Knot theory and the handcuffs puzzle at the Curious Minds Club (St Thomas of Canterbury Primary School, 8 November 2019)

We started Knot Theory in this week’s Curious Minds Club. The first activity was the Handcuffs Puzzle: in pairs both children had a length of rope attached to their wrists in such a way that they were linked to their partner; the challenge was to untangle themselves. It looks like the length of rope forms a closed loop for each child, but the solution lies in realising that there is a gap under each wrist: if a loop is threaded through in the right direction, passed over the fingers and back over the wrist again then the two pieces of rope do become detached. The children had fun trying this out, but I did need to show them the solution.

The next activity was to challenge the children to tie a knot in a length of rope without letting go of either end. I demonstrated that holding a length of rope in each hand forms a closed loop and that if you do not let go you end up tying your arm into the knot. The children were pleased when I showed them there is a solution which involves tying your arms into a knot before picking up the rope, then unknotting your arms. This works on the principle of the transference of curves: when you unknot your arms you transfer the knot that was on your arms onto the rope.

The final activity was to start to explore some mathematical knots. I had attached velcro to the ends of some shoelaces so that the ends could be joined. The children made the 3,1 (the trefoil) then the 5,1 and the 7,1. They made one crossing change and saw how this allowed them to transform their knot into the previous one in the series.

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