3.14. . Pi is an , minimal - meaning that every number exists somewhere in pi, converted into ASCII text, in that latenite string digits is the name at every pe
x
Click to expand

3.14

Pi is an , minimal - meaning that
every number exists somewhere in
pi, converted into ASCII text, in that latenite
string digits is the name at every persin we will ever
love. the date, time, and manner at your death, and the
sasl. vers' all the great quasar: rats as the universe.
tzoztm' ted into a bitmap, in that infinite string
at digits is a representation the first thing
we saw on this earth. the last thing we will see before
an lite leaves yen, and all the moments, memento HE and
mundane. that will wear between paints.
All ' : m that has ever existed er will ever exist, the
DNA at ever; being in the universe.
all in the rails at a
and a diameter.
...
  • Recommend tagsx
+612
Views: 33995
Favorited: 174
Submitted: 07/25/2013
Share On Facebook
Add to favorites Subscribe to antzell submit to reddit

Comments(214):

[ 214 comments ]
What do you think? Give us your opinion. Anonymous comments allowed.
#23 - damonisgay (07/26/2013) [-]
But it still can't tell why kids love the taste of cinnamon toast crunch
#28 to #23 - John Cena (07/26/2013) [-]
it would though.
#125 - mrwalkerfour ONLINE (07/26/2013) [-]
so the meaning of life is like, pie
#130 to #125 - thewisedane (07/26/2013) [-]
What you did there.

I saw it.
#112 - lemmieh (07/26/2013) [-]
It's a pie!
#179 to #112 - meuk (07/26/2013) [-]
holy shet
User avatar #94 - wiredguy (07/26/2013) [-]
>have studied advanced maths
>reading comments
>the pain
>it's too great
This is actually wrong. I promise you.
There is no law to say that you will eventually come across an exact pattern. It is infinite, but it doesn't work like that at all. Infinite doesn't mean all-inclusive, it just means never ending (loosely). Think about 1/3, that's 0.333... which is "infinite", but you can't say the same thing for it as OP has about pi; since pi is infinite, but just like 1/3, not all-inclusive.
This isn't so much to do with sequences any more, as it is possibility. Maybe the best way to get this point across is to make a more relatable analogy.

Take a fair coin, with 0.5 chance to land on either heads or tails, with each flip.
Now, imagine flipping that coin ten times, and seeing that it comes out heads every time in a row. It's extremely unlikely, but not at all impossible, Derren Brown proved this, but it took him over 9 hours.
Now throw it a billion more times. There is still a minute possibility that every single throw will be heads. It technically has exactly the same possibility as any other sequence of a billion and ten flips, it just stands out to the human perception.
Now, since we can say this for ten, and a billion, and a trillion, and so on, we can say that with an infinite amount of flips, tails never has to come up. It almost definitely will in reality, but it doesn't have to by any stretch of mathematics.

The same idea applies to pi.
#107 to #94 - wyldek (07/26/2013) [-]
I'm pretty sure that as time go to infinity, the chance of anything with a nonzero probability happening approaches one.
User avatar #109 to #107 - wiredguy (07/26/2013) [-]
>approaches
Think about exactly what you just said.

And besides, per individual instance, the chance remains totally unchanging based upon the circumstances.
Common misconception, wins gambling houses a lot of money.
#111 to #109 - wyldek (07/26/2013) [-]
Yeah, approaches. So, as t ->infinity , P=1.

They're called limits, and they're the only way we can mathematically confirm ANYTHING about infinity.

Think about it this way, no matter how far you go, you're not finished. If something CAN happen, it WILL happen.

Saying that it's possible that they're ALL heads is completely disregarding the way infinity works. They can't ALL be heads because there are an infinite amount of them. There is no such thing as ALL of them.
User avatar #115 to #111 - wiredguy (07/26/2013) [-]
I know what a limit is.

And alright, fair enough. I phrased it badly, but my point holds. Here:
No matter how far into infinity you stretch, a tails never has to land.

You can't say "all will be heads", for the reason you listed. But you can say what I said, which was the point I spent the whole comment trying to get across, and probably failing miserably.

Besides, like I said.
If you flip a fair coin, the chance of it landing heads is 0.5.
If you flip it 4 times, the chance of all three being heads is a 0.0625, a sixteenth, or 0.5^4. But the chance of the fourth throw itself landing heads is still just 0.5. Since the chance of it going heads, heads, heads, tails is exactly the same as them all being heads. All of them being heads just appears more significant to humans.

