Real MATHEMATICS – Strange Worlds #15

Human Knot Game

Inside a classroom divide students into groups such that each group has at least 5 students. Groups should stand up and form a circle before following the upcoming instructions:

      1. If there is an even number of student in a group:20190812_153400.jpg

  • Have each student extend his/her right hand and take the right hand of another student in the group who is not adjacent to him/her.
    20190812_153408.jpg
  • Repeat the same thing for the left hand.
    20190812_153415.jpg

      2. If there is an odd number of student in a group:

20190812_153325.jpg

  • Have each student (except one of them) extend his/her right hand and take the right hand of another student in the group who is not adjacent to him/her.
    20190812_153338.jpg
  • Then take the extra student and have him/her extend his/her right hand so that the extra student can hold the left hand of another student who is not adjacent to him/her.
    20190812_153345.jpg
  • Finally, repeat the process for the students whose left hands are free.
    20190812_153353.jpg

In the end, students will be knotted.

The-Human-Knot-Game-e1447920419118-663x375

Now, each group should find a way to untangle themselves without letting their hands go. To do that, one can use Reidemeister moves.

Reidemeister Moves

Back in 1926 Kurt Reidemeister discovered something very useful in knot theory. According to him, in the knot theory one can use three moves which we call after his name. Using these three moves we can show if two (or more) knots are the same or not.
For example, using Reidemeister moves, we can see if a knot is an unknot (in other words, if it can be untangled or not).

What are these moves?

Twist

First Reidemeister move is twist. We can twist (or untwist) a part of a knot within the knot theory rules.

Poke

Second one is poke. We can poke a part of a knot as long as we don’t break (or cut) the knot.

Slide

Final one is slide. We can slide a part of a knot according to Reidemeister.

One wonders…

After you participating in a human knot game, ask yourselves which Reidemeister moves did you use during the game?

M. Serkan Kalaycıoğlu

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