Definition:Hyperbolic Paraboloid/Definition 1

Definition

Let $\PP$ be a paraboloid.

Let $P_1$ and $P_2$ be two plane sections of $\PP$ such that both $P_1$ and $P_2$ are parabolas.

Let $P_3$ be a plane section of $\PP$ perpendicular to both $P_1$ and $P_2$.

Then $\PP$ is an hyperbolic paraboloid if and only if $P_3$ is a hyperbola.

Also see

• Equivalence of Definitions of Hyperbolic Paraboloid

• Results about hyperbolic paraboloids can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): paraboloid
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): paraboloid