I Proving radial properties of particular dimensionless surface plots?

  • Thread starter tade
  • Start date
462
11
surf_101.png


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

Science Advisor
Homework Helper
11,703
2,536
462
11
Obviously not ! Look at z(r) for e.g. ##\theta=\pi/4##
what's the equation of f(r,θ) ?
 

BvU

Science Advisor
Homework Helper
11,703
2,536
You are asking me ?
Or do you mean: if ##\theta=pi/4## then ##f(r,\theta) = f(x,x) ## with ##x=r/\sqrt 2## ?
 
462
11
You are asking me ?
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

Science Advisor
Homework Helper
11,703
2,536
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
 
462
11
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

Science Advisor
Homework Helper
11,703
2,536
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##
 
462
11
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

Science Advisor
Homework Helper
11,703
2,536
In which case your picture is wrongfooting any good-willing helper :rolleyes:
 
462
11
In which case your picture is wrongfooting any good-willing helper :rolleyes:
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

Science Advisor
Homework Helper
11,703
2,536
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

Science Advisor
Homework Helper
11,703
2,536
just wanted to make sure people got the idea of "surface plot" immediately
Well, this exercise creates more confusion than it removes
 
462
11
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.
 
462
11
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.
 

Want to reply to this thread?

"Proving radial properties of particular dimensionless surface plots?" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Top Threads

Top