Math + Making

A student blog for Math 189AH: Making Mathematics at Harvey Mudd College

Tying Knots with Stop Motion

Lucie Batista

I learned about Knot Theory for a Math Forum presentation that I did and it really spiked my interest. I wanted to see if I could actually produce some knots myself to see what they looked like and how the process of tying them goes. I also wanted to see the variation in different knots with the same number of crossings. For example, a 5_1 knot vs. a 5_2 knot. I decided pipe cleaners might work well to do this because they can hold their shape unlike string. They are also easy to bend. So I started by just making the basic trefoil (3 crossings). Even this was not incredibly easy, but it was very doable. I continued tying all knots with pipe cleaners up to the 6_1 knot. Here is a picture of the knots that I tied:

I then decided to progress my project I would try creating a stop motion video of how these knots are tied. Someone suggested it in class, and I thought it was a good next step for the project. I thought it would be cool to see the knots essentially tying themselves. However, since I wasn’t good at tying them correctly and putting them in the form they are in in the picture above on the first try I was not sure how this would go. I also have never made a stop motion video before and from what I understand it’s pretty difficult. I started with the trefoil, again, since it’s most basic. I just laid the pipe cleaner flat and tried to slowly move it and eventually tie the knot. I would take picture frequently and set up my phone so it was taking them from a birds eye view. I ended up messing this one up a few times because the pipe cleaner would pop out of shape and then there was no way to get it exactly back into the shape that I wanted and in the correct position. I also was not totally sure if I was going to end up adding in extra unnecessary steps for tying it and that would look silly so in the end I tried to avoid this by practicing a few times. It ended up taking a bit of time even though the video does not necessarily look incredibly impressive. Below, is the stop motion video of tying a trefoil:

The next knot that I tied was a 4_1 knot. This one was a bit more difficult because it has another crossing. It also was harder to get it into the right final position because the pipe cleaners are harder to just pull through a loop. But it ended up looking ok. Here’s the video:

Overall, I learned more about knots and how they are tied. It was nice to be able to see them in real life instead of just pictures online. I also learned how to make a stop motion video. Each of the videos I made had about 40 pictures, which seems like a lot but when you look at the video it’s not actually very many. I put the frame rate slightly slower because it’s clearer to see the knot being tied.

I think if I were to do this again I would probably continue tying more knots. But I might also try to make the videos more accurate by taking even more pictures. Using pipe cleaners ended up being harder for the stop motion. I actually think using string or wire might work better for stop motion.


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