Print Friendly, PDF & Email

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

The Impostor

5-crossing knot

5-crossing trefoil

7-crossing knot

7-crossing trefoil

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?

Next Activity:
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!