# Surface parametrization

by chaotixmonjuish
Tags: parametrization
 P: 287 I'm having problems understanding surface parametrization from differential geometry. We are given two general forms for parametrization: $$\alpha$$(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 $$\alpha$$(u,v)=(u, Cosh[v],0) x(u,v) = (u, Cosh[v]cos(u), Cosh[v]sin(u)) I think that's right.
 P: 1,412 I do not understand the notation in these "general forms". Which textbook are you using?
HW Helper
Thanks
P: 26,167
hi chaotixmonjuish!

(have an alpha: α and a theta: θ )
 Quote by chaotixmonjuish y=Cosh(x) about the x-axis $$\alpha$$(u,v)=(u, Cosh[v],0) x(u,v) = (u, Cosh[v]cos(u), Cosh[v]sin(u))
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 ?

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