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 was awakened at midnight by some heavy, low-flying bird, probably a loon, flapping by close over my head, along the shore. So, turning the other side of my half-clad body to the fire, I sought slumber again.”
—Henry David Thoreau (1817–1862)
“In this world, which is so plainly the antechamber of another, there are no happy men. The true division of humanity is between those who live in light and those who live in darkness. Our aim must be to diminish the number of the latter and increase the number of the former. That is why we demand education and knowledge.”
—Victor Hugo (1802–1885)