Hi, I found this problem in Do Carmos "differential geometry of curves and surfaces". it asks to show that the length of a parallel curve B to A given by: B=A-rn where r is a positive constant, and n is the normal vector, and A is a closed convex plane curve, positively oriented. is given by len(B)=len(A)+2*pi*r The obvious start would be to integrate both sides under a standard parametrization or the curves, but why is it true that integrating rn will give 2*pi*n exactly? any insight is appreciated. Thanks!