: Mathematics: tangent space

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tangent space

In mathematics, the tangent space of a manifold is a generalization of tangent lines to curves in two-dimensional space and tangent planes to surfaces in three-dimensional space in higher dimensions. In the context of physics the tangent space to a manifold at a point can be viewed as the space of possible velocities for a particle moving on the manifold.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Tangent_space)

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