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

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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'

I'm not crazy, my mother had me tested.

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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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 100,338

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.** **Thinking is cheating.**

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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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 100,338

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.** **Thinking is cheating.**

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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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 100,338

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.** **Thinking is cheating.**

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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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 100,338

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.** **Thinking is cheating.**

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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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 100,338

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.** **Thinking is cheating.**

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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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 100,338

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.** **Thinking is cheating.**

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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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 100,338

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.** **Thinking is cheating.**

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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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 100,338

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.** **Thinking is cheating.**

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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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 100,338

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.** **Thinking is cheating.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 15,955

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?

Here lies the reader who will never open this book. He is forever dead.

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: 100,338

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.** **Thinking is cheating.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 15,955

Maybe they are randomly placed but with a different distribution.

Here lies the reader who will never open this book. He is forever dead.

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: 100,338

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.** **Thinking is cheating.**

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