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:
“I cannot say what poetry is; I know that our sufferings and our concentrated joy, our states of plunging far and dark and turning to come back to the world—so that the moment of intense turning seems still and universal—all are here, in a music like the music of our time, like the hero and like the anonymous forgotten; and there is an exchange here in which our lives are met, and created.”
—Muriel Rukeyser (1913–1980)
“The growing good of the world is partly dependent on unhistoric acts; and that things are not so ill with you and me as they might have been, is half owing to the number who lived faithfully a hidden life, and rest in unvisited tombs.”
—George Eliot [Mary Ann (or Marian)