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  "body": "\n## Summary\n\nThe Hausdorff distance measures how far two subsets of a [[metric space|0VKD1TP7F3]] are from each other.\nIt is the smallest $\\varepsilon$ such that each set lies in the $\\varepsilon$-neighbourhood of the other.\nOn the nonempty compact subsets of a metric space it is a metric.\nWith it, the compact convex sets of $\\R^n$ form the basic space of convex geometry.\n\n## Explanations\n\n### L1 human\n\nTwo shapes are close in the Hausdorff distance if every point of each shape is near some point of the other shape.\nPicture thickening one shape by a margin $\\varepsilon$ until it swallows the other, and doing the same the other way round.\nThe smallest margin that works both ways is the Hausdorff distance.\nFor the intervals $[0, 1]$ and $[0, 2]$ on the line, the distance is $1$: the point $2$ is at distance $1$ from $[0,1]$.\n",
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