Ellipsoidikus

Ellipsoidikus is an adjective used to describe something that is related to or shaped like an ellipsoid. The term is used in several fields to refer to ellipsoid-like geometry, surfaces, or distributions. In English, the common equivalents are ellipsoidal or ellipsoidic; in some languages, including Hungarian, ellipsoidikus serves as the standard adjective. The concept arises from the ellipsoid, a closed quadric surface that generalizes a sphere by allowing three different radii.

In three-dimensional space, a centered ellipsoid with principal axes of lengths a, b, and c has the canonical equation x^2/a^2 + y^2/b^2 + z^2/c^2 = 1 when oriented with the coordinate axes. More generally, it can be rotated and translated, and can be represented as (x - x0, y - y0, z - z0)^T A (x - x0, y - y0, z - z0) = 1 with a positive definite matrix A. The ellipsoid's eigenvectors determine its principal axes; eigenvalues relate to axis lengths.

The volume of a tri-axial ellipsoid is V = 4/3 π abc. Surface area has no simple closed form in general, though formulas exist for special cases such as spheres (a = b = c) and spheroids (two axes equal). Ellipsoids are often distinguished as oblate (flattened at the poles) or prolate (elongated along one axis).

Ellipsoidikus objects appear in many applications: as a mathematical model of a quadric surface, as reference or bounding shapes in computer graphics and collision detection, and as the Earth’s shape approximation in geodesy and cartography (reference ellipsoids such as WGS84). In statistics, elliptical distributions have contours that are ellipsoids. The term emphasizes the ellipsoid-like nature of the object or distribution.