe is irrational. (hidden truth?)
##### S_Bilderback
2 / 5 (4) Oct 22, 2011
In the real world pi does resolve. Every circle has a finite number of quantum points, the digits of pi cannot exceed the number of quantum units of the circle. It is when the human mind perceives an infinite number of points or units is when pi becomes irrational.

Remember, infinity isn't empirical or a number - it's a human perception of the absents of a limit.
##### Skultch
not rated yet Oct 23, 2011
Can we add particles to the circle and it is still a 'perfect' circle?

Circles are an abstract mathematical concept. It is the set of all points equidistant from a geometrical point. What does this have to do with particles?

Circles have something to do with particles when we put particles in the shape of a circle. Get your head out of the textbook. It's called a thought experiment, and you aren't even trying.
##### Skultch
not rated yet Oct 23, 2011
Alright, that was a tad aggressive. Maybe you aren't seeing where I'm going. It's hard to tell when it isn't acknowledged. What I'm getting at, is the question: is there a granularity to spacetime? If the matter can only affect it down to the Planck scale, and the equation for Planck time includes the term Pi, then why can't we say that spacetime is granular to the resolution of the Planck distance? Couldn't that put at least a significance limit to the accuracy of Pi?
##### Grizzled
2.3 / 5 (3) Oct 23, 2011
Skultch, as others were trying to tell you before - "circle" is an abstract mathematical concept. You CAN'T place your particles in a circle. Not even as a thought experiment.

P.S. And yes, you are coming across as exceedingly aggressive. That's not a good sign in a suposedly scientific discussion. Not even as a thought experiment :-)
##### Grizzled
1 / 5 (2) Oct 23, 2011
Numerically, in base pi it's a rational number ... but then the rest of the universe is irrational. (hidden truth?)

Not all bases are created equal. If you delve into the fundamentals of math.analysis, you will discover that it depends on the definition of numerical axis whic in turn depends on the properties of the... rational numbers! If you try to redefine everything starting from scratch and use irrational base... Ummm, the very first question becomes - irrational in what sense? You haven't even defined what "irrational" means yet. Never mind any of its critically important properties. Like what kind of a set do those numbers form - is it a ring for instance? Speaking of irrational universe in this context is a little bit immature.... unless of course you meant it as a hint on what you think of the Universe at large :-)
##### Skultch
not rated yet Oct 23, 2011
Ok, I got annoyed by others not acknowledging my point, so I'll be fair and acknowledge yours.

I understand what an abstract math concept is. (Calc-1 was stupidly easy for me, albeit long ago, which is why I'm asking you guys this) What you are really saying, without actually saying it, is that perfection is unattainable. My question goes right to the heart of *why* a circle can only be abstract. The only reason that a material circle cannot be achieved is practical. I'm trying to transcend math here; to attempt to link it to the material.

There. It's exceedingly frustrating when people just echo a definition of a concept without supporting it with an explanation of "why," like what you guys are doing with your circle definition. Just repeating it does no one any good.
##### Skultch
not rated yet Oct 23, 2011
Skultch, as others were trying to tell you before - "circle" is an abstract mathematical concept.
yes, telling. not explaining.

You CAN'T place your particles in a circle. Not even as a thought experiment.

And yes, you are coming across as exceedingly aggressive. That's not a good sign in a suposedly scientific discussion

Supposedly being the key word there. We aren't actually having a scientific discussion, or any kind of discussion. Yet.
##### Deesky
5 / 5 (1) Oct 23, 2011
What I'm getting at, is the question: is there a granularity to spacetime?

Einstein would say no. Quantum Mechanics would beg to differ.

I'm trying to transcend math here

I doubt that is possible.

You confuse the issue by bringing up the mathematical concept of a perfect circle with observed reality. Your basic question appears to be as in the first quote of this post. And the answer is, as I've alluded to, that no one knows for sure.

There are arguments for both views, but it seems that the QM view is likely correct (ie, spacetime is discrete/granular at the finest level).
##### Blakut
not rated yet Oct 23, 2011
Hypothetical: We observe a (relatively) stationary string of particles configured in the shape of a circle. Each particle is 1.616199(97)10^(neg)35 meters apart. Can we add particles to the circle and it is still a 'perfect' circle?

(weird; Pi is in the formula for Planck time, but not length hmmm)

Yes you can. You'll get a slightly bigger circle, keeping the distance between the particles the same. You can have circles of all sizes, provided you have enough particles.
##### 137
not rated yet Oct 24, 2011
would pi have some sort of link to how different dimensions are formed ,i don't really think I'm educated enough to comment about this.
##### Skultch
not rated yet Oct 24, 2011
Thank you to those who took a couple minutes to try to understand my questions. I'm sorry for the aggression and the lack of understanding needed to ask the questions correctly. I don't know what was going through my head to expect people to help me when I behave like that.

Blakut, I should have said that we couldn't increase the diameter for that scenario, which I realize is practically ridiculous. There's no way they could be that close to each other and not interact.

I guess I should be asking: 1.) if Pi is (or could be) a fundamental constant needed to describe reality? and 2.) then how accurate could we theoretically get before any further accuracy is pointless?
##### thefurlong
1.8 / 5 (5) Oct 24, 2011
Hang on, if the sequence is random and non repeating then should we not eventually find Shakespeare's complete unabridged works including any obscure notes or shopping lists, somehow encoded in the string.
-YummyFur

That isn't necessarily true. Nobody has actually proven PI to have this property. It is a popular misconception.

A variable can be random without having a normal distribution. In fact, the distribution can be quite irregular, and some sequences can completely preclude specific sequences. As a trivial example, consider a rational number whose digits only include 1 and 0, but the sequence is otherwise unpredictable (random). Then, obviously, the sequence 222 will never appear.
##### Deesky
5 / 5 (2) Oct 24, 2011
1.) if Pi is (or could be) a fundamental constant needed to describe reality?

While pi is a mathematical constant, it is not a physical constant and therefore is no more or less important than any other mathematical constant in describing reality.

2.) then how accurate could we theoretically get before any further accuracy is pointless?

I think we've reached that point long ago. No one uses these ridiculously long sequences of computed digits in any practical way to solve everyday or even non-everyday problems. I would say that the interest in increasing accuracy is of some esoteric interest in certain fields of mathematics (and with computer geeks!), but that's about it.
##### albenza
not rated yet Oct 25, 2011
Seems like a waste of good calculating power. I mean, when will anyone, ever, have a need to know? (Keyword here is "NEED").

Hope he is happy with the result though. (Now use that power on something productive. :)
What is a waste of computing power is using computers for gossip or porn.

Nope. It's working for the LHC when not used for compiling or encoding. ;)
##### hush1
1 / 5 (2) Nov 08, 2011
The deviation between curvature to the arbitrarily defined (depending on users needs)straight or flat or line is pi.

So long the unprovable properties of the arbitrarily defined remain arbitrary, so long pi will remain transcendental.
##### hush1
1 / 5 (1) Nov 08, 2011
The above is where, in the broadest geometrical sense, pi comes from.

In the broadest numerical sense pi comes from all indistinguishable points. Points with labels are lines or distinguishable.