PlanetMath: ellipsoid

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ellipsoid

(Definition)

An ellipsoid is a subset of $\mathbbmss{R}^3$ consisting of points $(x,y,z)\in \mathbbmss{R}^3$ such that

$\displaystyle \left(\frac{x}{a}\right)^2+ \left(\frac{y}{b}\right)^2+ \left(\frac{z}{c}\right)^2=1$

for some

If , the ellipsoid reduces to a sphere.
If we fix the value of any of to some constant, say , we obtain an ellipse in the plane .
The ellipse determined by is the unit sphere of the norm
$\displaystyle \Vert v \Vert = v^T \operatorname{diag} (\frac{1}{a}, \frac{1}{b}, \frac{1}{c}) v, \quad v=(x,y,z)^T.$

"ellipsoid" is owned by matte.

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Cross-references: norm, unit sphere, plane, ellipse, fix, sphere, points, subset
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This is version 3 of ellipsoid, born on 2005-01-12, modified 2005-02-19.
Object id is 6637, canonical name is Ellipsoid.
Accessed 3226 times total.

Classification:

51M05 (Geometry :: Real and complex geometry :: Euclidean geometries and generalizations)

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