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Reference.org
Tangent space
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the tangent space of a <a href="/facts/Manifold/rXPERJtu">manifold</a> is a generalization of <a href="/facts/Tangent_line/sF0jH3EI">tangent lines</a> to curves in <a href="/facts/Plane_(mathematics)/tAUtRFcn">two-dimensional space</a> and <a href="/facts/Tangent/sF0jH3EI">tangent planes</a> to surfaces in <a href="/facts/Three-dimensional_space/KAqKWUbS">three-dimensional space</a> 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. </p>