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Paraboloid of revolution. 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 made by a plane parallel to the axis of symmetry is ...
A parabolic (or paraboloid or paraboloidal) reflector (or dish or mirror) is a reflective surface used to collect or project energy such as light, sound, or radio waves. Its shape is part of a circular paraboloid , that is, the surface generated by a parabola revolving around its axis.
Semicircular area [3] ... Solid paraboloid of revolution around z-axis: a = the radius of the base circle h = the height of the paboloid from the base cicle's center ...
The red paraboloid corresponds to τ=2, the blue paraboloid corresponds to σ=1, and the yellow half-plane corresponds to φ=-60°. The three surfaces intersect at the point P (shown as a black sphere) with Cartesian coordinates roughly (1.0, -1.732, 1.5).
Parabolic antennas are based on the geometrical property of the paraboloid that the paths FP 1 Q 1, FP 2 Q 2, FP 3 Q 3 are all the same length. Thus, a spherical wavefront emitted by a feed antenna at the dish's focus F will be reflected into an outgoing plane wave L travelling parallel to the dish's axis VF.
Paraboloidal coordinates are three-dimensional orthogonal coordinates (,,) that generalize two-dimensional parabolic coordinates.They possess elliptic paraboloids as one-coordinate surfaces.
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A surface is doubly ruled if through every one of its points there are two distinct lines that lie on the surface. The hyperbolic paraboloid and the hyperboloid of one sheet are doubly ruled surfaces. The plane is the only surface which contains at least three distinct lines through each of its points (Fuchs & Tabachnikov 2007).