Curvature and Torsion of Curves

In this chapter we illustrate the use of some global theorems regarding the curvature of curves. The definition and basic calculating formulas for the curvature and the torsion of a curve are given in Section 12.1. In Sections 12.2 –12.3 we calculate the geometrical characteristics of plane and space curves, plot the moving Frenet frame and an osculating circle, and present the the fundamental theorem of algebra as an example. Section 12.4 deals with the main theorem in the classical theory of curves. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.