Right on the head, Niko, great point! Seems like curvature is a horrible thing to define for curves in Euclidean space, it depends on a choice of parameterisation of the curve. But while curvature is axes-independent, it's still possible to find for a given pair of axes; for *functions* (ie, many-to-one) y=f(x) defined wrt the axes it can be found:k = y'' / (1+y'^2)^(3/2)(via wikipedia/mathworld). But your intuition of seeing how curvature can fluctuate where derivatives do not seems like the key. Perhaps to truly get to the bottom of this in a more general sense will require some serious calculus...