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One-sheet Hyperboloid
In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface (mathematics), surface generated by rotating a hyperbola around one of its Hyperbola#Nomenclature and features, principal axes. A hyperboloid is the surface obtained from a hyperboloid of revolution by deforming it by means of directional scaling (geometry) , scalings, or more generally, of an affine transformation. A hyperboloid is a quadric surface, that is, a surface (mathematics), 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 conical surface , cone or a cylinder, having a central symmetry, center of symmetry, and intersecting many plane (geometry), planes into hyperbolas. A hyperboloid has three pairwise perpendicular rotational symmetry, axes of symmetry, and three pairwise perpendicular reflection symmetry, planes of symmetry. Given a hyperboloid, one can choose a Cartesia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbolic 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. Every plane section of a paraboloid by a plane parallel to the axis of symmetry is a parabola. The paraboloid is hyperbolic if every other plane section is either a hyperbola, or two crossing lines (in the case of a section by a tangent plane). The paraboloid is elliptic if every other nonempty plane section is either an ellipse, or a single point (in the case of a section by a tangent plane). A paraboloid is either elliptic or hyperbolic. Equivalently, a paraboloid may be defined as a quadric surface that is not a cylinder, and has an implicit equation whose part of degree two may be factored over the complex numbers into two different linear factors. The paraboloid is hyperbolic if the factors are real; elliptic if the factors are complex conju ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
