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paraboloid    
n. 抛物面

抛物面

paraboloid
抛物面

paraboloid
n 1: a surface having parabolic sections parallel to a single
coordinate axis and elliptic sections perpendicular to that
axis

Paraboloid \Pa*rab"o*loid\ (-loid), n. [Parabola -oid: cf. F.
parabolo["i]de.] (Geom.)
The solid generated by the rotation of a parabola about its
axis; any surface of the second order whose sections by
planes parallel to a given line are parabolas.
[1913 Webster]

Note: The term paraboloid has sometimes been applied also to
the parabolas of the higher orders. --Hutton.
[1913 Webster]


Conoid \Co"noid\ (k[=o]"noid), n. [Gr. kwnoeidh`s conical;
kw^nos cone e'i^dos form: cf. F. cono["i]de.]
1. Anything that has a form resembling that of a cone.
[1913 Webster]

2. (Geom.)
(a) A solid formed by the revolution of a conic section
about its axis; as, a parabolic conoid, elliptic
conoid, etc.; -- more commonly called {paraboloid},
{ellipsoid}, etc.
(b) A surface which may be generated by a straight line
moving in such a manner as always to meet a given
straight line and a given curve, and continue parallel
to a given plane. --Math. Dict.
[1913 Webster]


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  • Paraboloid - Wikipedia
    Any paraboloid (elliptic or hyperbolic) is a translation surface, as it can be generated by a moving parabola directed by a second parabola
  • Paraboloid | Surfaces, Quadrics, Hyperbolic | Britannica
    Paraboloid, an open surface generated by rotating a parabola (q v ) about its axis If the axis of the surface is the z axis and the vertex is at the origin, the intersections of the surface with planes parallel to the xz and yz planes are parabolas (see Figure, top)
  • Paraboloid - from Wolfram MathWorld
    A paraboloid is a quadratic surface of either elliptic or hyperbolic type A circular paraboloid is the surface of revolution of a parabola about its axis and is the shape used in the reflectors of automobile headlights (Steinhaus 1999, p 242; Hilbert and Cohn-Vossen 1999)
  • PARABOLOID Definition Meaning - Merriam-Webster
    The meaning of PARABOLOID is a surface all of whose intersections by planes are either parabolas and ellipses or parabolas and hyperbolas
  • Paraboloid - Virtual Math Museum
    Parabolic mirror with focussed rays, anaglyph Anaglyph grid image of a parabolid
  • Paraboloid — Definition, Formula Examples
    A paraboloid is a bowl-shaped 3D surface where cross-sections parallel to the base are circles (or ellipses), and cross-sections through the central axis are parabolas The most common type, an elliptic paraboloid, opens upward or downward like an infinite satellite dish
  • Calculus III - Quadric Surfaces
    In this case the variable that isn’t squared determines the axis upon which the paraboloid opens up Also, the sign of $c$ will determine the direction that the paraboloid opens
  • 12. 6: Quadric Surfaces - Mathematics LibreTexts
    Identify a cylinder as a type of three-dimensional surface Recognize the main features of ellipsoids, paraboloids, and hyperboloids Use traces to draw the intersections of quadric surfaces with the coordinate planes
  • 4. 4: The Paraboloid - Physics LibreTexts
    The elliptic paraboloid lies entirely above the $xy$ -plane The Equation is a hyperbolic paraboloid, and its shape is not quite so easily visualized Unlike the elliptic paraboloid, it extends above and below the plane It is a saddle-shaped surface, with the saddle point at the origin





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