Daina Taimina explains hyperbolic planes.
The Institute for Figuring-Crochet Gallery of Hyperbolic Planes
My one ball of yarn hyperbolic plane.
I took a break from all other projects yesterday to make this.
Chain 16, sc in second chain from hook, sc in next 3 stitches, 2 sc in 5th stitch. Repeat until you reach the end, chain one to turn, all rows are worked the same way. 4 sc, 2 sc in next stitch until you reach the end of the row, chain one to turn.
Work until your ball of yarn is done. The big models are done with an increase every 12 stitches, but I just wanted a small one so to really show the way the plane increases, I made the increases more frequent. I made my model in worsted weight cotton (Sugar'n'Cream I think) and used a size F hook to keep it tight for the structure. I think this size hyperbolic planes would make nifty washclothes or toys for babies don't you? The varigated yarn adds so much interest.