# Proof - Express in Clyndrical Coordinates

1. Jun 25, 2012

### forestmine

Proof -- Express in Clyndrical Coordinates

1. The problem statement, all variables and given/known data

Show that when you express ds^2 = dx^2 + dy^2 +dz^2 in cylindrical coordinates, you get ds^2 = dr^2 + r^2d^2 + dz^2.

2. Relevant equations

x=rcosθ
y=rsinθ
z=z

3. The attempt at a solution

EDIT// I was really over thinking this...think I've got it figured out. Thanks anyways!

I'm somewhat confused about the notation here and how to really go about this. My first thought was just to plug in some values...

ds^2 = d(r^2*cos^2(θ)) + d(r^2*sin^2(θ)) + dz^2

The d(__) are really throwing me off here. I don't see how the second term in the right hand side of the proof goes to r^2d^2.

Ah really lost here. Just need some help in the right direction.

Thank you!

Last edited: Jun 25, 2012
2. Jun 25, 2012

### Muphrid

Re: Proof -- Express in Clyndrical Coordinates

You should interpret $dx^2$ as meaning $(dx)^2$.

3. Jun 25, 2012

### forestmine

Re: Proof -- Express in Clyndrical Coordinates

I think that was my hang up exactly. Thanks!