Definitions
from The American Heritage® Dictionary of the English Language, 5th Edition.
 noun A surface having parabolic sections parallel to a single coordinate axis and elliptic or circular sections perpendicular to that axis.
from The Century Dictionary.
 noun A solid or surface of the second degree some of whose planesections are parabolas.
 Paraboloidal.
 noun The solid generated by the revolution of a parabola about its axis; a parabolic conoid.
 noun A curve whose equation is of the form ax = y.
from the GNU version of the Collaborative International Dictionary of English.
 noun (Geom.) The solid generated by the rotation of a parabola about its axis; any surface of the second order whose sections by planes parallel to a given line are parabolas.
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 noun mathematics A
surface having aparabolic cross section parallel to anaxis , andcircular orelliptical cross sectionperpendicular to the axis; especially thesurface of revolution of aparabola .
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 noun a surface having parabolic sections parallel to a single coordinate axis and elliptic sections perpendicular to that axis
Etymologies
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Examples

A paraboloid is a threedimensional shape that has two terms of x, y, or z that are squared and one term of x, y, or z that is not.

When one squared term is negative and one is positive, like in the second equation, the paraboloid is a hyperbolic paraboloid (shaped like a saddle When both squared terms are positive, like in the first equation, the paraboloid is an

If you aren't quite sure what a hyperbolic paraboloid is, it's a mathematical term to describe a surface shaped like a saddle.

"Geometrically, it's a hyperbolic paraboloid, but that's not very sexy."

We're back to my hyperbolic, paraboloid, transitional floating zone.

Gaudi, of course, is the leading genius: his structural experiments took off from Catalan Gothic to produce amazing paraboloid arches; his rich details of fauna and flora in iron, stone or wildly colorful bits of tile drew on the work of the best Catalonian craftsmen.

It has 4 nester hyperboloid mirrors and 4 nested paraboloid mirrors to focus the xrays.

It is not the scope of the synagogue that sets it apart, or the technical marvel of his hallmark hyperbolic paraboloid roofs — which he describes as being shaped something like a Pringles potato chip.

The saddleshaped structure is also known as a hyperbolic paraboloid surface, or an anticlastic surface.

And interestingly, this turns out  the stomatopod saddle turns out to be the first described biological hyperbolic paraboloid spring.
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