If you flip the coin over and over for the infinite reaches of time, the chance of there being a tails in there somewhere approaches 1. But this has absolutely nothing to do with each individual throw, and in any measured amount of time during the infinity (a concept which is similar to an infinity itself) you can never say that there has to be a tails.

Again, I'm a student, no teacher.
I'm sure you know all of this perfectly well, and that I haven't explained it amply to enlighten you, even should you not have.
But oh well. It's all healthy thought.
User avatar #116 to #115 - wiredguy (07/26/2013) [-]
all four* being heads

Ah ***** .
You know what I meant.
#131 to #116 - John Cena (07/26/2013) [-]
what is the possibility of the coin not landing at all? factor that in to your fancy math
User avatar #132 to #131 - wiredguy (07/26/2013) [-]
I specifically stated that it was a fair coin with a 0.5 chance of landing on heads, and a 0.5 chance of landing on tails.

So the chance is 0, it has to land.
It's a hypothetical coin.
#143 to #132 - John Cena (07/26/2013) [-]
hypothetically the coin could be caught or just fly away, just because you proposed the hypothetical idea doesn't mean you are in direct control of its eventuality. your math has no place in the world of imagination, i would have imagined some one who had a degree in hard maths could tell any insolent electrician that maths is always fact.
#147 to #143 - RobsonT (07/26/2013) [-]
There's still plenty of time, go on... Do it...
#118 to #115 - wyldek (07/26/2013) [-]
Yeah, sure. If you break infinity into arbitrary segments, you won't have to find a tails in a segment. But if you break it into arbitrary segments each segment isn't infinite. You can't deal with infinity by dealing with segments of it, that defeats the entire point.

And since you agree that given infinite time, the chance of it landing tails does approach one, then even if you split infinity in an infinite amount of arbitrary segments, some of these segments must contain tails as well.

So for the same reason that in infinity there HAS to be a tails, there also has to be every possible combination of heads and tails.
#191 to #118 - ljetibo (07/26/2013) [-]
segmenting infinity into subsets is one of few ways you can deal with inf, i.e. for convergence of inf. sets you pick an arbitrary subset of the inf. set and check if that subset converges and then by some theorem (forgot whose) then the set converges uniformly.

anyhow, what wiredguy is saying is mostly correct. You can't expect any decimal number with randomly non-repeating digits to have the property of containing any finite permutation of digits.
I would like to point out that there exist such numbers, called normal numbers, that DO have their property. Normal numbers are numbers that when expanded in a base, if they obey expected limiting frequency, contain any and every finite pattern of numbers. Easiest constructed such number is actually pretty wide-spread. If you ever took IT class and dealt with binary numbers then you know that
0=0
1=1
10=2
11=3
100=4
if you just string those number together like: 0.1 10 11 100 101..... you get a normal number that means that number does whatever that poster says (alas only if you look at it in binary, if you take it as a decimal number (0-9) it is not a normal number anymore). Most, in fact I think all, of normal numbers were constructed "by hand".

HOWEVER I would also like to point out, especially to wiredguy, that although pi (sqrt(2) and some other) were never proven to be normal they are expected to have that property.

So it's wrong to say that "it's because pi is infinite and non-repeating" that is not why, and it is wrong to state that just because we're integrating to inf. probability of it happening has to be 1 (that is true for QM and has more to do with normalization of the wave equation then anything else, that's also why you're bound to find yourself made out of candy somewhere in the universe) but it's not wrong to say it is "expected" and you save yourself the wrath of mathematicians
(but in all seriousness wyldek you should read wiredguy again because his logic is less flawed then you think)
User avatar #194 to #191 - wiredguy (07/26/2013) [-]
Your approval makes me happier than I'd care to admit, hah, thank you.

And I'm picking up new information on these topics as I continue to read and comment.

One thing I don't get though, I think I mentioned in another comment.
From what I can glean from Wikipedia, I don't quite understand why normal numbers intrinsically contain every value at some point.
Like I said with the coin. If you construct a binary number by attributing 0 to heads, and 1 to tails, then flipping it fairly an infinite number of times, it makes a 2-normal number, doesn't it?
But like I said, a heads never technically has to come up. In which case, all sequences including a 0 would not appear in the number.

