Definition:Paraboloid/Elliptical

Definition

Definition 1

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 elliptical paraboloid if and only if $P_3$ is an ellipse.

Definition 2

An elliptical paraboloid is a paraboloid which can be embedded in a Cartesian $3$-space and described by the equation:

$\dfrac {y^2} {b^2} + \dfrac {z^2} {c^2} = 2 a x$

Also see

• Equivalence of Definitions of Elliptical Paraboloid

• Results about elliptical paraboloids can be found here.

Sources

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