Daina Taimina: A Modern Day Mathematical Model Maker

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.

Image of Crocheted Model of a Hyperboic Plane, about 2002.

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).

This model of the hyperbolic plane was crocheted by the Latvian-born mathematician Daina Taimina in about 2002. Although called a model of a plane, it is not flat like a Euclidean plane and its lines are not straight.
Description
This model of the hyperbolic plane was crocheted by the Latvian-born mathematician Daina Taimina in about 2002. Although called a model of a plane, it is not flat like a Euclidean plane and its lines are not straight. However, lines on any plane, Euclidean or hyperbolic, are still the shortest paths along the plane connecting two points.
The distinguishing difference between a hyperbolic plane and a Euclidean plane is that on a hyperbolic plane there are infinitely many lines parallel to a given line through a given point not on the given line. In this model lines are shown in yellow. The given line is the one closest to the top of the photograph and the given point is where the four other lines meet. None of those four lines will ever meet the given line, so they are all parallel to it.
On page 27 of her book, Crocheting Adventures with Hyperbolic Planes, (Wellesley, MA: A. K. Peters, 2009), Taimina has a photograph of a similar model, with only three yellow lines through the given point. On page 28 she has another photograph of that model with the caption: “The red line is a common perpendicular to only two of these yellow lines.” That photograph illustrates that on a hyperbolic plane, just as on a Euclidean plane, there is only one line through a given point not on a given line that is perpendicular to the given line.
Location
Currently not on view
date made
2002
maker
Taimina, Daina
ID Number
2002.0394.01
catalog number
2002.0394.01
accession number
2002.0394

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