Sfæroide

sfæroide, often translated as spheroid, is a solid of revolution generated by rotating an ellipse about one of its principal axes. The resulting surface is an ellipsoid of revolution, also called a spheroid. Unlike a general ellipsoid, a sfæroide has rotational symmetry around a fixed axis.

There are two common forms. An oblate spheroid is obtained when the ellipse is rotated about its minor axis, yielding an equatorial radius a larger than the polar radius c (a > c). A prolate spheroid arises when rotation occurs about the major axis, giving a polar radius larger than the equatorial (c > a). The sphere is the degenerate case in which a = c, producing equal radii in all directions.

If a is the equatorial radius and c the polar radius, the volume is V = 4/3 π a^2 c. A standard Cartesian representation for a sfæroide with symmetry about the z-axis is x^2/a^2 + y^2/a^2 + z^2/c^2 = 1. The surface area has closed-form expressions for both oblate and prolate cases and depends on eccentricity e, with e = sqrt(1 − (c^2/a^2)) for oblate and e = sqrt(1 − (a^2/c^2)) for prolate.

sfæroide shapes appear in natural and applied contexts. In astronomy and geodesy, many celestial bodies and Earth models are treated as oblate spheroids to account for rotational flattening. The Earth's approximate shape is commonly represented as an oblate spheroid with differing equatorial and polar radii. Sfæroide geometries also serve as convenient simplified models in biology, computer graphics, and architectural design.

The term sfæroide is used in some Nordic languages to refer to this geometric figure; in English, spheroid or ellipsoid of revolution is typical. See also: spheroid, ellipsoid, oblate spheroid, prolate spheroid, sphere.