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  "body": "\n## Summary\n\nThe Minkowski sum of two subsets $A$ and $B$ of a vector space is the set $A + B$ of all sums $a + b$ with $a \\in A$ and $b \\in B$.\nTogether with scaling $\\lambda A = \\set{\\lambda a : a \\in A}$, it makes the convex bodies of $\\R^n$ into a cone-like algebraic structure.\nVolume behaves well under this addition, which leads to the Brunn–Minkowski inequality and the theory of mixed volumes.\n\n## Explanations\n\n### L1 human\n\nTo add two shapes, place a copy of the second shape at every point of the first and take everything covered.\nAdding a disk of radius $r$ to a square gives a square with rounded corners, thickened by $r$ on every side.\nAdding two segments in different directions gives a parallelogram.\nAdding a shape to a single point just moves the shape.\n",
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