My exploration of the Museum of Arts and Design rendered me speechless in the exhibit “Crochet Coral Reef: TOXIC SEAS”, by Margaret and Christine Wertheim and the Institute For Figuring. The stunning, sweeping landscapes of coral made of yarn and various woven trash is firmly cemented in the mathematics of Daina Taimina, a Cornell professor, who found a method to display complex hyperbolic forms in crochet. This correlation of art and math inspired my 25-page math research paper, written for my Pre-Calculus class and the New York Science Fair. Below is an excerpt from my paper, “Hyperbolic Geometry In Artistic Pursuits,” including the paper’s introduction, the section on the artistic application, a rationale for my original idea component (hyperbolic crocheted bracelets), and the paper’s conclusion. Original idea is pictured (right):


Hyperbolic Geometry In Artistic Pursuits

“For God’s sake, please give it up. Fear is no less than the sensual passion, because it, too, may take up all your time and deprive you of your health, peace of mind and happiness in life.” Wolfgang Bolyai spoke to his fellow mathematician son Janos Bolyai in the 19th century, urging him to give up on his work in hyperbolic geometry. Mathematicians long believed that hyperbolic geometry was purely theoretical, and a model of hyperbolic planes was unimaginable. That is, until a Latvian mathematician merged complex mathematics with crochet. Hyperbolic geometry is seen throughout nature, yet humans could not grasp its complexities until very recently.


Daina Taimina’s revolutionary work in hyperbolic models paved the way for more public exhibitions of mathematics in a creative application. By making high-level geometry fun and accessible for students and the general public, hyperbolic crocheting has grown in popularity. One project in particular has worked closely with Taimina and have modified the “crochet code,” so to speak, of hyperbolic structures and created a Crochet Coral Reef. Margaret and Christine Wertheim, twin sisters hailing from Australia, discovered Taimina’s work in 2003, and were fascinated by the models. Margaret “studied physics and mathematics at a university for six years [and] is a science writer,” while her sister Christine “teaches in the critical studies department at CalArts in Valencia, California.” Their first show opened in 2005 in Los Angeles, and relied on “crocheting using Daina’s hyperbolic patterns… we explored it in many ways,” M. Wertheim explained in “Crossing Disciplines and Modalities” (40). Their contrasting styles, studying in drastically different fields of study and careers, convene in their work, highlighting the mathematical and artistic merit of hyperbolic structure. As Australians, they “grew up in Brisbane, Queensland, home of the Great Barrier Reef,” which compounds their personal connection to the project (Tanguy 39). Her sister Christine began “making aberrations [and] mutating the pattern” of Taimina’s work, which made “the pieces… look organic, like living things” (Tanguy 40). As M. Wertheim explains in their book, Crochet Coral Reef, “In the realm of aberrations that Reef organisms inhabit, algorithmic rhythms are interweaved with areas of freeform wilderness, creating an admixture of formality and improvisation” (Wertheim and Wertheim 46). [Fig. 4.1]

Their work soon expanded into “satellite reefs,” groups of “contributors, who are an amazing collection of people around the world [that] do their own embellishments… [which] lead to new and wondrous creatures.” These widespread variations in the code result in “this ever-evolving, crochet taxonomic tree of life… [with an] inner organic life of its own” (Wertheim 12:13). [Fig. 4.2]

By blending complex mathematics with an environmental statement, the Wertheims and their satellite contributors make a unique, artistic statement with hyperbolic crochet coral.


Furthering the idea of artistic mathematics, I made bracelets out of crochet. First, sticking to Taimina’s basic formula of “[increasing] the number of stitches in each row,” I created a simple dark blue band that reflected the strict mathematics of hyperbolic models. (“Crocheting the Hyperbolic Plane: An Interview with David Henderson and Daina Taimina”) I then mutated my formula while crocheting, resulting in more abstract and artistic hyperbolic bracelets.


The universe is not exclusively on an Euclidian plane, as mathematicians once thought. Finding a uniquely feminine solution to the problem of modelling an alternative geometry, Daina Taimina and her crochet hyperbolic forms. Artistic response to mathematical complexities result in stunning feats of geometry and artistic skill. By mutating Taimina’s code to resemble the natural hyperbolic structures, humans can achieve what leafy greens and sea creatures have been doing for thousands of years. Creative applications of mathematics makes its complexities accessible and stunning.