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

You are not logged in.

- Topics: Active | Unanswered

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Hi,

"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."

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,574

Hi;

I had to trick it into getting an answer. Those are pretty tough integrals.

Where do those problems come from?

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Yes, they are tough. What trick did you perform?

You have been there before: http://people.missouristate.edu/lesreid/Adv97.html

(b) was a part I did thinking the answer would be same as (a)

Will be back soon.

"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."

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,574

For one thing an assumption was necessary for theta and both integrals had to be done in pieces. For some reason this did the trick.

Forgot that place or lost the link.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

I see..

It's delightful to work on such problems.

"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."

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,574

I agree. But they can be trying too.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

That's true, many things can go wrong here.

Simulation helps a ton!

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,574

It sure does but sometimes even coming up with a simulation is difficult and time consuming.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Yeah, sometimes, particularly when involving a geometrical shape instead of just points and lines.

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,574

The circle is very tricky. I had to write new routines for generating points inside and on the circle that have the right distribution. It took a long time but next time I will be better prepared.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Mark H. told me how to get the points.

r^2 must be uniformly distributed in [0,a^2]. Then take the root of the generated values.

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,574

Hi;

What is that for?

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

'a' is the given radius (In our problem, a=1). 'r' is the distance of P from center.

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,574

So you used the square root of the random number you got from the uniform distribution twice to get (x,y)?

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Not twice, y can be fixed to 0.

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,574

But if you wanted to fill the circle with that idea you would have to use it for both (x,y)?

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

To fill a circle, obtain random angles in [0, 2π), then the points would be (r cos θ, r sin θ).

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,574

Hi;

That is close to what I did to. I will see you later, Thanks for the problems!

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Okay, see you later.

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

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,391

Hi gAr

You're right. I misread the problem and thought the P is a point **on** the circle.

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

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Hi anonimnystefy,

Okay.

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

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

New problem:

** There are two fair, six sided dice. 'A' throws a die till she gets a sequence of '11'. 'B' throws the other die till he gets a sequence of '12'.What is the probability that A throws the die more number of times than B?**

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,574

Hi gAr;

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Hi bobbym,

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,574

Hi gAr;

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline