Math and Crafts

Math and Crafts

Yes, it's every one's favorite irrational number, pi, featured on a quilt. ("Traditional as Apple Pi," by Mona Wilkers, 1998) Traditional crafts such as quilting, knitting, and needlepoint have often been dismissed as thoroughly non-intellectual, but a greater number of people are now realizing that our grandmothers (and grandfathers!) were exercising high-order mathematical thinking as they produced all those sweaters, blankets, and embroidered pillow shams. Fortunately, in recent decades, mathematicians have taken notice of the correlations between various needle crafts and mathematical principles, and have begun to explore how crafts can be used to deepen one's understanding of mathematics.

One great example comes from Eleanor Kent (click the link for more examples) who, among other media, knits fractals and algorithms in traditional color work techniques, like the one below. ("Magic Carpet," 1993)Quilters have also explored the fun that is fractals, like Rebecca Chaky did in her "Flow Snake" quilt (1983), which was inspired by a 1976 article on fractals by Martin Gardner. (Also of note: Martin Gardner specialized in "recreational mathematics." I'm so envious!)
Of course, a quilted or knitted fractal can never be a true fractal, as they cannot represent the pattern in its nth iteration. For those of us mortals who are unable to visualize the infinite, however, I think they are as good as the real thing!

As for 3-dimensional surfaces, Sarah-Marie Belcastro is a great resource for examples of mathematical knitting. Her knitted Mobius bands come with a patternand she also has examples of the one-, two-, and three-holed torus.Now, for the teachers in the audience, I have a few resources to help you bring crafts into your classrooms. For advanced math students (and advanced fiber arts students!), Sarah-Marie Belcastro has co-edited a book, Making Mathematics with Needlework, which pairs 10 different mathematical papers with corresponding knitting, crochet, embroidery, sewing and quilting projects that elaborate on their theses. (This one just knocked Madame Bovary out of the top slot on my reading list!) For younger students, check out this great article by Heather Taylor on how hands-on skills such as knitting help develop children's motor skills and prepare them to better understand abstract spatial and numerical concepts.

I know this has been a picture-heavy post, but I would be remiss if I didn't share all my favorite examples of mathematical crafting with you, and I have saved the ones that impressed me most for last. First, take a virtual visit to the Institute for Figuring to gawk at their gallery of crocheted hyperbolic planes. Crochet was one of the first methods used, in 1997, to model hyperbolic space, and remains one of the most practical, due to its strength and flexibility.
For those who are interested, here is the updated version of Daina Taimina's original paper, which contains instructions on how to crochet your own hyperbolic plane.

Finally, William H. Mitchell turned one of my favorite mathematical concepts, Pascal's Triangle, into the most stunning piece of needlepoint I have ever seen. Please click on the artist's name to find an explanation of the color symbolism he used to represent the numbers in the triangle. Enjoy!