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Transforming line elements

  1. Oct 19, 2016 #1
    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. jcsd
  3. Oct 20, 2016 #2

    strangerep

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    Science Advisor

    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.)
     
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