Let a Knot be parameterized by a Vector Function with , and let be a fixed Unit Vector in . Count the number of Relative 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.

**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.

© 1996-9

1999-05-25