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Paraboloidal coordinates are three-dimensional orthogonal coordinates (,,) that generalize two-dimensional parabolic coordinates. They possess elliptic paraboloids as one-coordinate surfaces. As such, they should be distinguished from parabolic cylindrical coordinates and parabolic rotational coordinates , both of which are also generalizations ...
Coordinate surfaces of the three-dimensional parabolic coordinates. 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).
In a suitable coordinate system, a hyperbolic paraboloid can be represented by the equation [2] [3] =. In this position, the hyperbolic paraboloid opens downward along the x -axis and upward along the y -axis (that is, the parabola in the plane x = 0 opens upward and the parabola in the plane y = 0 opens downward).
These surfaces intersect at the point P (shown as a black sphere), which has Cartesian coordinates roughly (2, -1.5, 2). In mathematics, parabolic cylindrical coordinates are a three-dimensional orthogonal coordinate system that results from projecting the two-dimensional parabolic coordinate system in the perpendicular -direction.
Pages in category "Three-dimensional coordinate systems" The following 19 pages are in this category, out of 19 total. This list may not reflect recent changes .
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.
Paraboloidal coordinates; Polar coordinate system; Prolate spheroidal coordinates; S. Spherical coordinate system; T. Toroidal coordinates This page was last edited ...
In the cylindrical coordinate system, a z-coordinate with the same meaning as in Cartesian coordinates is added to the r and θ polar coordinates giving a triple (r, θ, z). [8] Spherical coordinates take this a step further by converting the pair of cylindrical coordinates ( r , z ) to polar coordinates ( ρ , φ ) giving a triple ( ρ , θ ...