Crocheting Adventures with Hyperbolic Planes
Crocheting Adventures with Hyperbolic Planes
Daina Tamina has written a marvelous book linking the natural world to the human mind, to symbol-making, to art and to abstract mathematical concepts. The book begins with an overview of geometry and proceeds to the more specialized subject of hyperbolic geometry: "the intrinsic geometry of a surface with constant negative curvature that extend(s) indefinitely in all directions." Negative curvature is when a surface folds in on itself, as you can see in kale and many other natural objects, and in ruffles in fabric. Hyperbolic geometry -- where constant negative curl creates form -- is a mathematical concept, but mathematicians did not believe it could be given concrete form. Daina describes her own efforts to do so with crochet, and her stunning models -- each a real work of art -- attest to her success. In teaching math, she uses her crochet models to give difficult concepts a touchable form.
Perhaps taking her cue from the idea of infinite extension in all directions, Tamina takes off on several trajectories, with a chapter on geometric patterns in folk arts from the Maori, Incas, and Pacific Islanders. She shows how geometric symbols were used in human societies to convey cosmological knowledge, and how these symbols circulated via art. She then leads a grand tour through the development of geometrical concepts from building and construction, navigation and stargazing, and motion and machines. There are 300 photos of ancient objects. "It's a coffee table book about mathmatics," Daina told me in our interview.
It all amounts to an eye-and brain-opening journey connecting the history of ideas to their natural sources and practical applications. Lots to ponder. It takes a mind like Daina's to bring material like this together, and to convey it in scupltures that sit tranquilly in the natural landscape.
To see lots more photos of Daina's work and learn more about hyperbolic crochet, check out our Audio Interview of Daina here!