You sound far more educated than anyone else here, so rather than arguing, I'm just asking you exactly why that isn't right.
#196 to #194 - ljetibo (07/26/2013) [-]
educated, hah!

I'm not really "into" this topic as deep as you picture me to be but the main reason is because it's more like an approximation then a definite truth. You can use a Poisson's model to estimate the probability of n occurrences of an event (in this case the desired sequence of numbers) with rate r in number of trials t:
P(k) = (rt)^k/k! * e^(-rt)
and since you can see that we have a defined number r (mentioned above as the expectation frequency) for large enough k-s you apply Stirling formula and in the process you get a lot of (important) multiplicative stuff and your exp becomes something like:
exp(k-LT)
which when graphed (as an absolute because you can't have negative probabilities, so technically speaking what we're talking about here is probability density I think) looks like Gauss curve so when you integrate over large enough k you get 1.

but as I'm sure you'll pretty much notice that there's couple of problems here, first of all Stirling approx is....well....lacking, and Poisson process (aka complete permutation strings) is usually applied when there's no "memory" in the process like with the coin flipping, and this one obviously has one (the expectation frequency, albeit it is a little modeled to fit better with use of the r)

but alike with all thing numerically done, which is the only way to do this , sometimes you kind of give leeway to some things
and that's the reason why mathematicians hate physicist (too much freaking leeway)
#197 to #196 - ljetibo (07/26/2013) [-]
actually I made a boo-boo

after you get the stirling aprox you get:
e^-(k-LT)

otherwise it blows up....
User avatar #199 to #197 - wiredguy (07/26/2013) [-]
Blows up?
Now that sounds exciting
#200 to #199 - ljetibo (07/26/2013) [-]
I bet people here think only mythbusters blow things up
User avatar #198 to #196 - wiredguy (07/26/2013) [-]
In the time between typing my last comment, and reading your reply, the rum has hit me.
That's all you really need to know.

I'll try and figure all of that out tomorrow.
Maybe

Probably

Yeah. If I remember.
#206 to #198 - ljetibo (07/26/2013) [-]
actually I'll double post some **** here,
I went to wiki looking at the definition of normal number (what I listed above was what I remembered from a presentation held by one of the math staff professors trying to show e is a normal number via numerical analysis
we have this sciency presentations once a year on science week from students and profs about funny stuff you find in science, this one guy went to describe how people actually pick a seat in the bus and then connected that to google but that's not important here

just look at the definition of a normal number.
1) You pick some base and count how many digits b it contains (so for decimals it's 10, for binary it's 2 etc).
2) Then you take the number and turn it into a sequence (it's a set in which order matters).
3) Then you say that N is number of times a certain order of numbers appears in the first n series of digits.

now, if you know anything about probability you know that to calculate the probability of an event, you divide the number of outcomes that produce the event by the total number of outcomes.
(in the flip coin analogy you have 2 possible outcomes, tails and heads, and you only get 1 as a result of a toss, so it's 1/2 = 50%)
but lets say for a second we are dealing with probabilities of a continuous random variable in that case we have not the luxury of a finite set. Lets say a customer walked into a store, what would be the probability the customer spent 10min in there. Again lets start with the obvious: prob is #of wanted outcomes/#of possible outcomes
for us that is #of wanted outcomes = 1 (exactly 10min). But what is #of possible outcomes? Is it also possible the customer never exited the store? Yes, a ****** shot her, could it be 9.5min? 1.4? 1.3345624918392743804min? yes yes and yes...
you see #of possible outcomes in infinite, and that is why you have:
lim [t-->oo] (1/t) = 0
goddamn char count
#208 to #206 - ljetibo (07/26/2013) [-]
what the definition of a normal number is saying is:
lim [n-->oo] (N/n) = 1/b

so you see right away that the probability of finding N is not 0. Even worse it's stating that there can be more #of wanted outcomes in a watched part of sequence, even worse! because n is linearly going to zero N has to be a function that grows faster then n. That means that if lets say N would be a "to the power" function there would exists exact places where the re-occurrence are most likely to happen, and places where it would be 0, so for a polynomial function N you see that not only that the probability of finding that sequence is not 0! it also repeats itself on a regular basis (providing the polynomial order is high, even better a trigonometric function would work here, but I don't know what lim of it would be so I don't want to take it in)
User avatar #207 to #206 - wiredguy (07/26/2013) [-]
I understood all of that.
I'm very upset. I obviously haven't had enough booze yet.

