High Quality Content by WIKIPEDIA articles! In geometry, the tangent cone is a generalization of the notion of the tangent space to a manifold to the case of certain spaces with singularities. Let K be a closed convex subset of a real vector space V and ?K be the boundary of K. The solid tangent cone to K at a point x ? ?K is the closure of the cone formed by all half-lines (or rays) emanating from x and intersecting K in at least one point y distinct from x. It is a convex cone in V and can also be defined as the intersection of the closed half-spaces of V containing K and bounded by the supporting hyperplanes of K at x. The boundary TK of the solid tangent cone is the tangent cone to K and ?K at x. If this is an affine subspace of V then the point x is called a smooth point of ?K and ?K is said to be differentiable at x and TK is the ordinary tangent space to ?K at x.

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