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Author Topic: Why Calculate Pi to So Many Decimal Places ?  (Read 20815 times)

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
 

Offline Mr. Scientist

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Why Calculate Pi to So Many Decimal Places ?
« 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 :)
 

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?
 

Offline Chemistry4me

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Why Calculate Pi to So Many Decimal Places ?
« 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...
 

Offline Mr. Scientist

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Why Calculate Pi to So Many Decimal Places ?
« Reply #29 on: 31/12/2008 05:49:56 »
I don't know how that works out.
 

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?
 

Offline Chemistry4me

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Why Calculate Pi to So Many Decimal Places ?
« 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
 

Offline Mr. Scientist

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Why Calculate Pi to So Many Decimal Places ?
« 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.
 

Offline Chemistry4me

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Why Calculate Pi to So Many Decimal Places ?
« Reply #33 on: 31/12/2008 08:52:33 »
Isn't it 22/7?
 

Offline Mr. Scientist

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Why Calculate Pi to So Many Decimal Places ?
« 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.
 

Offline Mr. Scientist

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Why Calculate Pi to So Many Decimal Places ?
« Reply #35 on: 31/12/2008 08:58:10 »
(Which is a series, not to confuse matters further)
 

Offline Mr. Scientist

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Why Calculate Pi to So Many Decimal Places ?
« Reply #36 on: 31/12/2008 08:59:00 »
Isn't it 22/7?

Yes, sorry, muddled up.
 

Offline Chemistry4me

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Why Calculate Pi to So Many Decimal Places ?
« 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(]
 

Offline Mr. Scientist

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Why Calculate Pi to So Many Decimal Places ?
« 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.
 

Offline yor_on

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Why Calculate Pi to So Many Decimal Places ?
« 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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Why Calculate Pi to So Many Decimal Places ?
« Reply #39 on: 01/01/2009 13:32:54 »

 

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