Brightly colored crocheted hyperbolic planes spread across tables in the Mathematics Library, welcoming alumni and their families to a talk with Daina Taimina on her signature method of tactile exploration of hyperbolic geometry and the new second edition of her book, “Crocheting Adventures with Hyperbolic Planes: Tactile Mathematics, Art and Craft for All to Explore.”
Invented as a teaching tool in 1997 and successfully used in many high school and college geometry classrooms, starting in 2005 Taimina’s crocheted hyperbolic planes have since been in some 30 invited exhibits and several solo shows around the world – including the Smithsonian Institution. Numerous artists have created works based on Taimina’s hyperbolic crochet, such as the song Irish musician Donal Donahoe composed titled “Hyperbolic Guitar.” Donahoe calls it “an attempt to capture the exponential expanse of hyperbolic space in the rhythm of music.”
Taimina’s work has inspired collaborative projects in Sicily, United Kingdom, Finland and Latvia, as well as the international Hyperbolic Crochet Coral Reef project (the “Hyperbolic” was eventually dropped as the project shifted focus to environmental rather than mathematical concerns), organized by Margaret Wertheim, who learned of hyperbolic crochet from a 2001 article about Taimina in New Scientist.
In the second edition, Taimina described her 20 years with crocheted hyperbolic planes as “an amazing creative journey” but it is one she now carries on alone since the death of her husband, David Henderson,, professor emeritus of mathematics. “All my work was supported and inspired by David, whom I miss immensely,” said Taimina. “Thinking that my work keeps his vision of geometry alive helps me going now.”
Daina Taimina, right, demonstrates hyperbolic crochet to alumni during Reunion 2019
The crocheted mathematics has had far-reaching and sometimes unexpected impacts on people, described in a new chapter in the second edition, “Hyperbolic crochet goes viral.” writes Taimina, retired adjunct associate professor of mathematics: “Hyperbolic crochet has flown around the world like wind-blown seeds and has sprouted up in unexpected areas that are growing in number like the stitches in a crocheted model.”
One of Taimina’s favorite stories is from Amanda Shayna Ahteck, who learned of hyperbolic crochet from a section in the SAT she was taking in 2017, which recounted how Taimina had solved the problem of hyperbolic plane models with “a little insight” from crocheting. Ahteck went home and listened to Taimina’s TEDxRiga talk and eventually crocheted her own hyperbolic plane.
“This experience changed the way I look at mathematics,” Ahteck wrote to Taimina. “It was hard to find the equation intimidating when it’s a cuddly concept made of acrylic yarn...Suddenly I saw the connections between conic sections in my calculus class and the transformations to shapes and paths I could make as an amateur graphic designer in Adobe Illustrator vector graphics.”
In addition to the new chapter, Taimina has updated the sections on applications of hyperbolic geometry and historical strands of geometry, and responded to the suggestions of readers to include patterns in the appendix with step-by-step instructions and pictures. The new edition also includes more photos.
The first edition received the Euler Book Prize from the Mathematical Association of America, which noted that the book is “unlike any book on hyperbolic geometry previously written, and it is in a different universe from any book on crochet previously written. But, when you look at it, the idea makes such perfect sense that it seems inevitable.”