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.