Here is another picture of one of my crochet projects: a hyperbolic plane in fresh spring colours. It’s all curled up because it has a saddle shape everywhere, just like the blue hyperbolic plane I blogged about earlier. This one does not consist of regular triangles, however. It is basically a spiral of stitches, with every new round 3/2 times as long as the last.
On the picture on the right (click on it for a larger one) you can see how it all started: with a fairly small ring of maybe 20 stitches. At first, the whole thing was flat like a panckae (but with a hole in it), then it started to flare like a summer skirt or a stingray, and after a few more rounds it curled up into this fluffy ball.
If you like this sort of thing, check out the Institute for Figuring,
an educational organization dedicated to enhancing the public understanding of figures and figuring techniques. From the physics of snowflakes and the hyperbolic geometry of sea slugs, to the mathematics of paper folding and graphical models of the human mind, the Institute takes as its purview a complex ecology of figuring.