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

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

"You can never be too old or too young. A person's age is irrelevant." - bobbym

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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)*

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,856

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.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,525

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.

Some are given on this page:

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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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.

I wanna see this. Someone please help

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,856

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.**

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Very good!

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

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,856

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.**

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So, you knw it. Would you please show?

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,856

We start with the trig identitiy

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.**

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Ok, now?

'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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Sorry, I got it

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,856

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.**

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yes, I get it now

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,856

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.**

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

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,856

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.**

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ok

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,856

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.**

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No, after I finish painting..

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,856

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.**

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

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,856

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.**

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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.

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,856

About 10 minutes ago.

The mythology is where the meat is.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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