Harnack's curve theorem

Harnack's Curve Theorem is a result in the field of differential geometry and real analysis that pertains to curves in the plane. The theorem states that if you have a continuous curve that is smooth (differentiable) and does not intersect itself, then the curve can be parameterized in such a way that it is "locally" straightened out. More precisely, it concerns the properties of the distance between points on the curve.