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Student Research: An Empirical Exploration of the Poincare Model for Hyperbolic Geometry

Joe Dan Austin, Education, Rice University; Joel Castellanos, CRPC, Rice University; Ervan Darnell, Computer Science, Rice University; and Maria Estrada, Houston Community College

Conspicuously absent from current geometry software packages is an interactive exploration program for Non-Euclidean geometries. To fulfill this need, NonEuclid has been developed. NonEuclid is an entertaining and interactive program for high school and undergraduate students that allows them to investigate non-Euclidean hyperbolic geometry. It also provides greater insight into Euclidean geometry and abstract algebra.

The Poincare model for hyperbolic geometry maps into a Euclidean unit circle. Students are able to explore this geometry by manipulating and measuring points, lines and simple figures. This offers students experiential learning with both hyperbolic geometry and the more general concepts of Definition, Postulate, and Theorem, which are critical to understanding the process of a geometric proof.

NonEuclid was presented at the 1992 National Conference for Computers in Geometry Classrooms (St. Olaf Collage, Minnesota), and the software has already been included in the curriculum at number of high schools and colleges. A comprehensive description of NonEuclid and some of its applications will soon appear in the Journal for Computer and Mathematics Education.

The NonEuclid program runs on all Macintosh computers and is installed on the Softlib software distribution system. Two versions of NonEuclid exist: NonEuclid (no charge) and NonEuclid++ ($250). For more information, visit the NonEuclid web site or call Joel Castellanos at .

Editor's note: At the time of this project, Maria Estrada was an undergraduate at Houston Community College who contributed to this project as part of the "Spend a Summer with a Scientist" program.

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