This week I watched Carolyn Yackel’s (2020) presentation How Orbifolds Inform Shibori Dyeing. This is a Japanese dying technique, like tie-dying but the goal is to get a repeated pattern across the fabric. This is tricky, because you need to fold and clamp the fabric in ways that will allow spaces for the dye to access and spaces where it cannot go. (Which connects to the idea of absence again, and limitations of products and maths.) The result is really neat though. This example below is folded like a hexaflexagon: the fabric is pleated accordion-style into a strip and then folded in equilateral triangles and clamped before exposing to dye.

While this is a really neat exploration of folding (3D) and its resulting symmetries (2D), I’m not sure I would be brave enough to try dying with a whole class of students. Having just had paint and hot glue out for my final project activity, it doesn’t seem realistic. Maybe starting with a smaller group - a math club? 

Something more tangible for classroom exploring might be along the lines of Polster’s (2020) What is the Best Ways to Lace Your Shoes. Always finding that I need more lace to tie in my own shoes, I was quite interested in trying the shortest lacing methods to see if I could gain more tying length. It made sense that the shortest method would be the straightest distance, like a rectangle. But, wearing this one was not very supportive. The next shortest alternates rectangular straight sections with a criss-cross and this one I found just as supportive as my regular criss-cross all the way up, and it did leave more tying room!      

                                

Polster’s video also poses thought provoking questions besides shortest lacing like, longest, strongest, what would it look like with a shoe that has 100 eyelets, etc. He also explains how he came up with proofs for his findings which is kinda neat. I stopped at the Dollar Store to see if I could get bright laces - neon pink or green - but, they didn’t have any :( I would like to pick some up and try doing some of the more visual patterns and wear them into work just to see if they spark some mathematical conversions, like a little provocation. 

    

  Maybe bulk buying some funky coloured laces and letting students explore and create some of their own lace patterns would be a fun way to provide opportunity to explore and play. These themes, that we were first introduced to with Francis Su in 550, were something I noticed this week (and other weeks in this course too.) They are a key piece to finding new perspectives and learnings about/with maths. What happens if I try that with this medium? How can I get that outcome within the constraints of this medium? I think exploration and play are also key in accessing that space in between math and art, that Susan mentions in our introduction this week: “the 'flow' can go from mathematics to needlework, or from needlework to mathematics, or a third space can be created where mathematics and fiber arts inform each other!” 

References: 

Polster, B. (2020, June 20). What is the best way to lace your shoes? Dream proof [Video]. YouTube. https://www.youtube.com/watch?v=CSw3Wqoim5M

Su, F. (2020). Mathematics for Human Flourishing. Yale University Press.

Yackel, C. (2020). How orbifolds inform shibori dyeing [Video]. YouTube. https://www.youtube.com/watch?v=hjtc9LJ5ItI