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

Related Topics:
Mathematics - Quadric - Dimension - Ellipse - Cartesian coordinate system

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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.

Related Topics:
Positive - Real number - Spheroid - 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
 
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