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#1 2013-08-10 13:53:46

Amartyanil
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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

#2 2013-08-10 16:33:26

Agnishom
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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 (2013-08-10 16:34:04)


'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'
'Who are you to judge everything?' -Alokananda

#3 2013-08-10 20:51:10

bobbym
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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.

#4 2013-08-10 22:16:26

bob bundy
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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

#5 2013-08-10 22:43:26

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#6 2013-08-10 22:48:06

bobbym
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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.

#7 2013-08-10 23:08:48

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#8 2013-08-10 23:16:01

bobbym
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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.

#9 2013-08-10 23:22:58

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#10 2013-08-10 23:26:49

bobbym
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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.

#11 2013-08-10 23:32:54

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#12 2013-08-10 23:35:02

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#13 2013-08-10 23:37:26

bobbym
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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.

#14 2013-08-10 23:38:57

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#15 2013-08-10 23:41:40

bobbym
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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.

#16 2013-08-10 23:45:42

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#17 2013-08-10 23:47:24

bobbym
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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.

#18 2013-08-10 23:57:37

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#19 2013-08-10 23:59:48

bobbym
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Online

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.

#20 2013-08-11 00:09:04

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#21 2013-08-11 00:09:57

bobbym
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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.

#22 2013-08-11 00:16:59

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#23 2013-08-11 00:24:06

bobbym
Administrator

Online

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.

#24 2013-08-11 00:30:32

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#25 2013-08-11 00:34:26

bobbym
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Online

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.

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