# The symmetry of shoelaces and real world knots at the Curious Minds Club (St Thomas of Canterbury Primary School, 22 November 2019)

A move away from mathematical knots this week at the Curious Minds Club, and a look at real world knots. We started with a look at the symmetry of shoelaces. I made some ‘shoes’ out of felt and threaded them with one blue lace and one yellow lace. The instructions asked the children to make the base knot with the lace on the left leading first, then make the actual shoe lace knot with the lace on the right leading; this resulted in a neat and tidy, balanced knot with two types of rotational symmetry. I then asked the children to take the other shoe and make the base knot with the lace on the right leading, then make the actual shoe lace knot as above (right lace leading). This lack of alternation resulted in an ugly knot with one part facing the toes and the other part facing the heel; this is the knot which is much more likely to come apart. Ian’s Shoelace Site has more information and really good diagrams.

I then showed the children how to make some actual knots, specifically some loops and some bends.  I used the NetKnots website to learn these knots. The loops we tried were: Slip, Bowline, Hanson and True Lover’s. The bends we tried were: Square (Reef), Flemish and Fishermen’s.

To end the session, one group of children played the Knot Game. Another group had a go at solving some of Adrian Fisher’s Celtic Knot Playing Card puzzles: