Total curvature of a knot
( go to the article → https://www.johndcook.com/blog/2019/10/01/total-curvature-of-a-knot/ )
Tie a knot in a rope and join the ends together. At each point in the rope, compute the curvature, i.e. how much the rope bends, and integrate this over the length of the rope. The Fary-Milnor theorem says the result must be greater than 4π. This post will illustrate this theorem by computing numerically […]
Oct. 2, 2019, 4:18 a.m.