Hyperbolic paraboloid
= Hyperbolic paraboloid
A hyperbolic paraboloid is a saddle-shaped quadric such as $z=xy$. Its graph parametrization $(x,y,xy)$ has <Gaussian curvature> $-1/(1+x^2+y^2)^2$ and is regular everywhere. It is not a hyperboloid: their quadratic equations have different forms.