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

Amartyanil
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Registered: 2013-05-27
Posts: 39

π

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

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,820
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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'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 84,285

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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

bob bundy
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Registered: 2010-06-20
Posts: 6,294

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

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,820
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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.

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

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 84,285

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,820
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'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,285

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,820
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'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,285

Re: π

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,820
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'
'Humanity is still kept intact. It remains within.' -Alokananda

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,820
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'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,285

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,820
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'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,285

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,820
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'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,285

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,820
Website

Re: π

ok smile


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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,285

Re: π

Did you generate a few terms of that series?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,820
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'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,285

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,820
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'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,285

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,820
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'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,285

Re: π

About 10 minutes ago.

The mythology is where the meat is.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

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