Trefoil D. Knot
Wanted for: Impersonating more complex knots
Trefoil D. Knot is a master of disguise – the photo above is Trefoil’s most recognizable projection. However, at any given moment he may be disguised as the following knots:
The Real McCoys
This slippery little fellow has also been known to gallivant around disguised as other knots:
1. Here Trefoil is trying to look like the figure-eight knot, a four-crossing knot. Fortunately, this disguise can be stripped with a single Reidemeister move. Which Reidemeister move will accomplish this?
2. Which Reidemeister move is used in the 5-crossing example above?
3. Which Reidemeister moves are necessary in the 7-crossing example?
4. What differences do you notice between the “real” knots and the impostors?
5. How might we be able to tell more quickly if a knot is an impostor?
When you feel confident enough, join in the Hunt for the Elusive Trefoil Knot! See if you can see through the many disguises of the Trefoil!