Why Calculate Pi to So Many Decimal Places ?

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Offline neilep

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Why Calculate Pi to So Many Decimal Places ?
« on: 24/08/2008 18:12:12 »
Dearest Piologists and eaters of all things pastry lined !

see this Pi ?

[attachment=4231]

Nice eh ?...being delivered Tuesday !

As a sheep the nature of Pi taunts me every day and night !!

We can calculate Pi to a trillion decimal places !...I know this because I have counted them !.....but why ? Why calculate Pi to a trillion places when apparently only 40 decimal places is enough to calculate the circumference of the visible Universe ?

Whilst I await your answers, I think I'll count them again..I think i missed a '3' somewhere around 425 billion !

Thank Ewe


Hugs the Klevur peeps

Shmishes them too !


Neil
Pi Asker and Pie Eater

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Offline syhprum

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Why Calculate Pi to So Many Decimal Places ?
« Reply #1 on: 24/08/2008 19:11:36 »
I think the object is to test out algorithms for computing such numbers and to demonstrate computer power
syhprum

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Offline neilep

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Why Calculate Pi to So Many Decimal Places ?
« Reply #2 on: 24/08/2008 19:42:14 »
I think the object is to test out algorithms for computing such numbers and to demonstrate computer power

Thank Ewe syhprum

So, it's really just a mater of ' because we can '...but also as a tool to demonstrate efficiency....

.......I know this might be a silly question but how do we know if Pi to a trillion decimal places is calculated correctly ?
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lyner

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Why Calculate Pi to So Many Decimal Places ?
« Reply #3 on: 25/08/2008 23:55:36 »
One way of 'knowing' is based on various mathematical proofs which can show that pi must lie between two values which can actually be calculated - therefore they can say that they 'know' pi to a certain accuracy i.e. between those limits.
I'm not sure I put that in the most understandable way - sorry.

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lyner

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Why Calculate Pi to So Many Decimal Places ?
« Reply #4 on: 26/08/2008 15:11:30 »
The real answer to the "why?" question is that Mathematicians are all on a different track to the rest of us. Some of them are really loopy. Brilliant but loopy and what would be do without them?
Try to have an ordinary conversation with a good Mathematician about a commonly discussed topic and you can rely on them to take you to places that you would never normally go. Some of my best friends are Mathematicians, I have to say.

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blakestyger

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Why Calculate Pi to So Many Decimal Places ?
« Reply #5 on: 26/08/2008 19:13:16 »
Possibly...sometime, somewhere, someone will discover that after the umpteenth billion places you have counted up to...it will start to repeat itself. [:0]

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lyner

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Why Calculate Pi to So Many Decimal Places ?
« Reply #6 on: 26/08/2008 21:16:52 »
That would imply that pi is rational (a ratio of two integers). 'They' can prove, quite conclusively, that it isn't. So you won't find a repeat.

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Offline Alan McDougall

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Why Calculate Pi to So Many Decimal Places ?
« Reply #7 on: 27/08/2008 13:27:14 »
To see if there would be some pattern.
The Truth remains the Truth regardless of our beliefs or opinions the Truth is always the Truth even if we know it or do not know it (The Truth remains the Truth)

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lyner

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Why Calculate Pi to So Many Decimal Places ?
« Reply #8 on: 27/08/2008 20:51:43 »
If the sequence is constantly changing then you might expect the occasional, apparently meaningful, embedded pattern. But what would that prove? It's just like monkeys and typewriters.

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Offline Bored chemist

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Why Calculate Pi to So Many Decimal Places ?
« Reply #9 on: 28/08/2008 19:26:33 »
Any and all patterns will occur somewhere in pi. It might take a while to find them.
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Offline Make it Lady

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Why Calculate Pi to So Many Decimal Places ?
« Reply #10 on: 28/08/2008 19:54:04 »
The book, 'The Life of Pi' is much more interesting. The first few chapters are dull but then....wow! it is brilliant.

Sheepy, I think 7 decimal places is enough for anyone but I guess you can't have too much of a good thing.
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Offline syhprum

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« Reply #11 on: 29/08/2008 17:08:59 »
Parraleling the hunt for evermore digits of Pi the hunt for the 45th Mersenne number seems to have succeeded as reported in the Scientific American this when verified will earn a $100,000 prize
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Offline Glenn

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Why Calculate Pi to So Many Decimal Places ?
« Reply #12 on: 16/09/2008 09:30:00 »
Though I too am fascinated by the trillion digits of pi so far calculated, it's more important to know HOW to calculate it. For example, this continued fraction will do nicely:

         4    1^2   2^2   3^2   4^2        k^2
pi = ---- ----- ----- ------ ----- ... ------- ...
         1+    3+     5+     7+     9+        2k+1+