What's the t for though? In the limity approaching infinity.
#209 to #207 - ljetibo (07/26/2013) [-]
t = time, because all of the times are allowed even the outcome when she never gets out that means t-->infinity

god damit it's friday night and my best company is half drunk math geek
**** me
#210 to #209 - wiredguy (07/27/2013) [-]
Time.
Makes sense.
v=d/t, haha. Good ol' times.

Aww, I'm hurt.
You're loving it really.

So what're you currently studying and where? If I can ask.
#211 to #210 - ljetibo (07/27/2013) [-]
yeah you know that I do ashamed

trying to finish my thesis for physics minor so I can enroll in the major physics studies (not sure about the terminology though, it's the 4th year of college). It's informatics and physics study "combined" something like Computational physics not sure how to translate it properly, in Croatia.
I've run into normal numbers a couple of times (the best pseudo random source generators, and they provide a neat little explanation for entropy)
#201 to #198 - ljetibo (07/26/2013) [-]
don't
you'll just get distracted then you will stop giving a **** about things that are not itching your brain RIGHT NOW (aka college) and be a dropout working in McDonalds getting judged by people because you work there (although they might not even have a job)
#127 to #94 - ROTFLcopter **User deleted account** (07/26/2013) [-]
I think you're forgetting the "non-repeating" part.
User avatar #129 to #127 - wiredguy (07/26/2013) [-]
Er, no. No I didn't.
User avatar #138 to #94 - seventh (07/26/2013) [-]
This guy is correct. I was waiting for a comment like this to show up because everyone above is incorrect, including OP.

Even a person with high school level statistics should be able to see the flaws in OP's picture.
#184 to #94 - John Cena (07/26/2013) [-]
Your 1/3 analogy does not apply here, since .3333 is a repeating decimal. Your coin analogy is also flawed. Each separate toss is 50/50, but if you tossed it exactly 2 times, your possible results would be TT, TH, HH, HT, so the odds of a specific outcome vary.

The same idea does not apply to pi.

High school AP Algebra does not count as "advanced maths" as you so call them.
User avatar #187 to #184 - wiredguy (07/26/2013) [-]
Actually, I'm lucky enough to be being school in England.
I'm referring to my Advanced Level maths class.

The third analogy was simply to rule out the idea that infinite=all-inclusive. It was a single part of my explanation as to why pi is similarly not necessarily all-inclusive, not the whole of it.

Um.
I have no idea exactly what you're trying to point out.
Pi randomly selects (as it were), a digit from 0-9. So there are 100 possible outcomes, the 2-digit numbers 00 through to 99, I won't list them for you.
The odds of a specific outcome never vary though. Even if you have heads three times in a row, the odds of the fourth throw remain 50/50. Each throw can be viewed independently.
#152 to #94 - John Cena (07/26/2013) [-]
i think the point is, is that since pi never goes into an infinite series of the same number(as far as we know) it will eventually provide any combinations of the numbers 0-9 somewhere in its infinite sequence
User avatar #169 to #152 - wiredguy (07/26/2013) [-]
That's the idea presented in the post, yeah.

But, just above your reply there's a pretty **** , but hopefully acceptable paragraph explaining why I'm pretty sure it's wrong.
The idea is technically up for debate, according to a short (biased) article I read after posting it, but I still hold strongly with my explanation.
#178 to #169 - John Cena (07/26/2013) [-]
The thing is there are numbers with a base 10 expansion that contain every possible finite string of digits. These are called 10-normal, and of course all such numbers must be irrational. However, that does not mean that every irrational number is 10-normal, and specifically no mathematician has as yet proved that pi is 10-normal. As far as we know, it could go either way. In general, most mathematicians seem to think that pi is normal in every base, but this is a conjecture not a proven fact.
User avatar #181 to #178 - wiredguy (07/26/2013) [-]
Yes, I know that.
I was treating pi as a normal number in my comment.

Normal doesn't mean it does contains everything. It just means that it has an equal possibility to contain anything.
That doesn't make everything definite, or anything impossible.
I mean. I'm pretty sure. Does it?

