Ellipsoid | Wikipedia audio article
Channel: wikipedia tts
Date: 05/10/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Ellipsoid


00:01:31 1 Standard equation
00:03:00 2 Parameterization
00:03:11 3 Volume and surface area
00:04:03 3.1 Volume
00:04:12 3.2 Surface area
00:06:24 3.2.1 Approximate formula
00:10:32 4 Plane sections
00:11:30 4.1 Properties
00:11:59 4.2 Determining the ellipse of a plane section
00:12:08 5 In general position
00:12:49 5.1 As quadric
00:22:35 5.2 Parametric representation
00:22:44 6 Applications
00:24:34 6.1 Dynamical properties
00:31:55 6.2 Fluid dynamics
00:33:18 6.3 In probability and statistics
00:35:37 7 In higher dimensions
00:36:48 8 See also
00:37:20 9 Notes
00:39:40 10 References
00:40:11 11 External links



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SUMMARY
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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 quadric surface;  that is, a surface that may be defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces, an ellipsoid is characterized by either of the two following properties. Every planar cross section is either an ellipse, or is empty, or is reduced to a single point (this explains the name, meaning "ellipse like"). It is bounded, which means that it may be enclosed in a sufficiently large sphere.
An ellipsoid has three pairwise perpendicular axes of symmetry which intersect at a center of symmetry, called the center of the ellipsoid. The line segments that are delimited on the axes of symmetry by the ellipsoid are called the principal axes, or simply axes of the ellipsoid. If the three axes have different lengths, the ellipsoid is said to be tri-axial or rarely scalene, and the axes are uniquely defined.
If two of the axes have the same length, then the ellipsoid is an ellipsoid of revolution, also called a spheroid. In this case, the ellipsoid is invariant under a rotation around the third axis, and there are thus infinitely many ways of choosing the two perpendicular axes of the same length. If the third axis is shorter, the ellipsoid is an oblate spheroid; if it is longer, it is a prolate spheroid. If the three axes have the same length, the ellipsoid is a sphere.