Math and science sure are fun, but what are geeks to do once they go home after a long day under the fume hood?  There are many hobbies that can be adapted to soothe the nerdy soul and one that may even enhance mathematical prowess and intuition.

Brace yourselves, it’s crochet.  Yep, crocheting, just like your grandma and great aunt Ethel used to do can produce more than scratchy afghans to adorn your parlor.  It can answer questions like “will straight, parallel lines intersect on a curved surface” or “does my hypothetical pseudosphere agree with Bolyai-Lobachevskian geometry”?  Granted, non-Euclidean geometry sounds pretty fancy, but just watch as it unfolds before your eyes into a three dimensional and easily manipulated model when rendered with yarn and a hook.  (Visit the Institute For Figuring’s (IFF) online exhibit of hyperbolic space for a more extensive introduction.)

“But, I don’t know how to crochet.  My library only subscribes to scholarly peer-reviewed journals.”  Not a problem, check out Henderson and Taimina, 2001, Crocheting the Hyperbolic Plane.

Make your beginning chain stitches (Figure 2a). (Topologists may recognize that as the stitches in the Fox-Artin wild arc!) About 20 chain stitches for the beginning will be enough.

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 2b.)

For the next N stitches proceed exactly like the first stitch except insert the hook into the next chain (instead of the 2nd).

For the (N+1)st stitch proceed as before except insert the hook into the same loop as the N-th stitch.

Repeat Steps 3 and 4 until you reach the end of the row.

At the end of the row before going to the next row do one extra chain stitch.

When you have the model as big as you want, you can stop by just pulling the yarn through the last loop.

Mathematical Intelligencer, Vol. 23, No. 2, pp. 17-28, Spring 2001

The original instructions excerpted above describe crocheting back and forth in rows, but some people find it more satisfying to work in rounds.  In order to begin this method, simply join an initial chain of stitches into a circle by inserting the hook through one chain, hooking the yarn, and pulling the new loop through.  Then make single crochet stitches on the ring.  The examples in figure 1 were worked in this manner with 16 stitches in the starting round.

a. N=0 Single crochet twice in each stitch around.

b. N=1 Single crochet in one stitch, then single crochet twice in next stitch.  Repeat around.

c. N=2 Single crochet in two stitches, then single crochet twice in next stitch.  Repeat around.

d. N=3 Single crochet in three stitches, then single crochet twice in next stitch.  Repeat around.

e. N=4 Single crochet in four stitches, then single crochet twice in next stitch.  Repeat around.

Stay tuned for a future episode of the Science Sort Of… podcast for a chance to win this set of hyperbolic planes, and have fun making your own!