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**Amartyanil****Member**- Registered: 2013-05-27
- Posts: 39

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

"The most incomprehensible thing about the universe is that it is comprehensible." -Albert Einstein

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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)*

'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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,443

Hi Amartyanil;

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,383

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

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

'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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,443

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!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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+...)

'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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,443

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,443

We start with the trig identitiy

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Ok, now?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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Sorry, I got it

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,443

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

Do you follow?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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yes, I get it now

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,443

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,443

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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ok

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,443

Did you generate a few terms of that series?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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No, after I finish painting..

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,443

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

What are you painting?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,443

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,443

About 10 minutes ago.

The mythology is where the meat is.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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