While other methods converge to pi more quickly, this is the easiest-working.
« Last Edit: 17/09/2008 08:04:21 by Glenn »

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Offline neilep

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Why Calculate Pi to So Many Decimal Places ?
« Reply #13 on: 16/09/2008 13:40:03 »
Is it even possible to display a trillion digits ?
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Offline Chemistry4me

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Why Calculate Pi to So Many Decimal Places ?
« Reply #14 on: 31/12/2008 03:10:23 »
Though I too am fascinated by the trillion digits of pi so far calculated, it's more important to know HOW to calculate it. For example, this continued fraction will do nicely:

      4    1^2   2^2   3^2   4^2        k^2
pi = ---- ----- ----- ------ ----- ... ------- ...
      1+    3+    5+    7+    9+        2k+1+

While other methods converge to pi more quickly, this is the easiest-working.
How does that method work? I'm no maths wizz, actually I'm mathamatically dyslexic, but its not that uncommon, 436 people out of 34 have it... mwhahahaha

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Offline Mr. Scientist

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Why Calculate Pi to So Many Decimal Places ?
« Reply #15 on: 31/12/2008 04:22:59 »
Though I too am fascinated by the trillion digits of pi so far calculated, it's more important to know HOW to calculate it. For example, this continued fraction will do nicely:

      4    1^2   2^2   3^2   4^2        k^2
pi = ---- ----- ----- ------ ----- ... ------- ...
      1+    3+    5+    7+    9+        2k+1+

While other methods converge to pi more quickly, this is the easiest-working.
How does that method work? I'm no maths wizz, actually I'm mathamatically dyslexic, but its not that uncommon, 436 people out of 34 have it... mwhahahaha

They've used what is called a Infinite Series.
http://www.youtube.com/watch?v=SZGcNx8nV8U

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Offline Chemistry4me

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Why Calculate Pi to So Many Decimal Places ?
« Reply #16 on: 31/12/2008 04:49:53 »
So can somebody demonstrate for me how its done? How does this Infinite Series work? As I said, my maths isn't exactly out of this world... [:I] [:I]

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Offline Mr. Scientist

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Why Calculate Pi to So Many Decimal Places ?
« Reply #17 on: 31/12/2008 04:57:18 »
So can somebody demonstrate for me how its done? How does this Infinite Series work? As I said, my maths isn't exactly out of this world... [:I] [:I]

well, i only glanced very quickly at the math, but generally speaking, if you want to calculate something large, then it goes through a series.
http://www.youtube.com/watch?v=SZGcNx8nV8U

''God could not have had much time on His hands when he formed the Planck Lengths.''

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Offline Chemistry4me

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Why Calculate Pi to So Many Decimal Places ?
« Reply #18 on: 31/12/2008 04:59:38 »
Um... forgive me for saying this Mr. Scientist, but you are still talking in riddles. [:I] [:I]

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Offline Mr. Scientist

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Why Calculate Pi to So Many Decimal Places ?
« Reply #19 on: 31/12/2008 05:04:19 »
Um... forgive me for saying this Mr. Scientist, but you are still talking in riddles. [:I] [:I]

Do you know calculus? Or would you like me to hopefully explain this in some effecient way for you to understand?
http://www.youtube.com/watch?v=SZGcNx8nV8U

''God could not have had much time on His hands when he formed the Planck Lengths.''

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Offline Mr. Scientist

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Why Calculate Pi to So Many Decimal Places ?
« Reply #20 on: 31/12/2008 05:05:29 »
Even better,  here is a link

Series (mathematics) - Wikipedia, the free encyclopedia
A series may be ... However, infinite series of nonzero terms can also converge, ... The idea of an infinite series expansion of a function was ...
en.wikipedia.org/wiki/Series_(mathematics) - 73k - Cached
http://www.youtube.com/watch?v=SZGcNx8nV8U

''God could not have had much time on His hands when he formed the Planck Lengths.''

 ̿ ̿ ̿ ̿̿'\̵͇̿̿\=(●̪)=/̵͇̿̿/'̿'̿̿̿ ̿ ̿̿ ̿ ̿

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Offline Chemistry4me

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Why Calculate Pi to So Many Decimal Places ?
« Reply #21 on: 31/12/2008 05:13:00 »
Do you know calculus? Or would you like me to hopefully explain this in some effecient way for you to understand?
I know a little bit of calculus [:I] If you can explain how that Infinite Series works to solve π I would be very greatful [:)]

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Offline Mr. Scientist

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« Reply #22 on: 31/12/2008 05:23:17 »
Do you know calculus? Or would you like me to hopefully explain this in some effecient way for you to understand?
I know a little bit of calculus [:I] If you can explain how that Infinite Series works to solve π I would be very greatful [:)]

It will take me about 20 mins then to type it out. Hold on. :)
http://www.youtube.com/watch?v=SZGcNx8nV8U

''God could not have had much time on His hands when he formed the Planck Lengths.''

