Turning Number
One can also consider the winding number of the path with respect to the tangent of the path itself. As a path followed through time, this would be the winding number with respect to the origin of the velocity vector. In this case the example illustrated on the right has a winding number of 4 (or −4), because the small loop is counted.
This is only defined for immersed paths (i.e., for differentiable paths with nowhere vanishing derivatives), and is the degree of the tangential Gauss map.
This is called the turning number, and can be computed as the total curvature divided by 2π.
Read more about this topic: Winding Number
Famous quotes containing the words turning and/or number:
“The Harmless Torturers. In the Bad Old Days, each torturer inflicted severe pain on one victim. Things have now changed. Each of the thousand torturers presses a button, thereby turning the switch once on each of the thousand instruments. The victims suffer the same severe pain. But none of the torturers makes any victim’s pain perceptibly worse.”
—Derek Parfit (b. 1943)
“Not too many years ago, a child’s experience was limited by how far he or she could ride a bicycle or by the physical boundaries that parents set. Today ... the real boundaries of a child’s life are set more by the number of available cable channels and videotapes, by the simulated reality of videogames, by the number of megabytes of memory in the home computer. Now kids can go anywhere, as long as they stay inside the electronic bubble.”
—Richard Louv (20th century)