Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**Amartyanil****Member**- From: Calcutta, West Bengal, India
- Registered: 2013-05-27
- Posts: 40

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

Offline

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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,494

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,528

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

Offline

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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,494

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

Offline

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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,494

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

Offline

So, you knw it. Would you please show?

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,494

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.**

Offline

Ok, now?

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

Sorry, I got it

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,494

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.**

Offline

yes, I get it now

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,494

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

**In mathematics, you don't understand things. You just get used to them.**

Offline

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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,494

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.**

Offline

ok

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,494

Did you generate a few terms of that series?

**In mathematics, you don't understand things. You just get used to them.**

Offline

No, after I finish painting..

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,494

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.**

Offline

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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,494

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

**In mathematics, you don't understand things. You just get used to them.**

Offline

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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,494

About 10 minutes ago.

The mythology is where the meat is.

**In mathematics, you don't understand things. You just get used to them.**

Offline