**** me I'm only a kid, I'm sure many people, possibly even you, practice this professionally. I'm just taking what I know and applying it.
I promise I'll listen if you can make me understand, I'd hope for the same courtesy from anyone else. Though sadly, such an approach is a rarity in this world.
#186 to #181 - John Cena (07/26/2013) [-]
Just a student myself. I see what you're going for. You might be right that even if it were 10-normal, it might not contain every possible string of digits. The point is that there are numbers that contain every single string digits, for example:

0.1234567891011121314...

but that mathematicians don't know if pi is one of these numbers. There are many seemingly basic facts about numbers that remain unproven to this day, for example whether or not e+pi is irrational.
#195 to #186 - John Cena (07/26/2013) [-]
No wait, let me correct myself. wiredguy is wrong. For a 10-normal number the average frequency of a specific string of length n must converge to 1/10^n as you look at more and more digits. In particular, there is some finite truncation of the infinite sequence where the average frequency of that string is as close to 1/10^n as you want, and so the string must have in fact appeared multiple times in that finite truncation.
#192 - John Cena (07/26/2013) [-]
So somewhere there is secret to why kids love the taste of cinnamon crunch toast
#6 - unfitninjuh (07/25/2013) [-]
This blew my mind
#141 to #6 - John Cena (07/26/2013) [-]
It shouldn't since it's a lie.
#58 - athojew (07/26/2013) [-]
but can it see why kids love the taste of cinnamon toast crunch?
#114 to #58 - arcusolus (07/26/2013) [-]
Look at This
#61 to #58 - alexanderh (07/26/2013) [-]
Somewhere in there, the answer will be revealed.
User avatar #173 - unncommon (07/26/2013) [-]
So somewhere in there is the exact length in inches of my erect penis? Awhh yeahhh!
Oh wait...
...it's the first number.
#174 - asheskirata (07/26/2013) [-]
**asheskirata rolled a random image posted in comment #175 at British Customs **

I COME HERE FORE THE FUNNY, NOT TO LEARN MATH

but it was interesting, so have my thumbs.
#172 - icametocomment (07/26/2013) [-]
Comment Picture
User avatar #136 - huffe ONLINE (07/26/2013) [-]
if it is infinite though, there is bound to be repetition somewhere.
there are just so many ways ten digits can be configured
User avatar #137 to #136 - Keleth (07/26/2013) [-]
i think your missing what repetition is in math. you can't say OH LOOK 305 is in PI and 305 is there again several spots later!! IT REPEATS...not...repetitive is CONSTANT throughout the enter decimal. like .333333 or .12121212. series will repeat in pi, but not back to back, making it not repititive
User avatar #146 to #137 - huffe ONLINE (07/26/2013) [-]
but if it is infinite, there will be a point where the whole thing starts over
i do get what you're saying though. i'm probably thinking about it in a more philosophical manner, rather than a mathematical one
User avatar #148 to #146 - swordguyoxd (07/26/2013) [-]
1. You have to explain the first line, because atm it doesn't make sense
2. You obviously have no idea what philosophy is. It isn't just the idea of thinking
3. If you're saying the exact opposite of what he's saying, its obvious you dont get what he's saying
4. You're retarded
User avatar #160 to #148 - huffe ONLINE (07/26/2013) [-]
1. infinite means it has no end. that means all number combinations will happen at infinitely many points thoughout the sequence. this has the consequence that eventually, the numbers repeat themselves perfectly. this will also happen infinitely.

2. philosophy has many directions. getting philosophical about math is not math. I was just thinking about the theoretical implications derived from the term 'infinite'.

3. keleth was thinking more about more specific decimals like 1/3 and 4/33, which is the practical way of thinking about repeating fractions. you don't need too many decimal places to accurately find the diameter of the universe down to the width of an atom.
theoretically however, you could go on forever, and find that eventually the exact same numbers will repeat.
it's like with an infinite universe. there aren't many fundamental particles, so that eventually, if you went far enough, you would see an exact copy of our observable universe.

4.name-calling is hardly the way to go about this, is it? be a little more mature when discussing
User avatar #215 to #160 - swordguyoxd (07/27/2013) [-]
i'll tell you why i think its such a 'bad' comment.

