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2025-02-18T11:23:45Z

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	[[Category:Geometry]]		[[Category:Geometry]]
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			<gallery>
			File:Ellipsoide.svg\|Ellipsoid
			File:Ellipsoid-ebener-Schnitt.svg\|Ellipsoid with plane section
			File:Ellipso-eb-beisp.svg\|Ellipsoid example
			File:Ellipso-eb-ku.svg\|Ellipsoid curvature
			File:Ellipse-gaertner-k.svg\|Ellipse with gardener's construction
			File:Fokalks-ellipsoid.svg\|Focal axes of ellipsoid
			File:Fokalks-ellipsoid-xyz.svg\|Focal axes of ellipsoid in XYZ
			File:Ellipsoid-pk-zk.svg\|Ellipsoid with principal and secondary axes
			File:Ellipsoid-affin.svg\|Affine transformation of ellipsoid
			File:2003EL61art.jpg\|Ellipsoid
			</gallery>

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2024-02-22T19:49:56Z

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'''Ellipsoid''' is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. An ellipsoid is a type of quadric surface that is a higher dimensional analogue of an ellipse.

== Definition ==

In [[mathematics]], an '''ellipsoid''' is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. An ellipsoid is a type of quadric surface that is a higher dimensional analogue of an ellipse.

== Mathematical Description ==

The standard equation of an ellipsoid centered at the origin of a three-dimensional Cartesian coordinate system is

: <math>\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1</math>

where a, b, and c are positive real numbers.

== Properties ==

Ellipsoids have several interesting properties. They are closed, bounded, and smooth (i.e., they have a well-defined tangent at every point). They also have a well-defined volume and surface area, which can be calculated using integral calculus.

== Applications ==

Ellipsoids have many applications in various fields such as [[physics]], [[astronomy]], [[geology]], and [[medicine]]. For example, in medicine, the shape of red blood cells is often modeled as an ellipsoid.

== See Also ==

* [[Ellipse]]
* [[Sphere]]
* [[Quadric]]

== References ==

<references />

{{stub}}

[[Category:Mathematics]]
[[Category:Geometry]]
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Ellipsoid - Revision history

Prab: CSV import

Prab: CSV import