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:
“We Abolition Women are turning the world upside down.”
—Angelina Grimké (1805–1879)
“Envy has blackened every page of his history.... The future, in its justice, will number him among those men whom passions and an excess of activity have condemned to unhappiness, through the gift of genius.”
—Eugène Delacroix (1798–1863)