A geometric inequality for the total curvature of plane curves (Q1087148)

For a generic simply closed curve in \(E^2\) (smooth or polyhedral) the following numbers are well defined: \(K=\) total curvature, \(f=\) number of inflection points (or inflection edges in the polyhedral case), \(d=\) geometrical degree. The authors prove for \(f>0\) the inequality \(K<\pi f(1+d/2)\). Furthermore they show that this is sharp for \(f=2\), and that it is not sharp for \(f>2\).