# Parametrizing

• Mar 14th 2011, 06:18 AM
Student57
Parametrizing
http://i56.tinypic.com/rtkmir.png
Polar points in space

A point in space can be determined by its' polar coordinates.
On the figure above, P's polar coordinates are $\displaystyle (\rho,\phi,\varphi)$.
$\displaystyle \rho$ is the lenght |OP|. $\displaystyle \phi$ is the angle between the z-axe and the line OP, and $\displaystyle \varphi$ is the angle between the x-axes and the line OQ.

Two areas in the space is given by polar coordinates:
$\displaystyle A={(\rho,\phi,\varphi)|1 \leq \rho \leq 3, Pi/4 \leq \phi \leq Pi/3, 0 \leq \varphi \leq 3Pi/4$
$\displaystyle B={(\rho,\phi,\varphi)|2 \leq \rho \leq 4, Pi/4 \leq \phi \leq Pi/2, - Pi/4 \leq \varphi \leq Pi/4$

Find a parametrization for A and B and $\displaystyle A \cap B$

I'm so lost in this, I would really appreciate any help (Doh)
• Mar 14th 2011, 07:03 AM
HallsofIvy
What do you mean by "parameterization" for this? If you had a curve or surface, you could write them in terms of one or two parameters respectively. But these are three dimensional regions with the variables between fixed numbers. You will need three parameters to describe a three dimensional region- and the formulas you give are precisely such a parameterization.
• Mar 14th 2011, 01:12 PM
Student57
Quote:

Originally Posted by HallsofIvy
What do you mean by "parameterization" for this?

I need to find r(u,v) .. I have to translate from my own language, so if there is anything else, just ask and I'll try to explain differently.
:)