: Mathematics: hyperboloid

geometry > differential geometry > differential geometry of surfaces > ruled surface > hyperboloid

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topology > geometric topology > surface > ruled surface > hyperboloid

geometry > topological space > surface > ruled surface > hyperboloid

geometry > analytic geometry > surface > ruled surface > hyperboloid

geometry > geometric figure > quadric > hyperboloid

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. 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.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Hyperboloid)

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