Transfinite diameter

Summary

The transfinite diameter of a compact set $K$ in the plane measures how far apart many points of $K$ can be placed at once. For each $n$ one maximizes the geometric mean of the mutual distances of $n$ points of $K$, and then lets $n$ tend to infinity. For $n = 2$ this is the ordinary diameter, which explains the name. A theorem of Fekete and Szegő says that the transfinite diameter equals the logarithmic capacity of $K$.