Ellipsoid

In mathematics, an ellipsoid is a type of quadric that is a higher dimensional analogue of an ellipse. The equation of a standard ellipsoid in an x-y-z Cartesian coordinate system is

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:

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where a, b and c are fixed positive real numbers determining the shape of the ellipsoid. If two of those numbers are equal, the ellipsoid is a spheroid; if all three are equal, we have a sphere.

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If we assume a ≥ b ≥ c, then when:

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• a ≠ b ≠ c we have a scalene ellipsoid
• c = 0 we have a flat ellipsoid (two ellipses back to back)
• b = c we have a prolate spheroid (cigar-shaped)
• a = b we have an oblate spheroid (pill-shaped)
• a = b = c we have a sphere, as stated earlier
Ellipsoid: Volume ►



 

Quadric: In mathematics a quadric, or quadric surface, is any D-dimensional hypersurface defined as the zeros of a quadratic polynomial. In coordinates {x_0, x_1, x_2, ldots, x_D}, the general quadric is defined by the algebraic equation...

Dimension: Dimension (from Latin "measured out") is, in essence, the number of degrees of freedom available for movement in a space....

Ellipse: In mathematics, an ellipse (from the Greek for absence) is a plane algebraic curve where the sum of the distances from any point on the curve to two fixed points is constant. The two fixed points are called foci (plural of focus)....