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  "body": "\n## Summary\n\nThe transfinite diameter of a compact set $K$ in the plane measures how far apart many points of $K$ can be placed at once.\nFor each $n$ one maximizes the geometric mean of the mutual distances of $n$ points of $K$, and then lets $n$ tend to infinity.\nFor $n = 2$ this is the ordinary diameter, which explains the name.\nA theorem of Fekete and Szegő says that the transfinite diameter equals the [[logarithmic capacity|DBQXRTC0VN]] of $K$.\n\n## Explanations\n\n### L1 human\n\nPlace $n$ points in $K$ so that they are as spread out as possible, in the sense that the product of all their mutual distances is largest.\nTake the geometric mean of these distances.\nFor two points this is just the largest distance in $K$, the diameter.\nAs $n$ grows, the points must crowd together, and the mean distance decreases to a limit, the transfinite diameter.\nFor the unit circle the best points are the $n$-th roots of unity, and the limit is $1$.\n",
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