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Tuesday, January 2, 2018

Desmos Graphing Calculator

I've been hanging out at Quora lately. A fair number of math problems show up there. Many of them are inane, like 'What is 2+2?", or "What is 3+3 x 3?".* But some advanced ones show up as well. Some of them are really ugly, I've never seen the like before, don't know what they're good for, or why anyone would care, but they make me curious so I've taken to plotting them on the Desmos Graphing Calculator.  It would be nice if you could simply copy the equation from Quora and then paste in Desmos. You can, but it doesn't translate properly, so you have to go in and fiddle with it enough for Desmos to understand it. Plus sometimes the equation (or expression) you get from Quora is missing something, or didn't get entered properly, so you have to muck with it to get anything graphable.

The equation for the Middle Green Circle on the graph comes from this question on Quora.




Outer Orange circle    x^{2\ }+\ y^2\ =\ 16     
Middle Green circle    e^{\left(y^2\ +\ x^2\ \right)^{.5}}\ =\ 16
Inner Orange circle    e^{.5\left(y^2\ +\ x^2\ \right)}\ =\ 16

The original equation from Quora.

f(x,y) = e^sqrt (x^2+y^2)


Mucking about with above equation and then typing Ctrl-Z causes the graph above to be redrawn. Actually, it doesn't matter what you were doing before, if you have done anything at all in Blogger's Editor, Ctrl-Z (Undo) causes the graph to be redrawn.

Taking the Middle Green Circle and changing it to a function gives us this
f(x,y)=e^{(x^2+y^2)^{.5}}
but Desmos doesn't know how to graph it.

Note that I have replaced the call to sqrt with an exponent. Desmos treats sqrt as four variables (s, q, r & t) being multiplied together.

Also capital X and capital Y mean something special, so don't use them until you figure out they do.

This post started as a test to see if I could copy and paste the equations, but I can see it's expanded a bit.

About the Math
The difference between the 2nd and 3rd equations is that one multiples the exponent of e by .5 and the other raises it the power of .5 which should be equivalent according to math.com's article on exponents (see the Power Rule). I don't quite understand why the graphs of these two equations should be different, but Desmos evidently thinks otherwise.

I set the expression equal to a constant (16) to get it to graph. Properly, it should be set to Z and graphed using a 3D graphing calculator. I found one that looks like it should do the job, but I've been having some trouble with it, so that's going to have to wait for another day.

* What's even weirder is how many answers the inane questions get. I made some sarcastic replies, but it's just endless. Besides, since some people think these questions are worth answering, I am trying to train myself to Pass on these questions, but it's really hard not to click Answer and just let them have it with both barrels. Gee wilkers pops, everyone knows the answer is 42. I mean it's the answer to everything, ain't it?

P.S. I just discovered that Google has a plot function.

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