Instructions: put cursor into graphics window, and with left button pressed, drag the cursor. The knot shown will rotate. There are three other things one can do: translate, scale, and reset. To do these use pop-up menu at top of frame. The translating and scaling are done by dragging the cursor in the window as with rotation.

NOTE: the software used here is the JGV viewer written at the Geometry Center.

There are two knots shown---a right hand trefoil and a left hand trefoil. Note carefully how these differ at the crossings. These are mirror images of each other. In terms of rigid motions, this means there is an orientation ** reversing ** rigid motion that transforms one knot to the other.

These are not topologically equivalent knots (that is not easy to prove). However, you can convince yourself that there is no way of rotating one knot so that it coincides with the position of the other. Try it (below).

What does this show? It shows that the right hand trefoil and the left hand trefoil knots are not equivalent if one uses orientation preserving rigid motions.