Does Pi end or repeat?

[shadowlock]

Sometimes during my spare time I use a program called QuickPi - To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
It runs through the command line and allows you to calculate pi to whatever number you wish. The world record for a home PC was set with this program. You can easily calculate 100 million in about 10 minutes. You can also save to a file.

Someday I wish to break the record, or find some way for [ch960] to end or repeat. Do you think Pi will ever end or repeat?

EDIT: I personally think it will repeat.

[Voodoo Child]

It would be pretty ironic if pi, which has sort of an omnipresence in nature, turns out to be a never-ending never-repeating irrational number. Akin to how it'd be the height of irony if the Universe just turns out to be completely unorganized chaos, and the human invention we call mathematics can give nothing more than an approximation to the answers we seek.

Anyway, I don't really believe that, it would just be pretty damn funny. I think pi will eventually just end without really justifying why I think that (I don't really have a sufficient mathematical background to discuss why either). Just a gut-feeling, I guess.

[shadowlock]

Do you have a guess as to how many digits it will end at?

[Voodoo Child]

Well, I don't really think we will have the computational power to truly calculate pi for another decade or so. So I'm going to take a wild guess and say 3000 billion digits.

[shadowlock]

That quickpi lets you do whatever digits you want, it just takes time.

[bikerscars]

if it repeats then it also doesn't end

i think in much the same way the universe has no boundaries pi has no end...

we just do not comprehend the logic behind it all...

[Voodoo Child]

That quickpi lets you do whatever digits you want, it just takes time.
Yeah exactly, too much time! Hehe.
What I'm thinking though, will it truly matter? Even if it did end, or repeat for that matter, will we ever really need to use pi THAT accurately?
Guess I'm just trying to see the usefulness in it, not disputing that it'd be very interesting though. It will be fun to find out, if we ever do. ;)

[shadowlock]

It's just a slightly entertaining hobby...

[rwyatt365]

Personally, I expect Pi never to repeat...just a never-ending series of random numbers ad-infinitum. Humans believe that everything is knowable and that we can know everything. To have Pi go on and on would show that everything is NOT knowable.

[INTJohn]

According to my experiment and resultant observational data pi definately ends.

I made one a few days ago and had the last piece this morning for breakfast.

INTJohn

[rwyatt365]

According to my experiment and resultant observational data pi definately ends.

I made one a few days ago and had the last piece this morning for breakfast.

INTJohn
Apple, Cherry, or Bannana Cream?

[Jack]

According to my experiement and resultant observational data pi definately ends.

I made one a few days ago and had the last piece this morning for breakfast.

INTJohn

;DI like pumpkin pie!

if pi is infinite, the universe must be as well, a sphere, every heavenly body is spherical in some way of another, so the universe is a chaotic ball full of electrons being pulled and pushed by other balls of full of electrons of equal or lesser size.

What's on the outside of this dark sphere?...An un-imaginably massive star, that or universe is rotating around,this star is so big and bright we can't see it because it's so far away, An Alpha Solar System, with all the universes rotating around the heart of the "multiverse" together. It's very hard for me to imagine that our universe is the only one and that it's stationary in it's present position, and not orbiting another useless(to us)source of energy.

[INTJohn]

According to my experiement and resultant observational data pi definately ends.

I made one a few days ago and had the last piece this morning for breakfast.

INTJohn

;DI like pumpkin pie!

if pi is infinite, the universe must be as well, a sphere, every heavenly body is spherical in some way of another, so the universe is a chaotic ball full of electrons being pulled and pushed by other balls of full of electrons of equal or lesser size.

What's on the outside of this dark sphere?...An un-imaginably massive star, that or universe is rotating around,this star is so big and bright we can't see it because it's so far away, An Alpha Solar System, with all the universes rotating around the heart of the "multiverse" together. It's very hard for me to imagine that our universe is the only one and that it's stationary in it's present position, and not orbiting another useless(to us)source of energy.


So which way should this all go???

Diet & Nutrition or Cosmolgical Future of Mankind??

Pick a direction but we're gettin' off topic here.

INTJohn

[rwyatt365]

So which way should this all go???

Diet & Nutrition or Cosmolgical Future of Mankind??

Pick a direction but we're gettin' off topic here.

