Transforming line elements

1. Oct 19, 2016

joshua2112

1. The problem statement, all variables and given/known data
Consider the cone defined by z = √ x 2 + y 2 . By defining new coordinates ρ, φ where x = ρ cos φ, y = ρ sin φ, show that the line element on the cone is ds^2 = 2dρ^2 + ρ^2dφ^2 . Why does this result prove the cone has flat geometry?

2. Relevant equations
x=rcosφ
y=rsinφ

3. The attempt at a solution
ive tried several times but end up with cos and sin in my answer

Last edited: Oct 19, 2016
2. Oct 20, 2016

strangerep

No one can help you if you don't show your attempted solution. (And yes, now would be a good time to start learning how to do latex on this forum.)