There is something very seductive about mathematical models and equations. Whether it is their complexity and conciseness, orderly arrangement of symbols and numbers on the page, or their beauty as physical structures, they reflect the problem-solving process in action.
This crocheted and crennelated form, reminiscent of living coral, is a model of a mathematical structure known as hyperbolic space. The discovery that this type of geometric structure could be modeled in crochet was first made in 1997 by Dr. Daina Taimina, a mathematician working at Cornell University. Her inspiration was based on a suggestion put forward in the 1970s by an American geometer, William Thurston. Thurston’s model, however, was made of paper and taped together, making it inherently fragile and hard to handle. Taimina found that the essence of this construction could be implemented with crochet by increasing the number of stitches in each row. With each increase, the surface naturally began to ruffle and crenellate. The result is a model with a cohesive surface and dynamic form that exhibits many of the intrinsic properties of hyperbolic space. Because of the creation of this model these properties are now not only visible, but can also be experienced through handling the surface, making this textile an excellent and beautiful learning tool.