# Solving mazes and Mobius paper chains at the Curious Minds Club (St Thomas of Canterbury Primary School, 13 December 2019)

In our final week of this term at the Curious Minds Club we explored how to solve a maze. A maze is a type of topological puzzle. I showed the children a method of solving a maze by shading in all the dead ends: a dead end is chosen and shaded back to a point where a decision has to be made; at this point no further shading can be done so another dead end is chosen and the shading repeated. When no further dead ends can be found what remains is the solution to the maze. The children explored this method using some Christmas mazes I found online.

Last week we explored Borromean and Brunnian links. There was one activity we ran out of time for, so I brought it this week. Professor Tadashi Tokieda calls this a Borromean ribbon. His Numberphile You Tube video gives a great visual demonstration.

I tied some strips of ribbon into closed loops and showed the children how to set them up on one hand. The children soon got to grips with how to pull one ribbon down and come up with a surprising result.

The final activity was a make a Mobius paper chain to take home. I told the children we could have made regular Christmas paper chains, but they are boring. So much better to remember the session we did a few weeks ago on the Mobius loop. I had cut strips out of Christmas themed paper and reminded the children of the twist which produces the Mobius loop. The children then got to work, threading, twisting and taping. Here are some examples:

Year 5 boy:

Year 6 boy:

# Mobius loops at the Curious Minds Club (St Thomas of Canterbury Primary School, 4 October 2019)

We explored the Mobius loop in this week’s Curious Minds Club. The children made a straight loop and drew lines around the centre of the paper strip on the inside and the outside to prove the loop has two faces. They did the same along the edges to prove the loop has two edges. I showed they how to introduce a half twist, and how this changes the property of the new Mobius loop to only having one face and one edge.

The children cut the Mobius loop along its centre line to show that it does not fall into two pieces as expected, but becomes a loop with four half twists. I asked the children to predict what would happen if they cut a Mobius loop one third of the way in: some predicted two loops, and some predicted one twisted loop. They made the cut and were surprised to make two connected loops, one Mobius and one non-Mobius.

The next experiment was to connect together two straight Mobius loops. No one predicted that the result would be a square. Our final experiment was to connect together two Mobius loops of opposite chirality, one with a right half twist and one with a left half twist. The delightful result was two interconnected hearts!