hyperboloid

Also known as hourglass shape, elliptic hyperboloid

{| class=wikitable align=right |- align=center |150pxHyperboloid of one sheet |160pxconical surface in between |150pxHyperboloid of two sheets |} 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.

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Commons category: Hyperboloid

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Article

16 sections

Contents

Parametric representations
Generalised equations
Properties
Hyperboloid of one sheet
Lines on the surface
Plane sections
Hyperboloid of two sheets <span class="anchor" id="Two sheets"></span>
Other properties
Symmetries
Curvature
In more than three dimensions
Hyperboloid structures
Relation to the sphere
See also
References
External links

A hyperboloid is a quadric surface, that is, a surface defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces, a hyperboloid is characterized by not being a cone or a cylinder, having a center of symmetry, and intersecting many planes into hyperbolas. A hyperboloid has three pairwise perpendicular axes of symmetry, and three pairwise perpendicular planes of symmetry.