---
tag: F0RVAF11K9
kind: concept
name: Fekete points
msc: [31A15, 30C85]
sources:
  - url: https://en.wikipedia.org/wiki/Conformal_radius
---

## Summary

Let $K$ be a compact set in the plane.
Fekete points of $K$ are $n$ points of $K$ that make the product of their mutual distances as large as possible.
They realize the $n$-th diameter in the definition of the [[transfinite diameter|VSGTSQ7RY8]].
Let $K$ have positive capacity.
As $n$ grows, the uniform distribution on the Fekete points tends to the [[equilibrium measure|464NN2K4FZ]] of $K$.
They are used as interpolation nodes and as discrete models of an electric charge in equilibrium.

## Explanations

### L1 human

Put $n$ equal point charges on a conductor $K$ and let them push each other apart with the logarithmic law.
The positions where they come to rest with the least energy are the Fekete points.
On a circle they are $n$ equally spaced points.
On an interval they crowd near the two ends, just as the equilibrium charge of an interval is densest at its ends.