Surface parametrization

  1. I'm having problems understanding surface parametrization from differential geometry.

    We are given two general forms for parametrization:
    [tex]\alpha[/tex](u,v) = (u,v,0)
    and x(u,v)=(u,v,f(u,v))


    This is one I'm especially stuck on:

    y=Cosh(x) about the x-axis

    [tex]\alpha[/tex](u,v)=(u, Cosh[v],0)

    x(u,v) = (u, Cosh[v]cos(u), Cosh[v]sin(u))

    I think that's right.
     
  2. jcsd
  3. I do not understand the notation in these "general forms". Which textbook are you using?
     
  4. tiny-tim

    tiny-tim 26,044
    Science Advisor
    Homework Helper

    hi chaotixmonjuish! :smile:

    (have an alpha: α and a theta: θ :wink:)
    are you talking about the surface of revolution obtained by rotating y = coshx about the x-axis?

    if so, if one of your parameters (u) is equal to x, then the other sensible paramter to choose would be θ, an angle round the x-axis …

    (so you'll get a nice "square-ish" (x,θ) grid on the surface)

    anyway, your y will always be cosh(u), won't it, not cosh of some other parameter v ? :wink:
     
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