ABSTRACT
Chapter 3 turns to the local theory of space curves. After a short review of the calculus of space curves, we define, prove formulas for, and then develop an intuition for the Frenet frame, the curvature function and the torsion function of space curves. Considering objects of interest from the perspective of order of contact, we introduce the osculating plane, the osculating circle, and the osculating sphere to a space curve at a point. Like Chapter 1, this chapter ends with the Fundamental Theorem of Space Curves, which establishes that a given curvature and torsion function uniquely determina a space curve up to position and orientation in space.
