Monday, January 11, 2010

Scrunchies and a meditation on crochet-based geometry

[Warning, this post contains mathematics. :D]

My sister is going to be graduating from high school in March, and will hopefully be going on to cooking school after that. Since both her school uniform and her love for cooking require her to keep her longish hair under control, I'm making her a series of gifts that will see much use in the days to come: scrunchies, and quite possibly a headband or two.

In particular, there are these: a set of six hyperbolic scrunchies - three in her favorite colors, three more in black. [I SAID there was math involved, didn't I?]

These photos show two of the three colored scrunchies; I'm making the violet one later, and then the black ones. The pattern is based on Cayenne Boyer's Hyperbolic Scrunchie; I've modified the pattern by taking out the fourth and final round. [Pattern remains © Cayenne Boyer.]

The scrunchies take the form of a hyperbolic plane [see Wikipedia entry on hyperbolic geometry here]. For some reason, the craft of crochet has been used, in particular by the Institute for Figuring, as a way of visualizing this non-Euclidean form of geometry; they're the folks behind the Hyperbolic Crochet Coral Reef, based on the techniques of hyperbolic crochet created by the mathematician Daina Taimina.

In crochet terms, it actually comes down to a definite pattern of increases in a piece made in the round, causing the edges to ruffle up.

I don't claim to understand the math behind the scrunchies I'm making, but it makes for a fascinating crafting experience.

I hope my sister enjoys using these.

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