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]
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 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
Surface areaA prolate spheroid has surface area
- 2\pi\left(a^2+\frac\right)\,\! ；
where o\!\varepsilon=\arccos\left(\frac\right)\,\! . o\!\varepsilon\,\! is the angular eccentricity of the ellipse:
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)\,\! .
VolumeVolume is \frac\pi a^2b.\,\!
CurvatureIf 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) = .\,\!
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