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Offline Chemistry4me

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« Reply #23 on: 31/12/2008 05:27:09 »
WOW! Must be some complicated stuff [:o], never mind, I can wait... the mystery of pi shall be explained. Umm... pie... [:P] [:P] [:P] [:P]

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Offline Mr. Scientist

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« Reply #24 on: 31/12/2008 05:36:52 »
Right, first contemplate what is a string or a sequence of numbers:

1, 1/2, 1/3, 1/4, 1/5

if we dot it at the end like so,

1, 1/2, 1/3, 1/4, 1/5...

It means, ''and so on,'' in this particular pattern. We can now say that the n^th number is a_n, then one can evaluate that a_1 is 1, and a_2 is 1/2, so that implies that a_n=1/n. An infinite series of numbers will look something like this:

∑ = 1 + 1/2 + 1/4 + 1/8 + ...

Where again, the (+ ...) means an infinite continuation of the numerical processes. Since we can't add all of infinite numbers, we can however add the first lot of ''n'' terms like

∑_1 = 1
∑_2 = 1 + 1/2 = 3/2
∑_3 = 1 + 1/2 + 1/4 = 7/4

where ∑ just means the 'sum of.'

Does that help?




http://www.youtube.com/watch?v=SZGcNx8nV8U

''God could not have had much time on His hands when he formed the Planck Lengths.''

 ̿ ̿ ̿ ̿̿'\̵͇̿̿\=(●̪)=/̵͇̿̿/'̿'̿̿̿ ̿ ̿̿ ̿ ̿

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Offline Mr. Scientist

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Why Calculate Pi to So Many Decimal Places ?
« Reply #25 on: 31/12/2008 05:37:38 »
WOW! Must be some complicated stuff [:o], never mind, I can wait... the mystery of pi shall be explained. Umm... pie... [:P] [:P] [:P] [:P]

It's not really too complicated. It's just i had other things to do to lol
http://www.youtube.com/watch?v=SZGcNx8nV8U

''God could not have had much time on His hands when he formed the Planck Lengths.''

 ̿ ̿ ̿ ̿̿'\̵͇̿̿\=(●̪)=/̵͇̿̿/'̿'̿̿̿ ̿ ̿̿ ̿ ̿

٩๏̯͡๏۶

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Offline Mr. Scientist

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« Reply #26 on: 31/12/2008 05:38:36 »
Right, first contemplate what is a string or a sequence of numbers:

1, 1/2, 1/3, 1/4, 1/5

if we dot it at the end like so,

1, 1/2, 1/3, 1/4, 1/5...

It means, ''and so on,'' in this particular pattern. We can now say that the n^th number is a_n, then one can evaluate that a_1 is 1, and a_2 is 1/2, so that implies that a_n=1/n. An infinite series of numbers will look something like this:

∑ = 1 + 1/2 + 1/4 + 1/8 + ...

Where again, the (+ ...) means an infinite continuation of the numerical processes. Since we can't add all of infinite numbers, we can however add the first lot of ''n'' terms like

∑_1 = 1
∑_2 = 1 + 1/2 = 3/2
∑_3 = 1 + 1/2 + 1/4 = 7/4

where ∑ just means the 'sum of.'

Does that help?







(And i can't explain it any more simpler, i am afraid) - so don't ask :)
http://www.youtube.com/watch?v=SZGcNx8nV8U

''God could not have had much time on His hands when he formed the Planck Lengths.''

 ̿ ̿ ̿ ̿̿'\̵͇̿̿\=(●̪)=/̵͇̿̿/'̿'̿̿̿ ̿ ̿̿ ̿ ̿

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Offline Chemistry4me

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Why Calculate Pi to So Many Decimal Places ?
« Reply #27 on: 31/12/2008 05:47:48 »
Yeah, all of the stuff about the series I totally understand, what I don't get is how the series:

      4    1^2   2^2   3^2   4^2        k^2
pi = ---- ----- ----- ------ ----- ... ------- ...
      1+    3+    5+    7+    9+        2k+1+

adds up to find pi. What is the range of values for 'k' and what is the 1+ 3+ 5+ doing there?

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Offline Chemistry4me

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« Reply #28 on: 31/12/2008 05:49:14 »
I mean, am I not meant to substitute values of 'k' from 1 to infinity into the series? But doing it on my calculator, I've gotten nothing even close to pi...

