Loterre: Mathematics: paraboloid

geometry > differential geometry > differential geometry of surfaces > ruled surface > paraboloid

geometry > Euclidean geometry > surface > ruled surface > paraboloid

topology > geometric topology > surface > ruled surface > paraboloid

geometry > topological space > surface > ruled surface > paraboloid

geometry > analytic geometry > surface > ruled surface > paraboloid

geometry > geometric figure > quadric > paraboloid

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

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