# Tangent space

## Assignment of vector fields to manifolds / From Wikipedia, the free encyclopedia

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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.

Assignment of vector fields to manifolds