I have several times encountered the misconception when the curvature of the graph of a function was claimed to be its second derivative. This has led me to investigate several lines of attack for an ab initio derivation of the right formula. Three of them can be found in the following paper. The curvature there is interpreted as the radius of a circle fit, as the proportionality factor between the angle of an arc and the arc length and as an invariant with respect to coordinate axes rotations, respectively.

pdf: Curvature

Last modified: Tue Apr 21 11:40:02 CEST 2015