Knitting, Crocheting, and Mathematics.

  In most geometry classes, students spend time learning about angles, shapes, and relationships but we don't usually do much with them once the unit or units are over.

The other day, I scrolled through knitting and crochet books, looking for those on sale and found a book showing people how to crochet circles, squares, triangles, hexagons, pentagons and spirals. 

I remember seeing a baby blanket made up of a ton of squares sewn together.  After checking things out, it is possible to make a bunch of triangles, hexagons, or pentagons that are sewn together to create a blanket.  In addition, you can make spheres, cones, and cylinders to create heads, arms and legs, or tails.

If you prefer doing something a bit more mathematically esoteric, how about crocheting a hyperbolic plane that resembles the edges of a lettuce leaf.  Its too hard to make one out of paper that stays together so a math professor and her husband figured out a pattern based on an algorithm.  I've actually seen someone making one out of yarn.  I did put the link to the instructions.

You could also crochet the twisted ribbon structure of Lorenz manifold. If you are not up to date on the Lorenz manifold, it comes from a paper written back in 1963 about chaotic weather systems and is believed to be the start of chaos theory.  Further more, if you'd like to represent cyclic systems you could knit a tube which provides a great visual of following a pattern back to where it started.

If you wanted to move into fashion, you could knit Mobius cowls or a swan tea cozy.  Perhaps you could make a curve of pursuit pillow out of an equiangular spiral or perhaps a dragon?  Now if you'd like to explore a really cool site with all sorts of things like Klein bottle hats or hyperbolic baby pants, fractals, etc, go ahead.  Unfortunately, not all of the links are live.  Some are broken and some lead to patterns which do cost but some of the products are neat.

If you prefer to stay with the bare bones of math in regard to knitting or crocheting, there the pattern which uses repetitions of stitches, gauge based on a specific yarn so if you use a different yarn, you have to adjust.  When you increase the number of stitches, you are adding but when you remove or decrease stitches, you subtract.  If you need to calculate the cost of the project you use multiplication and if you are knitting a sock, you have to divide the number of stitches equally among the needles.

I think its awesome the way knitting and crocheting have expanded to create visual representations of all sorts of mathematics.  Check out Sarah-Marie Belcastro's webpage, the home of Mathematical Knitting with loads of links, examples, and articles on mathematical knitting.  She created the hyperbolic baby pants.

I'd love to hear what you think.  Drop me a line.