hyperboloid
Sign in to save{| 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.
Article
16 sectionsContents
- 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
{| 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.
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.