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Offline Mr. Scientist

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« Reply #29 on: 31/12/2008 05:49:56 »
I don't know how that works out.
http://www.youtube.com/watch?v=SZGcNx8nV8U

''God could not have had much time on His hands when he formed the Planck Lengths.''

 ̿ ̿ ̿ ̿̿'\̵͇̿̿\=(●̪)=/̵͇̿̿/'̿'̿̿̿ ̿ ̿̿ ̿ ̿

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Offline Chemistry4me

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Why Calculate Pi to So Many Decimal Places ?
« Reply #30 on: 31/12/2008 08:03:20 »
So we are back to square one, can anybody help me and my imcompetent mathematical brain to uncover the mystery of pi? Mainly, how is the serie/formula thing supposed to work?

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Offline Chemistry4me

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« Reply #31 on: 31/12/2008 08:37:12 »
I've just found pi to 1 million digits: http://www.eveandersson.com/pi/digits/1000000  [:o] [:o] [:o] [:o]

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Offline Mr. Scientist

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« Reply #32 on: 31/12/2008 08:50:27 »
I don't know why anyone would want to derive pi other than simply stating 7/22.
http://www.youtube.com/watch?v=SZGcNx8nV8U

''God could not have had much time on His hands when he formed the Planck Lengths.''

 ̿ ̿ ̿ ̿̿'\̵͇̿̿\=(●̪)=/̵͇̿̿/'̿'̿̿̿ ̿ ̿̿ ̿ ̿

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Offline Chemistry4me

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« Reply #33 on: 31/12/2008 08:52:33 »
Isn't it 22/7?

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Offline Mr. Scientist

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« Reply #34 on: 31/12/2008 08:54:42 »
I've solved the problem. Its a continued fraction, as found in wikipedia:

WEB RESULTSPi - Wikipedia, the free encyclopedia
Article about the mathematical constant, pi, including its history, appearances in formulae, trivia, and more. ... Retrieved from "http://en.wikipedia.org/wiki/Pi" ...
en.wikipedia.org/wiki/Pi - 182k - Cached

So here, the function that the person was using which caused so much confusion was in fact a continued fraction.
http://www.youtube.com/watch?v=SZGcNx8nV8U

''God could not have had much time on His hands when he formed the Planck Lengths.''

 ̿ ̿ ̿ ̿̿'\̵͇̿̿\=(●̪)=/̵͇̿̿/'̿'̿̿̿ ̿ ̿̿ ̿ ̿

٩๏̯͡๏۶

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Offline Mr. Scientist

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« Reply #35 on: 31/12/2008 08:58:10 »
(Which is a series, not to confuse matters further)
http://www.youtube.com/watch?v=SZGcNx8nV8U

''God could not have had much time on His hands when he formed the Planck Lengths.''

 ̿ ̿ ̿ ̿̿'\̵͇̿̿\=(●̪)=/̵͇̿̿/'̿'̿̿̿ ̿ ̿̿ ̿ ̿

٩๏̯͡๏۶

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Offline Mr. Scientist

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« Reply #36 on: 31/12/2008 08:59:00 »
Isn't it 22/7?

Yes, sorry, muddled up.
http://www.youtube.com/watch?v=SZGcNx8nV8U

''God could not have had much time on His hands when he formed the Planck Lengths.''

 ̿ ̿ ̿ ̿̿'\̵͇̿̿\=(●̪)=/̵͇̿̿/'̿'̿̿̿ ̿ ̿̿ ̿ ̿

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Offline Chemistry4me

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« Reply #37 on: 31/12/2008 09:00:38 »
Continued fraction? [???] You're forgetting that you are talking to a mathimatical dyslexic. [::)] hmmm... I think I'll leave the solving to the computers, with that formula I would need to imput millions of numbers into my calculator just to get a remotely accurate number... I'll be sitting here for days  [xx(] [xx(]

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Offline Mr. Scientist

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« Reply #38 on: 31/12/2008 09:02:23 »
Well, remotely accurate being 22/7. Its about as close as a human can get holding a calculator, without pressing the pi button.
http://www.youtube.com/watch?v=SZGcNx8nV8U

''God could not have had much time on His hands when he formed the Planck Lengths.''

 ̿ ̿ ̿ ̿̿'\̵͇̿̿\=(●̪)=/̵͇̿̿/'̿'̿̿̿ ̿ ̿̿ ̿ ̿

٩๏̯͡๏۶

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Offline yor_on

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« Reply #39 on: 01/01/2009 13:32:54 »
I must be going nuts?
I actually enjoyed reading that wiki about pie?
Especially rhubarb :)
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