Crafting Conundrums

Ungar-Leech Map bracelet from above.

If you've met me in person in the last couple years, you've probably heard me mention that my husband lives in Maryland while I live in Georgia. This is not my favorite living arrangement; and I can disavow the illusion that maintaining two households is a glamorous lifestyle. It is a major inconvenience, it is expensive, and it is a huge drain on my time. That said, we've all heard about making lemonade out of lemons. I've used the trips to Maryland to work with other Center for Knit and Crochet board members in person instead of over the phone or Internet, or to visit family in Pennsylvania, or to attend the Maryland Sheep and Wool Festival, or to shop at The Mannings or The Knitting Boutique. I've also been attending Southern Maryland Knitting Guild meetings when I can.

I met Dr. Susan Goldstine at one of these meetings. Susan is a professor of mathematics at St. Mary's College of Maryland. She is also a clever crafter. She has previously published a chapter called "Fortunatus's Purse" in Sarah-Marie Belcastro and Carolyn Yackel's compilation Making Mathematics with Needlework (ISBN: 978-1-56881-331-8) as well as the chapter "Perfectly Simple: Squaring the Rectangle" in their follow-up compilation Crafting by Concepts (ISBN: 978-1-56881-435-1). Susan and Dr. Ellie Baker (computer science) recently published Crafting Conundrums: Puzzles and Patterns for the Bead Crochet Artist (Boca Raton FL: CRC Press 2015; ISBN: 978-1-4665-8848-6).

Yes, this involves crochet. Please, keep reading.

Why should you try this?

• Bead crochet turns out to be a very pleasant craft. There is quite a bit of attention required in the bead stringing at the beginning. But once all the beads are strung -- correctly, I hope! -- the crocheting is straightforward. In this regard, it reminds me of weaving. There is lots of up front thought and planning and design, but then zen calm in producing.
• It offers lots of opportunity for individual design.
• The tactile quality of the fabric is fantastic!
• These projects give you a great excuse to acquire beads. Shiny! Pretty!
• It is fairly quick. I was able to string a complex bracelet in an evening (about 3 or 4 hours) and crochet it up over a few more evenings. Producing a bracelet a week is an attainable goal if you can commit a couple hours each night. Not quite instant gratification, but close.
• These bracelets would be perfect for holiday gift exchanges and last-minute gifts. You could easily amass a stash of them, ready at a moment's notice.
• While this is somewhat fine work, once the beads are strung the project is transportable if you keep it in a bag so the thread can't tangle. You could definitely work on these at sporting events or in waiting rooms.
• The math is fascinating.

For you Star Trek fans, bead crochet embodies the Vulcan proverb, "Infinite diversity in infinite combination." Or another way of thinking of this, out of something simple comes something complex. (This is where I like to think of DNA, how the bonding of merely two different pairs of molecules can lead to sequences of four different molecules that can "write" the genome of thousands of species and billions of individuals. Awesome!) A bead crochet bracelet is a torus -- the same shape as a doughnut or bagel. It turns out this shape has some amazing geometric properties. Also, beads in bead crochet pack in on a hexagonal grid, rather than an orthogonal grid. It is the intersection of these two geometries that make the bead crochet bracelet such a fascinating form that two women with doctorates from Harvard would write a book about it.

Ungar-Leech Map bracelet from below. Every color touches the other six.

The example I've made is the second pattern in the book (p. 135), the "Seven-Color Torus (Ungar-Leech Map)." There is a theorem that any planar or spherical map can be colored with only four colors so that no countries with adjoining boundaries are painted in the same color. I had heard of this theorem before, probably in high school geometry. But what I did not know is that if your map is on a torus, it is possible to have a map that requires seven colors. This bracelet is a model demonstrating such truth. Why didn't they teach this cool stuff in high school geometry?

Crafting Conundrums lays down a groundwork both for how to design in bead crochet in general, and how to play with some of the geometric peculiarities of the bead crochet torus in particular. In addition to seven-color tori, there are chapters on geometric cross sections, torus knots, Escher designs (i.e. tiling the torus with a single shape), and wallpaper groups. There is also a short chapter on knotted and linked bracelets, but that chapter feels incomplete. Perhaps it will be the seed for a second installment?

For those of us who love math, the book is a fascinating exploration into the stuff I wish I had learned in high school geometry. But even if you don't want to walk in those woods, there is plenty for you. The book contains 94 patterns for bracelets, plus three patterns for transformation necklaces (necklaces that slowly change patterns, imitating some works by M. C. Escher). Elements of the necklaces can be used to create bracelets as well, so you could easily work over 100 different bracelets just from the patterns. If you would rather create your own designs, the book provides accessible geometric explanations as to what will and won't work and how to tell before you string a whole bracelet and start to crochet. Bead crochet graph paper in two sizes is included at the back of the book, but you can also visit the publisher's page to download the .pdf files and print your own. Susan has posted a series of six videos on YouTube to walk you through the process of making a bracelet in case the thorough print tutorials in the book are insufficient. Thus, you can follow the paths Susan and Ellie have trail-blazed, or you can strike out on your own bead crochet adventure!

A note to any programmers out there. If you want to make a kick butt bead crochet bracelet design program for iPad, this book gives you the foundation math. Even a basic grid that allows you to paint beads and have the corresponding bead repeats paint simultaneously would be a huge help and great fun.