Part III of winter hats is here! And this time it’s math-based. Remember Part I? It featured a blue hat? Well, I had yarn left over, in prodigious amounts. So I decided to make something for myself. I had seen a Mobius scarf, which I had really liked the idea of. As you’ll see, mine didn’t turn out quite the way I’d pictured, but it works! I also made a knitted math hat. Peruse the pictures below!
Garment Data:
– Type: Hat, scarf
– Date made: Probably summer of 2008?
– Pattern: None. I looked at other hats/scarves in the math shapes I wanted, but then just went from there on my own.
– Fabric/Materials: Acrylic yarn (or maybe an acrylic/wool blend?)
– Trim: none
– Time to finish: I know it took a while! A few weeks, maybe?
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| The hat and scarf set. They don’t look like much, but I promise that they are mathematically cool! And yet warm to wear 😉 |
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| Here you can see them together. |
The scarf is actually a Mobius strip! In fact, instead of knitting a strip, putting a twist in, and having a seam, I actually took several tries to put the twist into my first row, so that as I knit, I actually went twice around and added to “both” edges before coming back to the beginning of my row!
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| Here you can see the twist in the scarf. This means that though it is “two-dimensional” (flat), the twist makes it 3D. |
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| It’s ribbed, 5 rows each of knit and then purl. Unfortunately this means it curls up into a narrow strand. |
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| I tend to wear it looped 3 times around my neck. |
The hat, though, is even cooler. It is a Klein bottle, which is a tube that connects to itself – but not at the ends, to make a donut (“torus”). Nope, it goes through itself!!
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| Here, from the outside, you can see the outer surface narrow and go in to meet the inner surface. |
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| Here’s a close-up of where the outside goes in. Instead of going through its own surface like a proper Klein bottle (explained below), since knitting is a “porous” surface, I had the small end of the tube go through a stretched hole. Then, from the other side, I widened the tube by knitting expansions into it, so that it could meet the inside tube. |
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| Here you can see the inside of the hat, where the outside comes through and joins (you can see the seam about 3 inches down from the crown). Because of the way a Klein bottle works, the hat is actually two layers. You can also kind of see that the top of the hat was knitted on smaller gauge needles. I go back and forth on whether that was a good decision or not – it made it harder to work, and also made it less “loopy” and thus less obviously a Klein bottle. |
This video has a pretty good visual explanation of what my hat does:
Video credit to bothmer for the excellent visual explanation of how a Klein Bottle is basically a 3D Mobius strip.
As to how it compares to my hat, the curly bottom part in the video is the top of my hat. And doubled over, almost donut-like top in the video is the two-layer part of the hat that goes on my head!
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| Here you can see the ribbed brim I added to the part of the shape that I decided would be the best “hat” part (the top of the shape in the video). This made the shape into a true hat, since now you can see which part to put on your head! |
Most sincerely yours,
~ Sarah