The curvature of rectifiable curves and an inequality of Chakerian- Fáry (Q1065363)

The curvature of rectifiable curves is defined by a limit process. Changing the approximating sequence based on inscribed spherical polygons gives a new notion of curvature that coincides with the classical one for smooth curves but gives strictly smaller values for nonsmooth curves. The new notion gives an improved version and the case of equality of an inequality of Chakerian-Fáry. The correct notion of curvature for nonsmooth curves depends on the problem to be treated.