tangentiell

Tangentiell is an adjective used in some European languages, notably German, to describe a relation to or characteristic of a tangent. In mathematical English the corresponding terms are tangent or tangential; tangentiell is encountered primarily in German-language texts and dictionaries or in bilingual works.

In geometry, a tangentiell object is one that touches a curve or surface at a point with first-order contact. The most common examples are the tangential line to a curve at a given point and the tangential plane to a surface at a point; these objects provide the linear approximation of the curve or surface near that point. The direction of tangentiell objects is given by the derivative or the tangent vectors to the curve or surface.

In physics and mechanics, tangential components refer to projections of vectors onto directions tangent to a path or surface; for example, tangential velocity is the component of velocity along a circular path.

Origin and usage: the term derives from Latin tangens via the concept of tangency; in German the suffix -ell forms adjectives, yielding tangentiell. In English technical writing, tangential or tangent are preferred; tangentiell may appear in translations or in multilingual glossaries to indicate similar meaning.

See also: Tangent, Tangency, Tangential component, Tangent plane, Differential geometry.