Let a knot be parameterized by a vector function with , and let be a fixed unit vector in . Count the number of local minima of the projection function . Then the minimum such number over all directions and all of the given type is called the crookedness . Milnor (1950) showed that is the infimum of the total curvature of . For any tame knot in , where is the bridge index.
Crookedness
See also
Bridge IndexExplore with Wolfram|Alpha
References
Milnor, J. W. "On the Total Curvature of Knots." Ann. Math. 52, 248-257, 1950.Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, p. 115, 1976.Referenced on Wolfram|Alpha
CrookednessCite this as:
Weisstein, Eric W. "Crookedness." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Crookedness.html