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Re: Going off on a tangent (kind of) : find y

Posted: May 18th, 2017, 6:15 pm
by Cuchulainn
Can someone explain why this is of any interest at all?!
You mean, like high-school geometry?

Re: Going off on a tangent (kind of) : find y

Posted: May 18th, 2017, 6:19 pm
by Cuchulainn
I am still waiting on a solution from Paul and T4A

OK what about [$]x^2  = 2[$]. Find x. All of them.

Re: Going off on a tangent (kind of) : find y

Posted: May 18th, 2017, 6:25 pm
by Paul
Have you been at the Brennivín again? Or did you fall down a volcano? We are worried about you.

Re: Going off on a tangent (kind of) : find y

Posted: May 18th, 2017, 6:29 pm
by Traden4Alpha
I am still waiting on a solution from Paul and T4A
Is y in degrees, gradians, radians, mils, arc-seconds, revolutions, .... or what?

Spacecraft have crashed over this issue!
OK what about [$]x^2  = 2[$]. Find x.
[$]x^2  = 2[$]
^ there it is!

Would you prefer -1.41421356237...?

Re: Going off on a tangent (kind of) : find y

Posted: May 18th, 2017, 6:37 pm
by Paul
I am still waiting on a solution from Paul and T4A

OK what about [$]x^2  = 2[$]. Find x.
It's a trick question. Notice the different typeface. So it's just after "Find"

Re: Going off on a tangent (kind of) : find y

Posted: May 18th, 2017, 6:48 pm
by Traden4Alpha
I am still waiting on a solution from Paul and T4A

OK what about [$]x^2  = 2[$]. Find x.
It's a trick question. Notice the different typeface. So it's just after "Find"
Damn! But it's worse than that. There's no EOL character or even a semicolon after the "x" so the find command is still incomplete.

Re: Going off on a tangent (kind of) : find y

Posted: May 18th, 2017, 6:50 pm
by Paul
Back to primary school for us!

Re: Going off on a tangent (kind of) : find y

Posted: May 18th, 2017, 6:57 pm
by Cuchulainn
I am still waiting on a solution from Paul and T4A

OK what about [$]x^2  = 2[$]. Find x.
It's a trick question. Notice the different typeface. So it's just after "Find"
Damn!  But it's worse than that.  There's no EOL character or even a semicolon after the "x" so the find command is still incomplete.
Ah! Back to multiple choice questions!
You are going off on a tangent. Focus.

I like "it's" here.

Re: Going off on a tangent (kind of) : find y

Posted: May 18th, 2017, 7:09 pm
by Cuchulainn
Back to primary school for us!
It is possible to write it using [$]\arcsin[$] if you prefer.

Re: Going off on a tangent (kind of) : find y

Posted: May 18th, 2017, 7:09 pm
by ppauper
I am still waiting on a solution from Paul and T4A

OK what about [$]x^2  = 2[$]. Find x.
It's a trick question. Notice the different typeface. So it's just after "Find"
Damn!  But it's worse than that.  There's no EOL character or even a semicolon after the "x" so the find command is still incomplete.
an old joke
Image

Re: Going off on a tangent (kind of) : find y

Posted: May 18th, 2017, 8:17 pm
by Traden4Alpha
It's a trick question. Notice the different typeface. So it's just after "Find"
Damn!  But it's worse than that.  There's no EOL character or even a semicolon after the "x" so the find command is still incomplete.
Ah! Back to multiple choice questions!
You are going off on a tangent. Focus.

I like "it's" here.
Ppauper already has the best answer for this specific problem as stated by this specific problem poster.

I did ponder building an analog computing version using a circle 0.2 meters in radius but that's when I realized that y could not be both an angle and a distance. Hence, units are a showstopper!

It's also interesting that if eccentricity is a variable, there's only a miniscule range of values (about [$]-3.8 < \varepsilon < +2.1[$]) where there's a unique solution. The whole system seems very non-robust to the broader parametric space but then I assume the numbers were carefully cherry-picked to lead the student to a particular approach to a numerical solution rather than a more general solution on the entire set of possible values of x and eccentricity.

Re: Going off on a tangent (kind of) : find y

Posted: May 18th, 2017, 8:27 pm
by Cuchulainn
But it took you 5 noisy posts to get this stage. 

The problem has nothing to do with units!!! It's a matematical (not engineering) problem that has 0, 1 or many solutions. That's the nub.(read Banach, for example).

Ppauper already has the best answer for this specific problem as stated by this specific problem poster.

How did you get to this conclusion? "best" in what sense? BTW ppauper gave two possible solutions.

Sadly, you have killed this thread before it even got off the ground.

It's also interesting that if eccentricity is a variable, there's only a miniscule range of values (about 3.8<ε<+2.1−3.8<ε<+2.1
) where there's a unique solution. The whole system seems very non-robust to the broader parametric space but then I assume the numbers were carefully cherry-picked to lead the student to a particular approach to a numerical solution rather than a more general solution on the entire set of possible values of x and eccentricity.


No kidding, Sherlock.

Re: Going off on a tangent (kind of) : find y

Posted: May 18th, 2017, 8:39 pm
by Paul
Five seconds with pencil and paper (and most of that time spent finding the pencil and paper) or half a second in your head, and you can sketch the problem and see what's happening. Great if this were a forum for twelve-year olds.

But I was waiting for the twist...and it never came. Compare and contrast the "Russian," "Arctan," "Cards," etc.

Re: Going off on a tangent (kind of) : find y

Posted: May 18th, 2017, 8:41 pm
by Traden4Alpha
But it took you 5 noisy posts to get this stage. 

The problem has nothing to do with units!!! It's a matematical (not engineering) problem that has 0, 1 or many solutions. That's the nub.(read Banach, for example).

Ppauper already has the best answer for this specific problem as stated by this specific problem poster.

How did you get to this conclusion? "best" in what sense? BTW ppauper gave two possible solutions.

Sadly, you have killed this thread before it even got off the ground.
Sorry!

But your thread title seemed to implicitly encourage tangents and no where was it stated that this was strictly a math problem. I often use my pocket calculator for brainteasers and it gives different answers for sin(y) depending on the angle mode.

----

What direction did you want this thread to go before my eccentricity collided with yours?

Re: Going off on a tangent (kind of) : find y

Posted: May 18th, 2017, 8:54 pm
by Cuchulainn
You need to read up on conic sections (you cannot have negative eccentricity as you claim) and there is an analytical formula for y for all values of the eccentricity. 

Please correct me if I have misunderstood your post.

The fixed point solutions is iterative and it does converge slowly ... check out Bessel's solution to Kepler's problem you will find a better exact solution.

But your thread title seemed to implicitly encourage tangents and no where was it stated that this was strictly a math problem. 
Then ask me to clarify if something is not clear. I did indeed not mention that it was Kepler's equation..