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Daina Taimina

Discoverer of Hyperbolic Crochet

A large symmetric hyperbolic plane by Dr Daina Taimina.
All photos on this page are courtesy of Dr Daina Tamina and used with permission.

For hundreds of years mathematicians tried to show that anything like hyperbolic space was impossible, until finally, in the nineteenth century, they accepted the "existence" of this aberrant geometry. Still many believed it wasn't possible to model the structure materially. They were thus surprised to learn in 1997 that Dr. Daina Taimina had done just that using the traditional art of crochet.


Daina Taimina's long-awaited book is now available. Entitled Crocheting Adventures wth Hyperbolic Planes, the book is a feast of information about all aspects of the mathematics of hyperbolic space. Complete with over 200 photos and diagrams, plus a detailed account of her discovery of hyperbolic crochet, the book is an invaluabe resource to mathematical and crochet enthusiasts everywhere. The IFF highly recommeds this lushy produced volume!

Purchase Dr Taimina's book here from the pubisher A.K. Peters

Three different "wrappings" of a large variegated symmetric hyperbolic plane by Daina Taimina.

A mathematician at Cornell University, Daina grew up in Latvia where at an early age she learned to knit and crochet. She is a superb knitter and when she initially had the inspiration that led her to then invention of hyperbolic handicraft the first method she tried was knitting. You can indeed knit hyperbolic structures but it quickly becomes unmanageable with so many stitches on the needles; Daina realized that crochet would be the better method. She and her husband, Dr David Henderson, use these models as pedagogical tools in their classes on non-Euclidean geometry at Cornell, where the crocheted surfaces prove to be an invaluable educational resource in this often counter-intuitive field. Daina's models have also been included in the American Mathematical Model Collection at the Smithsonian Institution.

Two of Daina's enormous hyperbolic planes in blue and pink, pictured in the wilds of Ithaca NY.

In her own artistic practice, Daina specializes in creating large, mathematically precise, symmetric hyperbolic planes. These are difficult to create as the crocheter must constantly change the rate of increase to keep the curvature of the surface constant. Daina has become so adept she can now do this by feel. For the rest of us, instructions for making these enimgatic forms are available in her newly published book.

Daina's elegant work has been shown in many art exhibitions and galleries around the world including Not The Knitting You Know at Eleven Eleven Gallery (Washington DC), Confini at the Musee d'Arte Nationale (Sardinia, Italy), and an exhibition curated by the Institute For Figuring at Machine Project gallery (Los Angeles).

More information about Daina's work can be seen on her Cornell website:

More photos of her work can be seen here on Flickr:

All images on this page are used with permission from Dr Taimina. If you wish to use her images please contact her directly through her website.

Pictured here is a very large red symmetric hyperbolic plane. On the left is the unwrapped configuration, which is the same structure as the ball-like models pictured above. Indeed all the forms on this page are exactly the same structure - they have just ben wrapped in different ways. On the right-hand side here we see the red model wrapped into 10 "flutes". This is just one of many wrappings that can be made of the form. Unlike a flat sheet of euclidean paper, which can only be wrapped into a simple cylinder or cone, a piece of "hyperbolic paper" can be wrapped into any number of flutes without deforming its geometry. Each different wrapping is formally known as "an emdbedding in 3-space." It is extremely difficult to imagine such complex embeddings, but Dr Taimina's crochet models make such abstract mathematical properties visible to our eyes.