ABSTRACT
This chapter introduces a curvature function that measures how much a space curve deviates from being linear and a torsion function that measures how much the curve twists away from being planar. As in the study of plane curves, one must take some care in defining what one means by a space curve. By a curve, one typically thinks of a connected set of points, and, just as with plane curves, the desired property is continuity. A cylindrical helix is a space curve that wraps around a circular cylinder, climbing in altitude at a constant rate. A curve is a helix if and only if the ratio of curvature to torsion is a constant. Curves that lie on torus are often knotted. The derivative of the unit binormal vector is parallel to the principal normal vector.
