Ellipsoid

In Mathematical, an ellipsoidal is a Surface of the second degree of the Euclidean Espace with three dimensions. It thus forms part of the Quadrique S, with for principal characteristic not having of point ad infinitum.

The ellipsoid admits a center and at least three plans of symmetry. The Intersection of an ellipsoid with a plan is a ellipse, a point or the empty set.

In a reference mark chosen well, its equation is form

$\{x^2\; \backslash \; over\; a^2\}\; +\; \{y^2\; \backslash \; over\; b^2\}\; +\; \{z^2\; \backslash \; over\; c^2\}\; =1$

where $a$, $b$ and $c$ are strictly positive parameters given, equal to the lengths of the semi-axes of the object.

In the very particular case where $a\; =\; B\; =\; c$, surface is a Sphère of ray $a$.

If only two parameters are equal, the ellipsoid can be generated by the Rotation of a ellipse around one of its axes. It is about a Ellipsoïde of revolution, which one finds in the form of elliptic mirrors in the projectors of cinema. It is also shown that this surface is optimal for the Dirigeable S.

Volume

The Volume of an ellipsoid defined by the equation above is equal to:

$\backslash \; frac\; \{4\}\; \{3\}\; \backslash \; pi\; abc$

Simple: Ellipsoid

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