Editing Tangent vector (section)

{{short description|Vector tangent to a curve or surface at a given point}}

In [[mathematics]], a '''tangent vector''' is a [[Vector (geometry)|vector]] that is [[tangent]] to a [[curve]] or [[Surface (mathematics)|surface]] at a given point. Tangent vectors are described in the [[differential geometry of curves]] in the context of curves in '''R'''<sup>''n''</sup>. More generally, tangent vectors are elements of a ''[[tangent space]]'' of a [[differentiable manifold]]. Tangent vectors can also be described in terms of [[Germ (mathematics)|germs]]. Formally, a tangent vector at the point <math>x</math> is a linear [[Derivation (differential algebra)|derivation]] of the algebra defined by the set of germs at <math>x</math>.