During the late nineteenth and early twentieth centuries mathematical models of surfaces were often used in teaching geometry. Although women constructed models during that period, the earliest model in the Smithsonian collection that can be attributed to a woman dates from about the year 2002. That model, unlike any of the earlier models, was crocheted.
Crocheted Model of a Hyperboic Plane, about 2002. Gift of Daina Taimina (2002.0394.01)
In 1997, Daina Taimina, a Latvian born and educated mathematician participating in a workshop on teaching geometry, came up with the idea of crocheting a surface to represent a hyperbolic plane. A hyperbolic plane is different from the Euclidean plane studied in high school geometry. A Euclidean plane is a surface that satisfies several axioms including the Euclidean Parallel Postulate from which it follows that there is only one line parallel to a given line through a given point. A hyperbolic plane is also a surface that satisfies the same axioms as the Euclidean plane except for the Euclidian Parallel Postulate. On a hyperbolic plane there are infinitely many lines parallel to a given line through a given point.
Daina Taimina has crocheted many hyperbolic planes and has written about them in her book Crocheting Adventures with Hyperbolic Planes, (Wellesley, MA: A. K. Peters, 2009).