My dog is really into hyperbolic space. Maisie’s favorite toy these days is a little model of a pseudosphere I crocheted using the guidance found in A Field Guide to Hyperbolic Space by Margaret Wertheim (and with a little extra guidance from tips found at Lion Brand). Creating crocheted mathematical models of non-Euclidean space was the genius work of mathematician Daina Taimina. Her models inspired the Institute for Figuring‘snow internationally famous crochet coral reef project. Wertheim’s excellent primer on hyperbolic space includes illustrated instructions for creating a variety of forms, and I recommend it if you’re interested in hands-on geometry for the layperson or in crocheting some coral.
But Maisie doesn’t care about geometry, space, or even crochet. She likes her pseudosphere because it’s as satisfying to chew as it is easy to pick up quickly with one’s mouth. She also seems to appreciate that, when we play catch with it, the pseudosphere doesn’t hurt her when it ends up bouncing off of her snout. Below are the basic instructions on making a hyperbolic dog toy like the one pictured. It’s pretty easy and requires only the most rudimentary crochet skills and a few supplies. Mathematically, it’s not a true pseudosphere because at the very start I increase from 1 to 6 in a single round instead of increasing consistently from the beginning. But your dog won’t know the difference.
What you need:
*A small amount of yarn of your choice. The amount will depend on how big you want your finished product to be. This project is a good way to use up leftovers from previous knit or crochet projects. This is also a project that is well suited to a tough acrylic yarn, because this seems to resist my dog’s dedicated chewing habits longer than does a natural fiber yarn.
*A crochet hook that will work nicely, size-wise, with your chosen yarn’s weight. (For the leafy green one pictured, I used some leftover worsted Vanna’s Choice and a size I hook.)
*Crochet a chain of two stitches.
*Single crochet 6 times into the second chain stitch from the hook, then slip stitch through the first chain stitch to end up with a little circle of six stitches. *From here on, simply single crochet two stitches into every stitch as you go round and round. Continue rounds until the toy is as large as you want it.
(The one pictured is made up of just six rounds, and it measures about 3.5 inches in diameter. In this last picture I’ve carefully pulled back the ruffled edges to reveal the center circle, but its more usual shape isthe ruffly, unruly sphere in the two other pictures.)