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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
    Every plane section of a paraboloid made by a plane parallel to the axis of symmetry is a parabola 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)
  • 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
    (1) The paraboloid which has radius a at height h is then given parametrically by x (u,v) = asqrt (u h)cosv (2) y (u,v) = asqrt (u h)sinv (3) z (u,v) = u, (4) where u>=0, v in [0,2pi) The coefficients of the first fundamental form are
  • 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
  • Paraboloid: Definition, Types Key Equations Explained - Vedantu
    A paraboloid is a three-dimensional surface that has volume and depth Think of a parabola as the drawing of an arch, while the paraboloid is the actual 3D archway you can walk through
  • Paraboloid Definition (Illustrated Mathematics Dictionary)
    Illustrated definition of Paraboloid: The 3D surface made when we spin a parabola around its axis It has exactly one axis of symmetry Makes an excellent
  • What is a Paraboloid? (with picture) - AllTheScience
    A paraboloid is a type of three dimensional surface that consists of the revolution of a parabola along its axis of symmetry
  • 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 Formulas - FormulaShapes
    A paraboloid, a 3D parabolic curve, focuses light in satellite dishes and sound in amphitheaters Its shape optimizes structural load distribution in bridges and roofing
  • Mastering Paraboloid in Calculus III - numberanalytics. com
    A paraboloid is a three-dimensional surface that is shaped like a parabola, extending upwards or downwards in a symmetrical manner In this section, we'll explore the definition, basic properties, and types of paraboloid, as well as its significance in real-world applications





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