On the length preserving approximation of plane curves by circular arcs

A technique for the length preserving approximation of plane curves by two circular arcs is analyzed. The conditions under which this technique can be applied are extended, and certain consequences of the proved results unrelated to the approximation problem are discussed. More precisely, inequalities for the length of a convex spiral arc subject to the given boundary conditions are obtained. Conjectures on curve closeness conditions obtained using computer simulation are discussed.