A new exhibit at Cornell Botanic Gardens showcases the intersections of art, mathematics, and the natural world. “Crocheting Adventures with Hyperbolic Planes” comprises crocheted hyperbolic planes by Daina Taimina, Ph.D., retired associate professor of mathematics in the College of Arts and Sciences. The colorful forms are a pocket of brightness during the often gray days of early spring. The crocheted planes range from the size of a baseball to as large as a basketball, each comprised of its own unique color palette. Each plane is a wavy and complex figure reminiscent of shapes that naturally occur in nature. Taimina crocheted these beautiful hyperbolic planes during her time as a professor in the mathematics department at Cornell University as a means of bringing an abstract mathematical concept to life.
Unlike Euclidean geometry where parallel lines remain equidistant, hyperbolic geometry allows for exponential space expansion, resulting in complex, curved forms resembling natural structures, such as coral reefs and ruffled leaves. Hyperbolic planes exist as a mathematical concept, Taimina says, yet they describe and can model the negative curvatures found in nature. Negative curvature is naturally occurring and can be observed in countless biological structures around the natural world.
Due to the complexity of hyperbolic geometry, it can be challenging to appropriately visualize or accurately model these geometric shapes. Taimina drew inspiration for these models from her own struggle with imagining these complex planes as a student. She had a moment of clarity visualizing the planes while attending a workshop on hyperbolic geometry, But she still lacked a dimensional model that could be touched and felt. This inspired her to create her own tactile models, eventually turning to crochet to bring these planes to life. These models provided a three-dimensional example for her students, making an abstract concept more accessible and understandable.
The colorful pieces were utilized as teaching tools in the geometry classes she taught, primarily Math 451. Taimina’s work strongly reflects the interdisciplinary approach to learning at Cornell University, highlighting how creativity and critical thinking can complement one another in unexpected ways.
To Taimina, these hyperbolic planes hold both intellectual and artistic values. “I love the way they can be turned into geometric manifolds, which are very interesting structures.” Her passion for mathematics and dedication to her students have resulted in a display that is both visually beautiful and strongly educational.
Visitors to the Nevin Welcome Center can interact with this curiosity-inspiring exhibit, now on display in the gallery of the Nevin Welcome Center at Cornell Botanic Gardens. Hours for the Nevin Welcome Center vary by season. See www.cornellbotanicgardens.org for open hours.
Noah Davis, ’28, is a communications assistant at Cornell Botanic Gardens.