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  "body": "\n## Summary\n\nA pointed cone is a [[convex cone|6VE4KA12VD]] that contains the origin.\nEquivalently, it is a nonempty set closed under sums and under multiplication by nonnegative scalars.\nSo it behaves like a subspace in which only nonnegative coefficients are allowed.\nThe word is not used uniformly: some authors call a cone pointed when it contains no line through the origin, a property also called salient.\n\n## Explanations\n\n### L1 human\n\nA pointed cone is a wedge that includes its tip at the origin.\nYou may add vectors of the cone, stretch them by any factor $t \\ge 0$, and shrink them all the way to $0$.\nThe closed first quadrant of the plane is a pointed cone.\nThe open first quadrant, without its two boundary half-lines and without the origin, is a convex cone that is not pointed in this sense.\n",
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