: Mathematics: tangent vector

geometry > differential geometry > differential geometry of surfaces > tangent vector

tangent vector

In mathematics, a tangent vector is a vector that is tangent to a curve or surface at a given point. Tangent vectors are described in the differential geometry of curves in the context of curves in Rⁿ. More generally, tangent vectors are elements of a tangent space of a differentiable manifold. Tangent vectors can also be described in terms of germs. Formally, a tangent vector at the point x is a linear derivation of the algebra defined by the set of germs at x.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Tangent_vector)

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