The writhe is the fundamental differential geometric invariant of a closed space curve. I think it is the most useful topological invariant outside mathematics- biologists use it to study circular DNA molecules, and chemists use it in the study of long polymers. For space curve $C(t)$ it's defined as the double integral
$\frac{1}{4\pi}\int_{C\times C}\frac{C^\prime(s)\times C^\prime(t)\cdot (C(s)-C(t))}{|C(s)-C(t)|^3}ds dt.$