INTJohn
...which is a common occurance around these here parts! ;)

[bikerscars]

in the interest of science we need to see your methodology...

i personally want to see if i get the same results when i replicate the experiment...

lots of questions need to be answered...

pumpkin, apple, cherry; with/without toppings...

[wise]

According to my experiement and resultant observational data pi definately ends.

I made one a few days ago and had the last piece this morning for breakfast.

INTJohn

;DI like pumpkin pie!

if pi is infinite, the universe must be as well, a sphere, every heavenly body is spherical in some way of another, so the universe is a chaotic ball full of electrons being pulled and pushed by other balls of full of electrons of equal or lesser size.

What's on the outside of this dark sphere?...An un-imaginably massive star, that or universe is rotating around,this star is so big and bright we can't see it because it's so far away, An Alpha Solar System, with all the universes rotating around the heart of the "multiverse" together. It's very hard for me to imagine that our universe is the only one and that it's stationary in it's present position, and not orbiting another useless(to us)source of energy.


So which way should this all go???

Diet & Nutrition or Cosmolgical Future of Mankind??

Pick a direction but we're gettin' off topic here.

INTJohn

It appears that you started this divergence. I prefer pecan.

[rwyatt365]

So. Need we start a "Pi(e) Preference" thread to answer these burning questions?

BTW - does/should drink preference factor into the outcome? Does that affect the duration?

[INTJohn]

According to my experiement and resultant observational data pi definately ends.

I made one a few days ago and had the last piece this morning for breakfast.

INTJohn

;DI like pumpkin pie!

if pi is infinite, the universe must be as well, a sphere, every heavenly body is spherical in some way of another, so the universe is a chaotic ball full of electrons being pulled and pushed by other balls of full of electrons of equal or lesser size.

What's on the outside of this dark sphere?...An un-imaginably massive star, that or universe is rotating around,this star is so big and bright we can't see it because it's so far away, An Alpha Solar System, with all the universes rotating around the heart of the "multiverse" together. It's very hard for me to imagine that our universe is the only one and that it's stationary in it's present position, and not orbiting another useless(to us)source of energy.


So which way should this all go???

Diet & Nutrition or Cosmolgical Future of Mankind??

Pick a direction but we're gettin' off topic here.

INTJohn

It appears that you started this divergence. I prefer pecan.

OK; OK........

I'll choose Cosmological Future of Mankind.........

Its similar to the flight of the amazing Whiffle Bird which flies in a never ending curve having an ever decreasing radius till it disappears up its own asshole hence proving the existence of a Black Hole..........

INTJohn

[Jack]

Its similar to the flight of the amazing Whiffle Bird which flies in a never ending curve having an ever decreasing radius till it disappears up its own asshole hence proving the existence of a Black Hole..........

INTJohn

Like goin down the toilet :-/

[INTJohn]

Its similar to the flight of the amazing Whiffle Bird which flies in a never ending curve having an ever decreasing radius till it disappears up its own asshole hence proving the existence of a Black Hole..........

INTJohn

Like goin down the toilet :-/

The spirit's movin' me so I think thats where the pi's headed.......

INTJohn

[Guido]

I'm really confused... is this a joke thread?

[ben from below]

No mathematicians here, eh? Pi is irrational; in fact it's transcendental, so, no, it doesn't end or repeat.

[Tarrick]

It would be pretty ironic if pi, which has sort of an omnipresence in nature, turns out to be a never-ending never-repeating irrational number. Akin to how it'd be the height of irony if the Universe just turns out to be completely unorganized chaos, and the human invention we call mathematics can give nothing more than an approximation to the answers we seek.

Anyway, I don't really believe that, it would just be pretty damn funny. I think pi will eventually just end without really justifying why I think that (I don't really have a sufficient mathematical background to discuss why either). Just a gut-feeling, I guess.

It's because we're using a base 10 number system. The universe is not necessarily on that type of number system, now is it?

[Voodoo Child]

It would be pretty ironic if pi, which has sort of an omnipresence in nature, turns out to be a never-ending never-repeating irrational number. Akin to how it'd be the height of irony if the Universe just turns out to be completely unorganized chaos, and the human invention we call mathematics can give nothing more than an approximation to the answers we seek.

Anyway, I don't really believe that, it would just be pretty damn funny. I think pi will eventually just end without really justifying why I think that (I don't really have a sufficient mathematical background to discuss why either). Just a gut-feeling, I guess.