Imagine a sequence that is made up of subsequent numbers, without "9"

12345678101112131415161718120

This sequence would be infinite, unrepeating (although it would follow a pattern which is different), and it wouldn't include "all the number combinations". I personally found it apparent, and so thought it was ridiculous for you to post what you did without having any kind of reasoning to go with your post. Imo, posting something that isn't common knowledge and acting like it is, not giving proof, is a stupid thing to do.
User avatar #214 to #160 - swordguyoxd (07/27/2013) [-]
You have to prove that an infinte sequence has an infinite amount of sequences in it that repeat themselves. You can't just say it and assume its common knowledge so everyone agrees once you point it out.

Philosophy is a broad subject, but this line doesn't justify your use of it in a mathematical context. For example, saying 1+1=2 is not philosophical, much like this fact your claiming about repeating numbers isn't. A question like "does math exist outside of humanity" might be, but things that can be proven or disproven, where opinions dont exist are never philosophical.

1/3 isn't a decimal....
Are you sure you meant to use the word "practical"? I dont see how thinking of numbers one way over another would help in life, or with a job for example
Again, you have to justify the idea that the numbers will repeat, instead of assuming everyone agrees and that its common knowledge

Name calling is appropriate sometimes. If somebody says an apple falls upwards and ignores gravity you dont argue with them, you just call them stupid and move on. That example is analgous to my view on your comment.



User avatar #183 to #160 - katraiko (07/26/2013) [-]
This guy...
I like this guy.
#185 to #183 - huffe ONLINE (07/26/2013) [-]
i am flattered
#144 to #137 - palindromia ONLINE (07/26/2013) [-]
wouldnt that mean then that pi is not infinite? i mean it if contains all possible number combinations by being infinite that would be that 33333 and 12121212 would have to occur right?
User avatar #156 to #144 - Ninotori (07/26/2013) [-]
Without repetition means that numbers CAN repeat themselves, but will not repeat themselves in a predictable pattern. You might see a series of several numbers together in the same fashion more than once, but you will not see them in a distinct pattern, like, never over and over, not three numbers apart, they will be random. I might see 777777 like eighty million times, but I cannot EVER predict where that will occur. That's random.
#36 - John Cena (07/26/2013) [-]
Well, what if it doesn't contain all that stuff? How can we be certain? I realize i might be wrong but how can one be certain about uncertainty?
User avatar #80 to #36 - zgbgydug (07/26/2013) [-]
Because it's infinite and random, the probability is technically 100% that t does.
User avatar #81 to #36 - davve (07/26/2013) [-]
Pi is proven to be infinite.
User avatar #24 - upyourarsinal (07/26/2013) [-]
gives a whole new meaning to the circle of life AH ZABENYA (The Lion King Song)
User avatar #48 - killingsin (07/26/2013) [-]
ITT: People pretending they know anything about advanced mathematics.
#8 - gremillionaire (07/26/2013) [-]
The same could also be said of e, another infinite, non-repeating decimal.
#9 to #8 - John Cena (07/26/2013) [-]
but then you could find large segments of pi in e
#51 to #8 - kiboz (07/26/2013) [-]
The golden ratio? Should work as well.
#41 - neocortex (07/26/2013) [-]
This image has expired
And it also includes pie, for pie is the best thing in the world
#42 to #41 - juuru (07/26/2013) [-]
Comment Picture
#43 to #42 - neocortex (07/26/2013) [-]
This image has expired
I totally misstook her for Misaka ^^
#78 to #43 - selfrazedzealot (07/26/2013) [-]
how can she have another... if its still a full pie
User avatar #45 to #42 - lurifax (07/26/2013) [-]
Why can't she just get Another
so fahny, yes I know
#38 - retfarcenim (07/26/2013) [-]
We simply can't know if this is true, i would say it is ******** , because maybe after a while there are no more 4's in pi, what still makes it infinite and nonrepeating but it won't contain every combination. It's hard to explain but what this post implies isn't as logical as it seems
User avatar #39 to #38 - zraven (07/26/2013) [-]
Do you happen to know how many digits in that 4's stop repeating?
#33 - John Cena (07/26/2013) [-]
just becouse it's infinite and nonrepeating dosen't mean it contains every finit sequens of numbers. consider somthing like 0.1234567891234567899.... where every time you get nine more its infinite and nonrepeating decimal that dosent contain 321 for example . i doubt you can proof your statement for pi, could be true anyway.
[ 214 comments ]
Leave a comment
 Friends (0)