. 
1) Get easily impressed friends.
2) This is a Trefoil Knot, and this is a Surgeon's Knot:
.
3) Splice the two knots together (note, of course, that the result is still knotted).
4) Gather four strands of the spliced together knots, as pictured:
5) Break the strands!
6) Give one full twist!!
7) Reattach the strands and VOICI!
myriad examples (including some infinite collections of rope tricks), various theorems, and one conjecture, click for my thesis . This example is due to K. Motegi.
Chaim Goodman-Strauss Dept. Mathematics Univ. Arkansas Fayetteville, AR 72701 strauss@comp.uark.edu 501-575-6332