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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?

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'
'The whole person changes, why can't a habit?' -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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

#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 ) that pi can be generated, approximately, by a number of series and recursive processes.

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.

'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'
'The whole person changes, why can't a habit?' -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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

#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'
'The whole person changes, why can't a habit?' -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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

#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'
'The whole person changes, why can't a habit?' -Alokananda

#10 2013-08-10 23:26:49

bobbym

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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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

#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'
'The whole person changes, why can't a habit?' -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'
'The whole person changes, why can't a habit?' -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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

#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'
'The whole person changes, why can't a habit?' -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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

#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'
'The whole person changes, why can't a habit?' -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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

#18 2013-08-10 23:57:37

Agnishom
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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'
'The whole person changes, why can't a habit?' -Alokananda

#19 2013-08-10 23:59:48

bobbym

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Re: π

Did you generate a few terms of that series?

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

#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'
'The whole person changes, why can't a habit?' -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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

#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'
'The whole person changes, why can't a habit?' -Alokananda

#23 2013-08-11 00:24:06

bobbym

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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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

#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'
'The whole person changes, why can't a habit?' -Alokananda

bobbym

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