Elliptische

Elliptische is the German adjective meaning elliptical, related to an ellipse. It is used in technical terms to describe shapes and mathematical objects associated with ellipses, and it appears in many German phrases such as elliptische Kurven (elliptic curves), elliptische Funktionen (elliptic functions), and elliptische Integrale (elliptic integrals).

In geometry, an ellipse is the set of points for which the sum of distances to two fixed points (the foci) is constant. Elliptische Kurven are smooth curves with a group structure that play a central role in number theory and modern cryptography. Elliptische Funktionen are doubly periodic complex functions discovered by Jacobi, and elliptische Integrale arise from arc length calculations and other problems; many elliptic integrals cannot be expressed by elementary functions.

In astronomy, elliptical describes orbits—Kepler's first law states that planetary orbits are ellipses with the Sun at a focus. Elliptische Galaxien are galaxies with a smooth, ellipsoidal light distribution, distinct from spiral or irregular galaxies.

In design and architecture, elliptical shapes appear in arches, tracks, and layouts, reflecting the geometric properties of ellipses. The term Elliptische thus spans a range of disciplines, anchored by the common geometric idea of an elongated closed curve.