Transforming Cone Line Elements: Proving Flat Geometry?

[joshua2112]

Homework Statement

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?

Homework Equations

x=rcosφ
y=rsinφ

The Attempt at a Solution

ive tried several times but end up with cos and sin in my answer

 

[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.)