The knot 03-001, also called the Threefoil Knot, which is the unique Prime Knot of three
crossings. It has Braid Word . The trefoil and its Mirror Image are not equivalent. The
trefoil has Alexander Polynomial and is a (3, 2)-Torus Knot. The Bracket Polynomial can be
computed as follows.

Plugging in

gives

The normalized one-variable Kauffman Polynomial

where the Writhe . The Jones Polynomial is therefore

Since , we have shown that the mirror images are not equivalent.

**References**

Claremont High School. ``Trefoil_Knot Movie.'' Binary encoded QuickTime movie. ftp://chs.cusd.claremont.edu/pub/knot/trefoil.cpt.bin.

Crandall, R. E. *Mathematica for the Sciences.* Redwood City, CA: Addison-Wesley, 1993.

Kauffman, L. H. *Knots and Physics.* Singapore: World Scientific, pp. 29-35, 1991.

Nordstrand, T. ``Threefoil Knot.'' http://www.uib.no/people/nfytn/tknottxt.htm.

Pappas, T. ``The Trefoil Knot.'' *The Joy of Mathematics.* San Carlos, CA: Wide World Publ./Tetra, p. 96, 1989.

© 1996-9

1999-05-26