Model Of Hyperbolic Space (USA)

The distinctly crenulated, irregular, and wavy features exhibited in this textile are reminiscent of forms seen in living corals, which are examples 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 created with crochet by increasing the number of stitches in each row. With each increase, the surface naturally begins to ruffle. The result is a model with a cohesive surface and dynamic form that exhibits many of the intrinsic properties of hyperbolic space. This particular textile was commissioned specifically for our collection, and is comprised of a crocheted model approximately 16–18 inches in diameter. Taimina also created a similar “please touch” sample to encourage museum visitors to directly experience the surface of the piece. Textiles are often used as tools for learning. This work, for example, enhances the understanding of hyperbolic space as a particular mathematical structure in a tangible form that can be experienced and carefully studied. In this way, it is not unlike the museum’s exceptional collection of embroidered samplers, which were stitched “practice sheets” for young girls in the 18th and 19th centuries and, ultimately, became a record of their expertise. These crocheted models of hyperbolic space not only exemplify textiles as “tools,” but also highlight textiles associated with women and the craft tradition, contributing a new meaning and significance to the historical continuum.