Profile Curve

**Student57** · March 11th 2011, 01:06 PM

This is translated from my own language, so feel free to correct me if I'm using a wrong translation.

A profile curve in (x, z)-plan is given by the graph of the function z = ln (x), where
x $\epsilon$ [1, 2]. The profile curve is rotated the angle $Pi$ around z-axis counterclockwise as seen from the z-axis'
positive end. This yields the rotation surface F.

Find a parametrization for the profile curve and F.

**zzzoak** · March 13th 2011, 02:01 PM

$ F=ln(\sqrt{x^2+y^2}) $

In cylindrical coordinates

$ F=ln \ r \ . $

**Student57** · March 14th 2011, 01:18 PM

Still need to find r(u,v) any help here?

**zzzoak** · March 14th 2011, 02:31 PM

If this helps:

$ u=x $

$ v=y $

$ F=ln \sqrt{u^2+v^2} $

where

$ v>=0 \ and \ 1<=\sqrt{u^2+v^2}<=2 \ . $

**Student57** · March 15th 2011, 03:11 AM

I think I'm being misunderstood.
I need to find the parametrization/parametric equation for the profile curve and F.

I was given this general equation:
$r(u,v)=(x(u,v),y(u,v)$

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