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I also use Python

'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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**LeoC123****Member**- Registered: 2013-02-23
- Posts: 3

Yeah, I'm currently using Python because it is so much cleaner in style. It really just teaches you the concepts of computer science without really having to focus too much on syntax

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I do not understand the program at podt #1

'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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,640

Hi;

He is making use of a geometric probability to evaluate pi.

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

**If it ain't broke, fix it until it is.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,646

I do not tend to use Python at all anymore.

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Hi bobbym,

I don't understand at all.

'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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,640

Hi Agnishom;

You are picking random numbers in the range 0 - 1 for x and y, yes?

Do you follow so far, I can not upload a drawing so I will talk you through.

*Last edited by bobbym (2013-02-24 21:30:01)*

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

**If it ain't broke, fix it until it is.**

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Yes, two random numbers b/w 0 & 1

Then they are checking how many of them satisfy x^2 + y^2 < 1

So?

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

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,640

You can pair the x's and y's to make points. They would all be inside of a 1 x 1 rectangle in the first quadrant. Do you agree?

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

**If it ain't broke, fix it until it is.**

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Ya.. All the points within a radius of 1 in the 1st quadrant

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

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,640

Not yet. You are jumping ahead. If we generate x's from 0 to 1 and y's from 0 to 1 and form ordered pairs and then plot them we would get something like this:

*Last edited by bobbym (2013-02-25 00:37:05)*

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

**If it ain't broke, fix it until it is.**

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And then we check how many of them are within a radius of 1 ?

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

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,640

Yes, and form the ratio

if you throw a lot of points it will approximate π/4.

This is called "Monte Carlo Simulation" and is a very powerful technique.

*Last edited by bobbym (2013-02-25 00:57:14)*

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

**If it ain't broke, fix it until it is.**

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Wonderful!

However that would hugely depend on the capability to generate random numbers

I think it would be a better idea to try this

```
...
for x in xrange(0.1, 1.0, 0.01):
for y in xrange(0.1, 1.0, 0.01):
.....
```

So that the points are not taken at random

*Last edited by Agnishom (2013-02-25 02:05:29)*

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

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,640

Hi;

The randomness is very important. It is the whole key to the algorithm.

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

**If it ain't broke, fix it until it is.**

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Why??? What If we try all the possible points?

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

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,640

It would take too many to try them all there are an infinite number. The random generator samples the points that your scheme might miss.

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

**If it ain't broke, fix it until it is.**

**Online**

I will see which is better .... I shall do the experiment

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

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,640

It is easy to design areas that a uniform spread of points such as yours might miss.

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

**If it ain't broke, fix it until it is.**

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I did it.

You seem to be correct........

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

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,640

Hi;

That was an interesting idea though.

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

**If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 15,937

Hi bobbym

Is it just me or do the points in the plot in post #36 look a little denser near the line x=1/2?

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,640

Yes, that was when we could not upload any pictures and I had to use one from the internet. Unfortunately I chose one from a math forum. The guy who wrote the routine did a bad job and the points are not randomly placed.

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

**If it ain't broke, fix it until it is.**

**Online**

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 15,937

Maybe they are randomly placed but with a different distribution.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,640

Nah, his method of generating random numbers was not good.

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

**If it ain't broke, fix it until it is.**

**Online**