Here is a game to play with a group of about ten people.  Many of you may have played it before:
  • Stand in a tight circle and have each person reach into the middle with his or her left hand and grab someone else's left hand.  If you have an odd person out, she should hold someone else's right hand with her left.
  • Then have everyone reach into the middle of the circle with his or her right hand and grab the right hand of a different person (i.e. not the person whose right hand they're holding).
  • Now, without letting go of hands, try to untangle the knot to the simplest form you can manage.  You might have to climb over or under other people in the knot to get untangled.  See what happens!
Knot theory is a real branch of mathematics where we look at squiggles with the ends connected together and try to figure out what shapes they become if we simplify them by uncrossing lines and untwisting loops.  The simplest knot isn't a knot at all: it's a circle, and it's called the unknot.  You can think of twisting up a rubber band until it's a mess of tangles.  No matter what you do, it will still untwist back into a circular shape.

We can also have interlocking unknots, called loops.  Think of these like the magician's magic rings, except instead of magically separating into separate unknots, they stay linked together.

A third common type of knot is the trefoil knot.  Tie an overhand knot in a piece of yarn and then tie the two ends of the yarn together.  Pull out the loops of the knot and lay it out until it looks like this:

Beautiful, isn't it?

Now, try your human knot game again, but this time see if you can figure out what to do at the start to purposefully get one of these three types of knots in the end.  

If you want to see a video with more knot theory games, check out Vi Hart's video about doodling in math class.

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