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The Invertible Trefoil

Age 14 to 16
Challenge Level

Work with this topic is most productive when the theme can be given some time.

Because it is not traditional school mathematics it offers a good opportunity for students to explore something new and experience the emergence of structure for themselves.

Having some good weight rope is helpful and the use of tubing allows easy closure to present a closed path in three dimensional space.

Allow plenty of time for discussion :

How do we begin to talk about something which for most of us is just a tangle of string or a tied knot we do so automatically, like a shoe lace or a reef knot, that we hardly think about it ?

A knot collection might make a stimulating talking point for students in a classroom.