# Dictionary Definition

spheroid n : a shape that is generated by
rotating an ellipse around one of its axes; "it looked like a
sphere but on closer examination I saw it was really a spheroid"
[syn: ellipsoid
of revolution]

# User Contributed Dictionary

## English

### Noun

spheroid# Extensive Definition

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

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

- If the ellipse is rotated about its minor axis, the surface is an oblate spheroid (somewhat similar to the shape of the planet Earth).

- If the generating ellipse is a circle, the surface is a sphere (completely symmetric).

Alternatively, a spheroid can also be
characterised as an ellipsoid having two equal equatorial
semi-axes (i.e., ax = ay = a), as represented by the
equation

- \frac+\frac+\frac=\frac+\frac=1.\,\!

where
o\!\varepsilon=\arccos\left(\frac\right)\,\! . o\!\varepsilon\,\!
is the angular
eccentricity of the ellipse:

- e=\sin(o\!\varepsilon)\,\!

where e\,\! is the eccentricity of the
ellipse:

An oblate spheroid has surface area

- 2\pi\left[a^2+\frac \ln\left(\frac\right)\right]\,\! ；

where
o\!\varepsilon=\arccos\left(\frac\right)\,\! .

## Volume

Volume is \frac\pi a^2b.\,\!## Curvature

If a spheroid is parameterized as- \vec \sigma (\beta,\lambda) = (a \cos \beta \cos \lambda, a \cos \beta \sin \lambda, b \sin \beta);\,\!

- K(\beta,\lambda) = ;\,\!

- H(\beta,\lambda) = .\,\!

## See also

## External links

spheroid in Afrikaans: Sferoïde

spheroid in Catalan: Esferoide

spheroid in German: Rotationsellipsoid

spheroid in Spanish: Esferoide

spheroid in French: Sphéroïde

spheroid in Italian: Sferoide

spheroid in Hungarian: Szferoid

spheroid in Malayalam: ഗോളാഭം

spheroid in Dutch: Sferoïde

spheroid in Portuguese: Esferóide

spheroid in Russian: Эллипсоид вращения

spheroid in Swedish: Rotationsellipsoid

spheroid in Thai: ทรงคล้ายทรงกลม

spheroid in Chinese: 類球面