Ellipsoid
Ellipsoid
An Ellipsoid (pronunciation: /ɛˈlɪpsɔɪd/) is a type of Geometric shape in Three-dimensional space that is a higher-dimensional analogue of an ellipse.
Etymology
The term "Ellipsoid" comes from the Latin word "Ellipsis", meaning "omission", and the Greek suffix "-oid", meaning "similar to". This is due to the shape's similarity to a squashed or stretched circle.
Definition
An Ellipsoid is defined as the set of points in three-dimensional space such that the sum of the distances from any point on the surface to two fixed points, called the foci, is constant. This is similar to the definition of an ellipse, but extended to three dimensions.
Properties
An Ellipsoid has three mutually perpendicular axes of symmetry that intersect at the center of the Ellipsoid. These axes, called the semi-major axis, semi-minor axis, and intermediate axis, determine the shape of the Ellipsoid. The lengths of these axes can be used to calculate the volume and surface area of the Ellipsoid.
Related Terms
- Sphere: A special case of an Ellipsoid where all three axes are of equal length.
- Oblate spheroid: An Ellipsoid obtained by rotating an ellipse about its minor axis.
- Prolate spheroid: An Ellipsoid obtained by rotating an ellipse about its major axis.
- Elliptical cone: A type of cone with an elliptical base, which can be considered as a degenerate Ellipsoid.
External links
- Medical encyclopedia article on Ellipsoid
- Wikipedia's article - Ellipsoid
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