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Hi gAr;
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
 Always satisfy the Prime Directive of getting the right answer above all else.
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"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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Hi gAr;
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
 Always satisfy the Prime Directive of getting the right answer above all else.
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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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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.
If it ain't broke, fix it until it is.
 Always satisfy the Prime Directive of getting the right answer above all else.
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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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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
The knowledge of some things as a function of age is a delta function.
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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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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
The knowledge of some things as a function of age is a delta function.
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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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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
The knowledge of some things as a function of age is a delta function.
Offline

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

"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

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

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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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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Not yet!
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
 Always satisfy the Prime Directive of getting the right answer above all else.
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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."
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Do you mean a simple or complex quadrilateral?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
 Always satisfy the Prime Directive of getting the right answer above all else.
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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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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.
If it ain't broke, fix it until it is.
 Always satisfy the Prime Directive of getting the right answer above all else.
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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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Did you use the same ellipse? What did you get?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
 Always satisfy the Prime Directive of getting the right answer above all else.
Offline

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."
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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.
If it ain't broke, fix it until it is.
 Always satisfy the Prime Directive of getting the right answer above all else.
Offline