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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,571

Hi;

**What is the expected distance between 2 points that are randomly placed in a square that is 1 foot by 1 foot?**

There is an analytical method but let's see what geogebra can do. Or rather, what I can do with geogebra.

For this one we will use some different features of geogebra like the spreadsheet.

1) Open up a spreadsheet and in column A,B,C and D put at the top random(). Pull the 4 columns down till you have 4 columns of 1000 random numbers.

2) Highlight columns A and B and right click and create a list of points.

3) Use the regular polygon tool to draw and click on (0,0) and (1,0) and enter 4 sides.

4) You should see something like the figure below.

5) In column E write Distance[(A1,B1),(C1,D1)] and pull it down until you have 1000 distances.

You should have 5 column of 1000 entries in each.

Enter in column F, Mean[E1:E1000] and see what you get. I got .51349 which is quite close to the exact analytical answer of

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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Could you please enlighten us with the analytical solution?

'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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,571

Hi Agnishom;

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

Here's a simulation with j

```
samp =: 100000
(+/%#)((((?samp$0)-(?samp$0))^2)+((?samp$0)-(?samp$0))^2)^%2
```

A result I got ≈ 0.520588

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Hi gAr

I see you know J! How good are you with it.

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

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi anonimnystefy,

That was my first program for a simulation!

I was thinking that it may be a good choice for simulations: fast to code and execute.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

It's fast to code in it only when you have a certain proficiency with it. Otherwise it takes a lot of time looking at the glossary for each individual character. I am guessing you've been using J for a while then?

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

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

That's right, we must know the glossary first.

Spent a couple of days going through that, this is my first j program of some use.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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