arts & Crafts
arts & Crafts
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I've been knitting and crocheting almost since birth, but I dabble in hand-sewing, embroidery, origami, digital art...you name it. There are certainly mathy crafters out there who produce much more polished pieces with much more high-quality materials, but I like to use dollar store yarn and audacity (and sometimes staples) for my own entertainment. I've done some very fun and meditative modular origami, mostly using Sonobe units, but they're hanging from the ceiling in my Math Center. You can explore YouTube for many good tutorials.
A crocheted unzippable Mobius strip. Most of us cut apart Mobius strips in elementary school, but this way you can undo the process.
The unzipped Mobius strip -- which becomes a loop with four half-twists. Getting it zipped back up is a fun adventure, but not too hard.
A crocheted six-colored Mobius strip (read about it here).
A knitted torus with the Utilities Problem embroidered on it. For the base torus, I utilized the pattern generator by Amy Szczepanski. My mother was visiting and chose the buttons from my random button collection.
Top view.
View from underneath.
A crocheted model of a Klein bottle. This is a nonorientable surface whose inside is also its outside... In 3D space it must intersect itself, so the blue part passes into the body of the bottle.
You can see how it kinda cuffs like a sock to meet the purple part.
Another crocheted Klein bottle, showing how it can be constructed by "gluing" together two Mobius strips of opposite chirality.
I believe I saw one of these at the 2023 JMM by Beyza Aslan. Mine is certainly clunkier than the excellent specimen I saw there!
Crocheted "hyperbolic surfaces," which are made in the round by continuously increasing the number of stitches. Many people have made very cool versions of these, but I've been making them since childhood, when I thought I would be a marine biologist and liked coral...
A crocheted model of the real projective plane, following the "glue a disk to the edge of a Mobius strip" construction. The white strip is the original Mobius band that I started with. In 3D space, it has to pass through itself, which makes this fun to play with, as you can eternally pull it through.
Various crocheted prime knots: in particular, 3_1 (trefoil), 5_1 (cinquefoil), and 7_4.
Two crocheted trefoil knots interlaced.
This is also a model of the real projective plane, using the "glue together sides of a rectangle" construction. The top and bottom sides of a rectangle are sewn together with a half-twist as if making a Mobius strip. Then the left and right sides of the rectangle are sewn together, also with a half twist. It just so happened that the only rectangular piece of fabric I had in the house was this cat print... My cat Millie came to inspect the result, which is a Fortunatus's purse whose inside is also its outside...
Speaking of gluing, here is a genus-2 surface formed by "gluing" certain edges of an "octagon" together. The left picture shows the unglued octagon, and when color-coded edges are sewn together, the result is the kinda repulsive object on the right. I based this off of this diagram.
This is a genus-2 surface made following this amazing video by Shiying Dong. Not gonna lie, getting the two foundation chains linked together almost killed me, but I made it in the end. The blue boundary is a trefoil knot.
IMG_8025.MOVThese are crocheted versions of "flexagons" which you can make out of paper. The 3D one on the left shows three colors at any given time while "hiding" the fourth color faces folded inward. The hexaflexagon on the right can be seen as a flattened Mobius strip and flexes to reveal a third color.
IMG_8034.MOVPage updated
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