Knot energy

A conformation of a knot is a particular embedding of a circle into three-dimensional space.

Depending on the needs of the energy function, the space of conformations is restricted to a sufficiently nicely behaved class.

Coulomb's law states that two electric charges of the same sign will repel each other as the inverse square of the distance.

Thus the knot will evolve under gradient descent according to the electric potential to an ideal configuration that minimizes the electrostatic energy.

With some additional restrictions, O'Hara showed there were only finitely many knot types with energies less than a given bound.