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## #1 2013-08-09 15:53:46

Amartyanil
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From: Universe
Registered: 2013-05-27
Posts: 60

### π

How to find the pi's value? What is the requirement of Pi?

'I think I can safely say that nobody understands quantum mechanics.' - Richard Feynman

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## #2 2013-08-09 18:33:26

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,829
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### Re: π

Amartyanil wrote:

How to find the pi's value?

http://rosettacode.org/wiki/Pi

What is the requirement of π?

This question is not sensible. π is. And that is a truth

Last edited by Agnishom (2013-08-09 18:34:04)

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #3 2013-08-09 22:51:10

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: π

Hi Amartyanil;

You can compute digits of pi to the limits of your machines and software but pi is a never ending decimal.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #4 2013-08-10 00:16:26

bob bundy
Registered: 2010-06-20
Posts: 8,075

### Re: π

Amartyanil wrote:

What is the requirement of Pi?

The original definition of pi is circumference / diameter in a circle.

But it can be shown (but don't ask me to do this ) that pi can be generated, approximately, by a number of series and recursive processes.

http://en.wikipedia.org/wiki/Pi

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #5 2013-08-10 00:43:26

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,829
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### Re: π

But it can be shown (but don't ask me to do this  ) that pi can be generated, approximately, by a number of series and recursive processes.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #6 2013-08-10 00:48:06

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: π

You already know how to use some programs to do this because I taught you the spigot algorithm.

Do you want to see a series done in another way?

To cover this right we will have to get into series, continued fractions, AGM, geometric construction, and the newest methods that offer amazing convergence for billions of digits.

Get access to maxima or whatever powerhouse you like and let's go!

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #7 2013-08-10 01:08:48

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,829
Website

### Re: π

Very good!

But I wanted to know that how can you show that Circumference/Diameter = 4(1/1 - 1/3 + 1/5-1/7+...)

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #8 2013-08-10 01:16:01

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: π

That is easy, it is based on the Taylor series for arctan(x).

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #9 2013-08-10 01:22:58

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,829
Website

### Re: π

So, you knw it. Would you please show?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #10 2013-08-10 01:26:49

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: π

Now Gregory a long time ago used the Taylor series or something else to derive this formula:

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #11 2013-08-10 01:32:54

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,829
Website

### Re: π

Ok, now?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #12 2013-08-10 01:35:02

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,829
Website

### Re: π

Sorry, I got it

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #13 2013-08-10 01:37:26

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: π

If we take this formula and plug in x = 1 we get

Do you follow?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #14 2013-08-10 01:38:57

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,829
Website

### Re: π

yes, I get it now

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #15 2013-08-10 01:41:40

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: π

Then you have seen what Leibniz saw over 300 years ago:

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #16 2013-08-10 01:45:42

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,829
Website

### Re: π

But wasn't the value of pi known to Archimedes too?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #17 2013-08-10 01:47:24

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: π

He established it between an upper and a lower bound but as far as I know he had no exact form for the answer. We will look at his method later.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #18 2013-08-10 01:57:37

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,829
Website

### Re: π

ok

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #19 2013-08-10 01:59:48

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: π

Did you generate a few terms of that series?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #20 2013-08-10 02:09:04

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,829
Website

### Re: π

No, after I finish painting..

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #21 2013-08-10 02:09:57

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: π

You will get a nice surprise when you do...

What are you painting?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #22 2013-08-10 02:16:59

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,829
Website

### Re: π

The bengali goddess of snakes. We are going to build a 9 feet scroll

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #23 2013-08-10 02:24:06

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: π

I have seen some pictures, good looking but bad tempered.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #24 2013-08-10 02:30:32

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,829
Website

### Re: π

When did you see them?

I never liked that part of the mythology. She became violent to a guy who refused to worship her. That story is so very pesimistic, stupid and western-like.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #25 2013-08-10 02:34:26

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606