A hyperbolic plane is a mathematical object. I first made its acquaintance through the work of Daina Taimina, author of Crocheting Adventures with Hyperbolic Planes. The photograph in the previous post is of a crocheted hyperbolic plane I made this past summer.
Taimina’s book won the Diagram Prize for Oddest Book Title of the Year for 2009 (the prize was originally conceived as a way to avoid boredom at the annual Frankfurt Book Fair, and has been awarded annually for more than 30 years.) In her blog, Taimina writes, “Best of all, in The Booksellers announcement I liked what Mr. Bent said about my book:
I think what won it for Crocheting Adventures with Hyperbolic Planes is that, very simply, the title is completely bonkers. On the one hand you have the typically feminine, gentle and wooly world of needlework and on the other, the exciting but incredibly un-wooly world of hyperbolic geometry and negative curvature. In Crocheting Adventures with Hyperbolic Planes the two worlds collide—in a captivating and quite breathtaking way.”
Mr. Bent’s reaction to the book was mine as well. I was drawn to the paradox, the incongruity. I had no interest in math, and really no interest in crochet either, but the idea of the book stayed with me. I don’t recall how I first heard of the book, but I think it was before the award was announced. Perhaps my brother, Nat Kuhn, who has a Ph.D. in Mathematics (his dissertation adviser William Thurston–winner of the Fields medal–wrote the introduction) told me about it. I know I bought a copy in the Winter of 2010 for my students in the Olin College of Engineering extracurricular “Fiber Arts for Engineers.” Then in September 2010, Taimina spoke at the Common Cod Fiber Guild at MIT (fiber guild? a bunch of knitters at MIT? Absolutely!) Of course I had to go.
At her talk, Taimina answered the question you are probably asking too: what IS a hyperbolic plane? Her simple and accessible answer is more or less as follows: an orange is a surface of constant positive curvature; a banana has both positive and negative curvature; and a hyperbolic plane has constant negative curvature. Imagine the ruffled edge on a leaf of kale, my personal favorite hyperbolic vegetable. Or the ruffles found on other natural things, such as some seaweed or the inhabitants of the coral reef (the inspiration for the Crocheted Coral Reef, an effort sparked by Taimina’s work.) These real life objects, of course, are not perfect models of the mathematical ideal–but they bring us close, and are lovely inspirations to mathematical inquiry.
In spite of all this inspiration, it was not until this past February that I finally decided to try my hand at hyperbolic crochet. I bought some cheap fuzzy synthetic yarn at a local big box store and set to work. The directions in the book were fairly minimal, and minimal is all you need–if you already know something about crochet. I struggled with my yarn, and soldiered on, but as I did my misgivings grew. What was I doing wrong? What was I doing right? I had no idea. I didn’t even have much idea about how to get help. At last I came up with the idea to go to drop-in night at my local independent yarn store, and I did get a little lesson on how to crochet. Finally, the penny dropped when I went to an hour-long workshop on “crocheting a hyperbolic dishcloth” (yes, you read that right) at Common Cod’s spring Fiber Camp. Thanks to Rachel, my teacher, who helped me see the light. My skills are still extremely rudimentary, but they are good enough to allow me to churn out the hyperbolic planes at the rate of one every week or two since March! Thank you, Daina!