Spheroid

A spheroid is a quadric surface in three dimensions obtained by rotating an ellipse about one of its principal axes.

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If the ellipse is rotated about its major axis, the surface is called a prolate spheroid (similar to the shape of a rugby ball or cigar).

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If the minor axis is chosen, the surface is called an oblate spheroid (similar to the shape of the planet Earth).

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A spheroid can also be characterised as an ellipsoid having two equal semi-axes, as represented by the equation

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:rac{x^2}{a^2}+rac{y^2}{b^2}+rac{z^2}{b^2}=1

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A prolate spheroid has one semiaxis longer than the other two, (a > b); an oblate spheroid has one semiaxis shorter than the other two (a < b) and can resemble a disk.

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Prolate spheroid.

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Oblate spheroid. -->

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The sphere is a special case of the spheroid in which the generating ellipse is a circle.

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Quadric: In mathematics a quadric, or quadric surface, is any D-dimensional hypersurface defined as the zeros of a quadratic polynomial. In coordinates {x_0, x_1, x_2, ldots, x_D}, the general quadric is defined by the algebraic equation...

Surface: In mathematics (topology), a surface is a two-dimensional manifold. Examples arise in three-dimensional space as the boundaries of three-dimensional solid objects. The surface of a fluid object, such as a rain drop or soap bubble, is an idealisation. To speak of the surface of a snowflake, which has...

Ellipse: In mathematics, an ellipse (from the Greek for absence) is a plane algebraic curve where the sum of the distances from any point on the curve to two fixed points is constant. The two fixed points are called foci (plural of focus)....