Ellipsoid
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[edit | edit source]
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[edit | edit source]
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[edit | edit source]
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[edit | edit source]
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[edit | edit source]
References[edit | edit source]
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Contributors: Prab R. Tumpati, MD