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  "body": "\n## Summary\n\nA convex combination of finitely many points is a weighted sum of the points whose weights are nonnegative and add up to $1$.\nIt is the special kind of [[affine combination|0KJH6SRFZK]] in which no weight is negative.\nThe [[convex hull|0FQSDC2EQ2]] of a set is exactly the set of all convex combinations of its points.\nA [[convex set|02AS45T3H9]] is a set closed under convex combinations.\nSo convex combinations are the basic operation of convex geometry.\n\n## Explanations\n\n### L1 human\n\nThink of the weights as masses placed at the points, with total mass $1$.\nThe convex combination is the centre of mass of this system.\nBecause all masses are nonnegative, the centre of mass always lies inside the shape spanned by the points.\nFor example, with the points $0$ and $10$ on the real line and weights $0.3$ and $0.7$, the convex combination is $0.3 \\cdot 0 + 0.7 \\cdot 10 = 7$, which lies between $0$ and $10$.\n",
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