Surface parametrization

  • Thread starter Tony11235
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My problem is finding a surface parametrization of the surface x^2-y^2=1, where x>0, -1<=y<=1 and 0<=z<=1.

I know that x and y in x^2-y^2=1, can be represented as cosh(u) and sinh(u), but I'm not sure what to do for the z part. Any quick help?
 

EnumaElish

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Tony11235 said:
My problem is finding a surface parametrization of the surface x^2-y^2=1, where x>0, -1<=y<=1 and 0<=z<=1.
Did you intend your equation not to contain any z terms?
 
EnumaElish said:
Did you intend your equation not to contain any z terms?
Should it contain a z component? I was assuming it should because it is a surface parametrization but maybe not.
 

EnumaElish

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Does a line on the XY plane contain a y component? Unless it's a vertical line, it does.
 

HallsofIvy

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A parametrization of a surface, a 2 dimensional figure, necessarily involves 2 parameters. Since there is no "z" in your equations, you might consider taking z itself as a parameter or say z= v where v is a parameter, then look for a parametrization of the hyperbola x2- y[/sup]2[/sup]. Since it is a hyperbola, the hyperbolic functions leap to mind!
 

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