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ellipsoid    音标拼音: [ɪl'ɪpsɔɪd]
n. 椭圆体

椭圆体

ellipsoid
adj 1: having the nature or shape of an ellipsoid [synonym:
{ellipsoid}, {ellipsoidal}, {spheroidal}]
n 1: a surface whose plane sections are all ellipses or circles;
"the Earth is an ellipsoid"

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]


Ellipsoid \El*lip"soid\, n. [Ellipse -oid: cf. F. ellipsoide.]
(Geom.)
A solid, all plane sections of which are ellipses or circles.
See {Conoid}, n., 2
(a) .
[1913 Webster]

Note: The ellipsoid has three principal plane sections, a, b,
and c, each at right angles to the other two, and each
dividing the solid into two equal and symmetrical
parts. The lines of meeting of these principal sections
are the axes, or principal diameters of the ellipsoid.
The point where the three planes meet is the center.
[1913 Webster]

{Ellipsoid of revolution}, a spheroid; a solid figure
generated by the revolution of an ellipse about one of its
axes. It is called a prolate spheroid, or prolatum, when
the ellipse is revolved about the major axis, and an
oblate spheroid, or oblatum, when it is revolved about the
minor axis. Ellipsoid


Ellipsoid \El*lip"soid\, Ellipsoidal \El`lip*soi"dal\, a.
Pertaining to, or shaped like, an ellipsoid; as, ellipsoid or
ellipsoidal form. Elliptic


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  • Ellipsoid - Wikipedia
    An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation An ellipsoid is a quadric surface; that is, a surface that may be defined as the zero set of a polynomial of degree two in three variables
  • Ellipsoid -- from Wolfram MathWorld
    The general ellipsoid, also called a triaxial ellipsoid, is a quadratic surface which is given in Cartesian coordinates by (x^2) (a^2)+ (y^2) (b^2)+ (z^2) (c^2)=1, (1) where the semi-axes are of lengths a, b, and c In spherical coordinates, this becomes (r^2cos^2thetasin^2phi) (a^2)+ (r^2sin^2thetasin^2phi) (b^2)+ (r^2cos^2phi) (c^2)=1
  • Ellipsoid - Math. net
    An ellipsoid is a 3D geometric figure that has an elliptical shape It can be viewed as a stretched sphere An ellipsoid gets its name from an ellipse Any plane that cuts through an ellipsoid forms an ellipse Two ellipsoids are shown in the figure below Real life examples of an ellipsoid include an egg or a blimp
  • Ellipsoid | Surfaces, Axes, Foci | Britannica
    Ellipsoid, closed surface of which all plane cross sections are either ellipses or circles An ellipsoid is symmetrical about three mutually perpendicular axes that intersect at the centre
  • The ellipsoid - Math Insight
    Just as an ellipse is a generalization of a circle, an ellipsoid is a generalization of a sphere In fact, our planet Earth is not a true sphere; it's an ellipsoid, because it's a little wider than it is tall As you can verify below, all of the cross sections of an ellipsoid are ellipses
  • Ellipsoid: Definitions and Examples - Club Z! Tutoring
    An ellipsoid is a three-dimensional shape that is symmetrical along three axes It can be defined as the surface that results from the rotation of an ellipse about one of its axes
  • Ellipsoid - Encyclopedia of Mathematics
    An ellipsoid is a closed central surface of the second order (see Figure 1) The canonical equation of an ellipsoid has the form $$ \frac {x^2} {a^2} + \frac {y^2} {b^2} + \frac {z^2} {c^2} = 1 $$ The positive numbers $a$, $b$ and $c$ and the segments of corresponding lengths are called the semi-axes of the ellipsoid
  • Ellipsoid - Explanation, Equation, Volume and FAQs - Vedantu
    An ellipsoid is a closed quadric surface which is a 3-D analogue of an ellipse The standard equation of momental ellipsoid centered at the origin of a Cartesian coordinate plane
  • Flexi answers - lt;p gt;What is an ellipsoid? lt; p gt; | CK-12 Foundation
    An ellipsoid is a three-dimensional geometric shape that resembles a stretched or compressed sphere It is a type of quadric surface, which means it is defined by a second-degree equation in three variables Mathematically, an ellipsoid is described by the equation: x 2 a 2 + y 2 b 2 + z 2 c 2 = 1
  • Geometry - Ellipsoids - TechnologyUK
    An ellipsoid is a three-dimensional shape for which all plane cross-sections are either ellipses or circles The ellipsoid has three axes which intersect at the centre of the ellipsoid





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