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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.
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.
ellipt. paraboloid, parabol. cylinder, hyperbol. paraboloid as translation surface translation surface: the generating curves are a sine arc and a parabola arc Shifting a horizontal circle along a helix. Simple examples: Right circular cylinder: is a circle (or another cross section) and is a line.
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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 to the edge Solid ellipsoid: a, b, c = the principal semi-axes of the ellipsoid
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Hyperbolic-paraboloid.jpg Made with the following source (Gnuplot) set terminal svg enhanced size 640 423 set output "Hyperbolic-paraboloid.svg" unset key unset xtics unset ytics unset ztics set view 70, 19, 1.2, 1.15 set isosamples 10, 10 splot [-2:2] [-2:2] x*y with lines