Obviously not ! Look at z(r) for e.g. ##\theta=\pi/4##z only depend on θ?
what's the equation of f(r,θ) ?Obviously not ! Look at z(r) for e.g. ##\theta=\pi/4##
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.You are asking me ?
sorry, what's the equation of the counter-example function?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
If x and y do not occur, then f itself is a constant, therefore independent of r, but equall indepndent of ##\theta##f(x,y) only contains dimensionless constants
Oh, so just z = c , the surface plot being just a flat plane?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##
Well, it's certainly not an r-independent function, though I just wanted to make sure people got the idea of "surface plot" immediately.In which case your picture is wrongfooting any good-willing helper
I don't see what the dimensionlessness of f or its contained constants has to do with itAs long as the function satisfies the two conditions
Well, this exercise creates more confusion than it removesjust wanted to make sure people got the idea of "surface plot" immediately
Well, no equations are given, the image not referenced, cos its a general conjecture.Well, this exercise creates more confusion than it removes
Its part of the conjecture. Unless its possible to expand the generality of the conjecture even further.I don't see what the dimensionlessness of f or its contained constants has to do with it