- #1
Karnage1993
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Homework Statement
Let S be the self-intersecting rectangle in ##\mathbb{R}^3## given by the implicit equation ##x^2−y^2z = 0##. Find a parametrization for S.
Homework Equations
The Attempt at a Solution
This is my first encounter with a surface like this. The first thing that came to my mind was letting ##z = f(x,y)## so that the parametrization can be given as:
##\Phi(u,v) = (u,v,\displaystyle \frac{u^2}{v^2})##
The problem I'm having is finding the limits for ##u## and ##v##. When I plugged the implicit equation into Mathematica, the surface looks like an X shape from above, though I had to expand the range for the axes by a very large amount for it to look like that. I do know that ##v## has to be non-zero, but that's pretty much it.
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