Crossword clues for ellipsoid
The Collaborative International Dictionary
Conoid \Co"noid\ (k[=o]"noid), n. [Gr. kwnoeidh`s conical; kw^nos cone + e'i^dos form: cf. F. cono["i]de.]
Anything that has a form resembling that of a cone.
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(Geom.)
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.
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.
Douglas Harper's Etymology Dictionary
1721; see ellipse + -oid. From 1861 as an adjective (earlier adjective was ellipsoidal, 1831).
Wiktionary
a. 1 shaped like an ellipse; elliptical. 2 (context mathematics English) Of or pertaining to an ellipse. 3 (context botany English) Having the tridimensional shape of an ellipse rotated on its long axis. n. 1 (context mathematics English) a surface, all of whose cross sections are elliptic or circular (includes the sphere) 2 (context geography English) Such a surface used as a model of the shape of the earth.
WordNet
n. a surface whose plane sections are all ellipses or circles; "the Earth is an ellipsoid"
adj. in the form of an ellipse [syn: ellipsoidal, spheroidal, non-circular]
Wikipedia
An ellipsoid is a closed quadric surface that is a three-dimensional analogue of an ellipse. The standard equation of an ellipsoid centered at the origin of a Cartesian coordinate system and aligned with the axes is
$${x^2 \over a^2}+{y^2 \over b^2}+{z^2 \over c^2}=1,$$
The points (a,0,0), (0,b,0) and (0,0,c) lie on the surface and the line segments from the origin to these points are called the semi-principal axes of length a, b, c. They correspond to the semi-major axis and semi-minor axis of the appropriate ellipses.
One can assume without loss of generality that a ≥ b ≥ c. If all three semi-axis are different, then it is a generic tri-axial or (rarely) scalene ellipsoid. If two or three semi-axis are equal ( parameter degeneracy), then the ellipoid is an 'ellipsoid of revolution', which is also called a spheroid. More specifically:
- a = b > c — oblate ellipsoid of revolution ( oblate spheroid);
- a = b < c — prolate ellipsoid of revolution ( prolate spheroid);
- a = b = c — sphere.
Mathematical literature often uses 'ellipsoid' in place of 'tri-axial ellipsoid'. Scientific literature (particularly geodesy) often uses 'ellipsoid' in place of 'ellipsoid of revolution' and only applies the adjective 'tri-axial' when treating the general case.
Any planar cross section of an ellipsoid forms an ellipse on its surface: this degenerates to a circle for sections normal to the symmetry axis of an ellipsoid of revolution (or all sections when the ellipsoid degenerates to a sphere.)
Ellipsoid may refer to:
- Ellipsoid, a three-dimensional geometrical shape.
- Ellipsoidal coordinates.
Usage examples of "ellipsoid".
He bent his eyes on the ellipsoid as though weighing the matter in his mind.
Not a meteorite but a metallic ellipsoid, half-buried in the ground and slowly cooling?
Not a minute later there was a ringing and clanking from the ellipsoid that everybody heard.
At the clangor from the mysterious ellipsoid, only one thing prevented the latter.
Flares ripped through the roiling photosphere, followed by a blinding armada of ellipsoid faeros ships that collided with a thousand diamond-hulled warglobes in the sea of flames.
Behemoth-sized shadows moved, nightmarish ellipsoid hulls with flat heads, blazing optical sensors, and multiple murderous arms.
Sirix had launched a grappling cable from his ellipsoid body core: a hook and an attached line spinning across space.
The warship, nearly Nova-class size itself, was growing clearer by the second as its delicately spined ellipsoid form began to fill the display.
Juggernaut pulled away, five of the flaming ellipsoids emerged from Oncier like blazing comets.
The incandescent ellipsoids continued to block the worst of the sunstorm from the flotilla of crowded ships until the Roamers had reached a safe distance.
Ahead, he could see the spectacular Prism Palace composed of hemispheres and ellipsoids, spires, balconies, and arched bridges.
Rising through the ionized clouds was a cluster of fiery ellipsoids, vessels shaped out of sheets of flame and controlled thermal energy.
The size and shape of the surface are properties of the embedding, not of the manifold itself-so a sphere and an ellipsoid are two different embeddings of exactly the same manifold--but a particular embedding in Euclidean space can he used to supplement a manifold with the geometrical concepts needed to make it into a Riemannian space.
And flying in groups and pairs, without formation, came swooping the strange ellipsoid black forms of cormorants, twenty or thirty of them, more than Will had ever seen flying together.
They had erected an ellipsoid force field for the protection of the entire group, for the all-purpose vehicles, the cross-country jeeps containing radar and radio installations, the mobile kitchen, the trailer with airtight living quarters, and the small carriage on caterpillar tracks on which their laser beam sender had been mounted.