I'm trying to understand Menger curvature in terms of shape determination in isolated cases of 3 well-distributed (defining) coordinate points that could form part of a shape that may be either a circle or an oval.
It seems that the menger curvature will generate a smaller number for bigger circles (inverse R), but can this be used to determine the simple geometrical shape of three points, i.e, whether in the plane, they are a circle or oval (oblong)?