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Hyperboloid vs. Paraboloid — What's the Difference?

Hyperboloid vs. Paraboloid — What's the Difference?

Difference Between Hyperboloid and Paraboloid

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Hyperboloid

In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal axes. A hyperboloid is the surface obtained from a hyperboloid of revolution by deforming it by means of directional scalings, or more generally, of an affine transformation.

Paraboloid

In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry.

Hyperboloid

Either of two quadric surfaces generated by rotating a hyperbola about either of its main axes and having a finite center with certain plane sections that are hyperbolas and others that are ellipses or circles.

Paraboloid

A surface having parabolic sections parallel to a single coordinate axis and elliptic or circular sections perpendicular to that axis.

Hyperboloid

A particular surface in three-dimensional Euclidean space, the graph of a quadratic with all three variables squared and their coefficients not all of the same sign. Category:en:Surfaces
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Paraboloid

(mathematics) A surface having a parabolic cross section parallel to an axis, and circular or elliptical cross section perpendicular to the axis; especially the surface of revolution of a parabola. Category:en:Surfaces

Hyperboloid

A surface of the second order, which is cut by certain planes in hyperbolas; also, the solid, bounded in part by such a surface.

Paraboloid

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.

Hyperboloid

Having some property that belongs to an hyperboloid or hyperbola.

Paraboloid

A surface having parabolic sections parallel to a single coordinate axis and elliptic sections perpendicular to that axis

Hyperboloid

A quadric surface generated by rotating a hyperbola around its main axis

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