How to do it

Adapted from: http://www.math.cornell.edu/~dwh/papers/crochet/crochet.html with thanks and acknowledgement to Dr Daina Taimina

How to Crochet the Hyperbolic Plane

In order to make the crocheted hyperbolic plane you need just very basic crocheting skills.

All you need to know is how to make a chain (to start) and how to single crochet. That’s it! Now you can start. See Figure 1 for a picture of these stitches, which will be described further in the next paragraph.

Figure 1. Crochet stitches for the hyperbolic plane.

First you should choose a yarn that will not stretch a lot. Every yarn will stretch a little but you need one which will keep its shape. Now you are ready to start the stitches:

N = any number you choose. For your first piece I suggest a number between 5 and 8.

1. Make your beginning chain stitches (Figure 1a). About 20 chain stitches for the beginning will be enough.
2. For the first stitch in each row insert the hook into the 2nd chain from the hook. Take yarn over and pull through chain, leaving 2 loops on hook. Take yarn over and pull through both loops. One single crochet stitch has been completed. (Figure 1b.)
3. For the next N stitches proceed exactly like the first stitch except insert the hook into the next chain (instead of the 2nd).
4. For the (N+1)st stitch proceed as before except insert the hook into the same loop as the N-th stitch.
5. Repeat Steps 3 and 4 until you reach the end of the row.
6. At the end of the row before going to the next row do one extra chain stitch.
7. When you have the model as big as you want, you can stop by just pulling the yarn through the last loop.

Be sure to crochet fairly tight and even. Now you can go ahead and make your own hyperbolic plane. You have to increase (by the above procedure) the number of stitches from one row to the next in a constant ratio, N to N+1. You can experiment with different ratios BUT not in the same model. You will get a hyperbolic plane ONLY if you will be increasing the number of stitches in the same ratio all the time.

Crochet Patterns from the Sydney Hyperbolic Coral Reef project.

http://api.ning.com/files/G2EJhF1dJ8MQoEWlYh9uo26KjZUDcJ9yunVySop4YKNZrHaWs9s4KMe6a0O0odFSPw-B4Ob8i1ZXDeawxrJBLI2YagVu5Fpi/coralreefcrochet.pdf

Theresa’s blog. She has the best video instructions on how to crochet, easily followed. She also has lots of crochet patterns and stitches. Excellent for anyone just starting to crochet.

http://crochet-mania.blogspot.com/

Ravelry: knitters and crocheter’s community!

http://www.ravelry.com/tour/getting-started

How to crochet with instruction for crocheting a moebius strip

http://www.csiro.au/helix/sciencemail/activities/Crochet.html.