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

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#2426 2013-10-09 23:31:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,260

Re: What do you think?

Hi gAr;


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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#2427 2013-10-09 23:35:27

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

Re: What do you think?


"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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#2428 2013-10-09 23:54:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,260

Re: What do you think?

Hi gAr;


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.

Online

#2429 2013-10-09 23:58:06

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

Re: What do you think?

That's nice!


"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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#2430 2013-10-10 00:01:28

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,260

Re: What do you think?

Hi gAr;

Thanks for the nice solution and this problem is done!


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.

Online

#2431 2013-10-10 00:06:35

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

Re: What do you think?

You're welcome and thank you too for the problem!


"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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#2432 2013-10-10 00:37:24

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

Re: What do you think?

Hi gAr

One question for the solution in #2424: Doesn't P change as well? It isn't always (a,0)?


“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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#2433 2013-10-10 00:43:53

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

Re: What do you think?

Hi anonimnystefy,

We keep that fixed as a reference point, it won't change the answer and we'll have one less integral to calculate..


"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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#2434 2013-10-10 00:49:11

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

Re: What do you think?

But, then all of the trangles have one point in (a,0).


“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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#2435 2013-10-10 00:54:28

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

Re: What do you think?

Yes, but we still get all possible triangles.


"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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#2436 2013-10-10 00:57:36

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

Re: What do you think?

Are you sure?


“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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#2437 2013-10-10 01:05:33

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

Re: What do you think?

Yes, checked varying the third point too.


"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

#2438 2013-10-10 01:17:31

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

Re: What do you think?


"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

#2439 2013-10-10 02:04:50

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

Re: What do you think?

Hm, okay then. Thanks for the solution!


“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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#2440 2013-10-10 05:57:17

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

Re: What do you think?

You're welcome.


"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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#2441 2013-10-10 21:41:43

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

Re: What do you think?

Anybody tried for expected area of quadrilateral in an ellipse?


"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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#2442 2013-10-10 22:00:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,260

Re: What do you think?

Not yet!


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.

Online

#2443 2013-10-10 22:06:31

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

Re: What do you think?

Okay,  the answer I derived was double that of simulated result. Don't know which one's incorrect!


"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

#2444 2013-10-10 22:10:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,260

Re: What do you think?

Do you mean a simple or complex quadrilateral?


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.

Online

#2445 2013-10-10 22:13:35

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

Re: What do you think?

Simple quadrilaterals.


"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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#2446 2013-10-10 22:14:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,260

Re: What do you think?

That complicates the simulation. The order of the points seem to be important.


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.

Online

#2447 2013-10-10 22:18:42

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

Re: What do you think?

I sorted the angles four angles first, then calculated the area during simulation.


"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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#2448 2013-10-10 22:28:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,260

Re: What do you think?

Did you use the same ellipse? What did you get?


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.

Online

#2449 2013-10-10 22:36:59

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

Re: What do you think?

For the same ellipse, the simulation showed about 3.03286.


"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

#2450 2013-10-10 22:40:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,260

Re: What do you think?

Hi gAr;

Okay, I will start to work on it now and see if I can get an answer close to that.


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.

Online

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