It's because we're using a base 10 number system. The universe is not necessarily on that type of number system, now is it?
I don't really see your logic, personally I wouldn't say the Universe is on any kind of number system.

No mathematicians here, eh? Pi is irrational; in fact it's transcendental, so, no, it doesn't end or repeat.
Yeah I feel kind of silly now, I knew pi was irrational so I guess I should've made the connection. Not a mathematician though so I guess I can hide behind that. ;)

[Guido]

No mathematicians here, eh? *Pi is irrational; in fact it's transcendental, so, no, it doesn't end or repeat.

Yeah... that's why I asked if this was a joke thread o.0 PI doesn't end and it doesn't repeat. This has been proven.

[Rei]

No mathematicians here, eh? *Pi is irrational; in fact it's transcendental, so, no, it doesn't end or repeat.

That's what I thought... I was wondering why there's any discussion at all about this... *:suspicious:
Made me think that maybe it was one of those things teachers liked to lie to students about...

It would be pretty ironic if pi, which has sort of an omnipresence in nature, turns out to be a never-ending never-repeating irrational number. Akin to how it'd be the height of irony if the Universe just turns out to be completely unorganized chaos, and the human invention we call mathematics can give nothing more than an approximation to the answers we seek.

You were being sarcastic right? Because that's exactly what I think is true.

[The Rose]

I don't think pi will start to repeat itself.
I think it's infinite (as infinite as numbers can be).

[rwyatt365]

Hey Rose, welcome back! Thought you had abandoned us. :thumbsup:

[The Rose]

Thanks!

[Quincunx]

Hasn't it been mathematically proven that it will never repeat?

I think there's also a speculation that any finite combonation of digits can be found within pi. That's sort of cool.

[thegnat]

Hasn't it been mathematically proven that it will never repeat?

I think there's also a speculation that any finite combonation of digits can be found within pi. That's sort of cool.



I think it has. at least according to this website:

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and you can memorize digits of pi if you want

3.141592653589793238462643383.....

[logan235711]

No mathematicians here, eh? Pi is irrational; in fact it's transcendental, so, no, it doesn't end or repeat.
yes, I was really depressed reading this thread until i found your post U_U thank-you

Hasn't it been mathematically proven that it will never repeat?
yes it has...in 1761...and it's transcendental nature in 1882 since i'm such a nice guy i will show a proof right here for you. This is a proof by contradiction, it required basic calculus understanding:

Suppose pie is rational (compared to irrational). Given any integer n+, we define the polynomial function:

ƒ(x) = (xn*(a - bx)n) / n! , where x[ch949]R and denote by

F(x) = ƒ(x) + ... + (-1)jƒ(2j)(x) + ... + (-1)nƒ(2n)(x) (the alternating sum of ƒ and its first n even derivatives)

C1: F(0) = F(pie)
Pf: Since

ƒ(x) = bn(xn*(pie - x)n) / n! = ƒ(pie - x) , where x[ch949]R

the chain rule ((ƒ o g)`(x) = ƒ`(g(x))*g`(x)) and mathematical induction imply

ƒ(j)(x) = (-1)jƒ(j)(pie - x) , where x[ch949]R for all derivatives, then

ƒ(2j)(0) = ƒ(2j)(pie) for j = 1, 2, ..., n

C2: F(0) is an integer
Pf: Using the binomial formula (x + y)n = [ch931]nk=0(n! / (k!*(n - k)!))*xn - k*yk to expand (a - bx)n and the index transformation j = k + n, we get

ƒ(x) = (1 / n!)*[ch931]2nj=n(n! / ((j - n)!*(n - (j - n))!))*a2n - j*(-b)j - n*xj

Since the coefficients of x0, x1, ..., xn - 1 are zero and the degree of the polynomial ƒ is at most 2n, we have ƒ(j)(0) = 0 for j < n and j > 2n such that

ƒj(0) = (j! / n!)*[ch931]2nj=n(n! / ((j - n)!*(n - (j - n))!))*a2n - j*(-b)j - n for n [ch8804] j [ch8804] 2n

Since j [ch8805] n, the fraction of the two factorials is an integer (the same for the binomial coefficient). Hence ƒ and every derivative of ƒ at 0 is an integer and so is F(0).

C3: ½ [ch8992]pie0ƒ(x)*sin(x)*dx = F(0)
Pf: Since ƒ2n + 2 is a zero polynomial, then

F`` + F = ƒ

Hence the product rule ((ƒg)` = ƒ`*g + ƒ*g`) implies

(F`(x)*(sin x) - F(x)*(cos x))` = F(x)*(sin x) (since the derivatives of the sine and cosine function are (sin x)` = cos x and (cos x)` = -sin x, h), thus

½ [ch8992]pie0ƒ(x)*sin(x)*dx = ½ (F`(x)*(sin x) - F(x)(cos x) |x = piex = 0

Since sin (0) = sin (pie) and cos (0) = -cos (pie) = 1, C3 follows from C1.

Thus, since ƒ(x) > 0 and sin (x) > 0 for 0 < x < pie (because pie is the smallest positive zero of the sine function), C2 and C3 show that F(0) is a positive integer. Since

x*(pie - x) = (pie / 2)2 = (x - (pie / 2))2 [ch8804] (pie / 2)2 , x[ch949]R

and 0 [ch8804] sin (x) [ch8804] 1 for 0 [ch8804] x [ch8804] pie, follows

½ [ch8992]pie0ƒ(x)*sin(x)*dx [ch8804] (bn / n!)*(pie / 2)2n + 1

which is smaller than 1 for large n, hence F(0) < 1 by C3 for these n. Contradiction. Thus pie is an irrational #. m5

[ShaiGar]

i like the shape of the graph

[HackerX]

I think the problem is that mathematicians are looking at the wrong number (pi). I think they should be searching for a more generic (higher dimension) solution to the problem without referencing pi.

That's about as much thought as I've put into that, so run with it.

[Mechanical Messiah]

I'm no mathematician... differential equations was enough math to satisfy me. But I think of pi as a definition rather than an actual number. Much like e.

[Antares]

Personally, I expect Pi never to repeat...just a never-ending series of random numbers ad-infinitum. Humans believe that everything is knowable and that we can know everything. To have Pi go on and on would show that everything is NOT knowable.

I agree with the notion that everything is NOT knowable. Currently, there are many limits to us understanding everything. (And I know this is philosophical, but I think that Socrates' quote holds some truth in it :thumbsup:)

I don't think Pi will ever end nor will it repeat, but I have no real mathematical background and I'm by no means a good math student, so take this as a mere opinion.

[Mechanical Messiah]

It just happens to be a demonstrably correct opinion, though.

[Race]

The definition of Pi says it will never repeat or end. Question answered.

[Nolen]

It's because we're using a base 10 number system. The universe is not necessarily on that type of number system, now is it?

That doesn't matter. Think about the way the rational numbers are defined; ratios of integers with the equivalence relation x/y = a/b if bx = ay. The way the integers are labeled doesn't matter, meaning the base system chosen doesn't matter. Thus a real number being irrational is independent of the choice of base system used to express it.





Nolen added to this post, 2 minutes and 33 seconds later...

The definition of Pi says it will never repeat or end. Question answered.

I'm curious what definition of pi says that. I have never seen a definition of pi that had as an axiom its rationality.

[Zilal]

This is the sort of stuff I love thinking about. Have you all read Carl Sagan's Contact? There is an interesting twist with Pi at the end.

"I think there's also a speculation that any finite combination of digits can be found within pi. That's sort of cool."

I got into an argument once with someone about this, and maybe one of you can shed some light on it. I said that we could NOT say for certain that there was, for instance, a string of a hundred 4s somewhere in Pi. That the probability may be as close to 100% as you like, but it couldn't be 100%. They disagreed with me, saying that there MUST be a string of a hundred 4s somewhere in Pi, just because it goes on infinitely with infinite combinations. I thought my argument was a bit more nuanced. What do you think?

[Mechanical Messiah]

It would be pretty ironic if pi, which has sort of an omnipresence in nature, turns out to be a never-ending never-repeating irrational number. Akin to how it'd be the height of irony if the Universe just turns out to be completely unorganized chaos, and the human invention we call mathematics can give nothing more than an approximation to the answers we seek.

Much of that is demonstrably true... and a good case can be made for the rest.

[ikihi]

The definition of Pi says it will never repeat or end. Question answered.

Going by the accepted definition doesn't necessarily answer anything. Science has constantly disproved old definitions. The same could be true for pi.