I Proving radial properties of particular dimensionless surface plots?

We have a surface function z = f(x,y) ; f(x,y) only contains dimensionless constants, and is itself dimensionless.

If we convert it to cylindrical co-ordinates, z = f(r,θ) , does z only depend on θ?
Meaning we can remove r from the equation, literally.

BvU

Homework Helper
z only depend on θ?
Obviously not ! Look at z(r) for e.g. $\theta=\pi/4$

Obviously not ! Look at z(r) for e.g. $\theta=\pi/4$
what's the equation of f(r,θ) ?

BvU

Homework Helper
Or do you mean: if $\theta=pi/4$ then $f(r,\theta) = f(x,x)$ with $x=r/\sqrt 2$ ?

I thought you had come up with a counter-example to prove the conjecture false, so I was wondering what that counter-example function was.

BvU

Homework Helper
Conjecture: z is independent of r
Counter example: along the diagonal I see z go up, down, up again and then down again -- clearly not independent of r

Conjecture: z is independent of r
Counter example: along the diagonal I see z go up, down, up again and then down again -- clearly not independent of r
sorry, what's the equation of the counter-example function?

BvU

Homework Helper
However, I see an interpretation of
f(x,y) only contains dimensionless constants
If x and y do not occur, then f itself is a constant, therefore independent of r, but equall indepndent of $\theta$

However, I see an interpretation of
If x and y do not occur, then f itself is a constant, therefore independent of r, but equall indepndent of $\theta$
Oh, so just z = c , the surface plot being just a flat plane?
That's a trivial case and the conjecture is that there'll be r-independence in all cases, whichever function you use. As long as the function satisfies the two conditions.

BvU

Homework Helper
In which case your picture is wrongfooting any good-willing helper

In which case your picture is wrongfooting any good-willing helper
Well, it's certainly not an r-independent function, though I just wanted to make sure people got the idea of "surface plot" immediately.

BvU

Homework Helper
As long as the function satisfies the two conditions
I don't see what the dimensionlessness of f or its contained constants has to do with it

BvU

Homework Helper
just wanted to make sure people got the idea of "surface plot" immediately
Well, this exercise creates more confusion than it removes

Well, this exercise creates more confusion than it removes
Well, no equations are given, the image not referenced, cos its a general conjecture.

I should add some details in the OP though, but its too late now.

I don't see what the dimensionlessness of f or its contained constants has to do with it
Its part of the conjecture. Unless its possible to expand the generality of the conjecture even further.

"Proving radial properties of particular dimensionless surface plots?"

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