GEOMETRY
What coral reefs, chaos, and the bias cut have in common.
Dr. Daina Taimina strides up to the podium in eager looks. Mathematical fashion may not have hit
an elaborate crocheted skirt. She’s speaking the big time yet, but the intersection of crafting
at the Gathering for Gardner, an invitation- and science is definitely on the rise.
only mathematics event in honor of Martin Gardner, Margaret Wertheim, for one, is thrilled about it.
the famed mathematician and puzzler (he wrote a A science journalist, she founded the Institute For
column in Scientific American for almost 50 years). Figuring in 2003 with the idea of drawing attention
Her talk is about crocheting math, a subject to what she calls the “poetic and aesthetic aspects”
that has garnered her increasing media attention of science and mathematics. Taimina and her hus-
in recent years. Much of the audience is well-versed band, geometrician David Henderson, were among
in the geometry of the hyperbolic plane, but most the first people invited to lecture. Ever since then, the
people haven’t had a chance to play with some of Institute has been tackling topics like knot theory,
the best hyperbolic models to come out of academia: tensegrity structures, and paper folding, as well as
Taimina has crocheted them. continuing to explore hyperbolic crochet. They coor-
Models existed before, but they were fairly fragile. dinate lectures and exhibitions, drawing the attention
She explains: “William Thurston made a paper and of the art and design worlds to objects like Taimina’s.
tape model around 1986. In 1997, I was going to teach The Institute has a number of exhibitions coming
a class and thought, ‘I can’t use this; it’s falling apart!’ up in the next year (as well as supporting her with
So I decided to crochet one.” a grant), including the display of a collaborative
With the mathematical programming inherent in crocheted coral reef at the LACE gallery. Responding
a crochet pattern, she was able to make a sturdy, to Taimina’s work with hyperbolic space, Wertheim
pliable model that really gets across the physicality and her sister Christine, a co-director of the Institute,
of the hyperbolic plane, even to ordinary observers. started playing around and crocheting their own
Her students went nuts. forms, including shapes that looked like kelp and
“It’s not that you haven’t seen it before,” she points cactuses. “We had them arranged on our dining
out. “Here are pictures from my garden.” Slides flash room table,” says Wertheim, an Australian,“and as
by of ruffled lettuce, curly kale, the rippled edges of they grew, we realized that it looked like a coral reef.”
a sea slug. “Well, the sea slug is not from my garden,” A crocheted reef is no coincidence; like kelp, coral
she laughs. She goes on to explain what geometrists reefs have hyperbolic geometry in them.
already know: while a sphere has constant positive The sisters started inviting people to contribute
curvature, a hyperbolic plane is the opposite of a pieces of the reef, and soon had so many submissions
sphere, having constant negative curvature. It is that they ended up in the position of curating cro-
always curving away from itself, causing the ripple chet. In the process of looking for a space to exhibit,
we see in nature and in math textbooks. they were surprised and delighted to find that a
Having the physical models on hand allowed number of other textile artists were also making coral
Taimina to explore new ideas and prove new con- reefs independently. The show is tentatively titled
nections. “The other realization is that maybe this
can be a fashion line for mathematicians!” she says, This amazing crocheted Lorenz manifold took Dr. Hinke Osinga 85 hours
twirling her skirt. She gets a big laugh and some and 25,511 stitches to complete. >>
References:
Archives