STEP 1: Why Crochet Hyperbolic Planes?

In 1997 a math professor at Cornell University, Dr. Daina Taimina, discovered that it was possible to create a physical model of a hyperbolic plane using the art of crochet. Many mathematicians thought a physical model was impossible to create. A 2005 article in the New York Times explains: Professor Lets Her Fingers To The Talking.

In an interview for Cabinet magazine, Dr. Taimina and her husband, David Henderson, discuss crocheting hyperbolic planes: “Until the nineteenth century, mathematicians knew about only two kinds of geometry: the Euclidean plane and the sphere. It was a deep shock to their community to find that there existed in principle a completely other spatial structure, whose existence was only discerned by overturning a two-thousand-year-old prejudice about “parallel” lines. The discovery of hyperbolic space by the Hungarian mathematician Janos Bolyai and the Russian mathematician Nicholay Lobatchevsky in the 1820’s and 1830’s marked a turning point in mathematics and initiated the formal study of non-Euclidean geometry. Almost two centuries later, Daina Taimina a mathematician at Cornell University made a physical model of the hyperbolic plane – a feat many mathematicians had believed was impossible – using, of all things, crochet. Taimina and her husband David Henderson, a geometer at Cornell, are the co-authors of “Experiencing Geometry,” a classic textbook on Euclidean and non-Euclidean space.”

Dr. Taimina has written a book on the subject and also has a blogShe explains hyperbolic geometry using crocheted models in the video, Geometries Beyond Euclid from the Annenburg Learner website, Mathematics Illuminated.

In Chapter 9 of her award-winning book, Dr. Taimana discusses how hyperbolic geometry has applications in many fields and is of interest to those studying computer science, mathematics, biology, chemistry, medicine, network security, music, art, and physics. Hyperbolic geometry is even used to help us visualize the world wide web.

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WATCH THIS VIDEO

UNDERSTANDING HYPERBOLIC GEOMETRY
The Beautiful Math of Coral

Taking the concept of hyperbolic crochet models further, science writer Margaret Wertheim uses this technique to create museum exhibits of crocheted coral reefs.  She explains on this stunning Ted Talks video, The Beautiful Math of Coral, citing the work of Dr. Taimina.  She and her sister, Christine, founded the Institute for Figuring, which is “… is an educational organization dedicated to enhancing the public understanding of figures and figuring techniques. From the physics of snowflakes and the hyperbolic geometry of sea slugs, to the mathematics of paper folding and graphical models of the human mind, the Institute takes as its purview a complex ecology of figuring.

Here is their explanation of hyperbolic space: Hyperbolic Spaces Online Exhibit.

You might also want to check out Margaret Wertheim’s book, A Field Guide To Hyperbolic Space in which she explores the intersection of higher geometry and feminine handicraft.  This book includes patterns for crocheting a wide variety of hyperbolic models.

Are you ready to create your own crocheted hyperbolic plane?  Proceed to Step 2 if you need to learn to crochet.  If you already know how to crochet, proceed to Step 3Have fun!

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