Trying to study knots with 5 crossings

We’ve been doing a little bit of work with knots lately. Today we were studying the knot with 5 crossings, and it wasn’t so easy.

I’d guess ahead of time that 5 crossing would be tricky. There’s a lot to keep track of! Even what seems like a simple task – making a knot with 5 crossings out of rope – isn’t so easy. See if you can spot the problem:

The boys didn’t notice the problem with their knot, yet, but the problem quickly became clear when they started playing with it:

So, we started over . . .

Having now made a knot with 5 crossings, we ended the project by trying to determine which of the two knots with 5 crossings that it was. We got a little bit of a surprise when it turned out that we’d actually made the mirror image of one of the knots we printed. That was an accidental good lesson, though – mathematicians consider those two knots to be the same even though they are not always the same.

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Comments

3 Comments so far. Leave a comment below.
  1. What do you do with all of the shapes from your 3d printing projects? Is this the start of another MoMath branch?

    • Sometimes I send them to people – I saw Evelyn Lamb do a talk one time where she said “oh, I wish I had this shape” and I had it so I sent it to her.

      I’m not sure what I’m going to do with all of the knots, though. They would be helpful for a high school-level project on knots, I think.

      maybe you and I can put something together when you arrive here!

  2. Sounds good, Back in the mists of time, I knew something about knots and it would be fun to re-learn it.

    Your torus wire frame reminded me of this:
    Go on a Torus. We are currently obsessed with go.

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