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To parameterize" by itself means "to express in terms of parameters". [ 2 ] Parametrization is a mathematical process consisting of expressing the state of a system , process or model as a function of some independent quantities called parameters .
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.
The butterfly curve can be defined by parametric equations of x and y.. In mathematics, a parametric equation expresses several quantities, such as the coordinates of a point, as functions of one or several variables called parameters.
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).
Paraboloidal coordinates are three-dimensional orthogonal coordinates (,,) that generalize two-dimensional parabolic coordinates.They possess elliptic paraboloids as one-coordinate surfaces.
Consider a cylinder of radius and height , circumscribing a paraboloid = whose apex is at the center of the bottom base of the cylinder and whose base is the top base of the cylinder. Also consider the paraboloid y = h − h ( x r ) 2 {\displaystyle y=h-h\left({\frac {x}{r}}\right)^{2}} , with equal dimensions but with its apex and base flipped.
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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 ...