## The Hyperbolic Toolbox:

Non-Euclidean Constructions in *Geometer's Sketchpad*

- Introduction: Models for Non-Euclidean Geometry
and
*Geometer's Sketchpad*
- Selling the Tools: A Pedagogical Argument
- Background: Credit where Credit is Due
- What's in the Toolbox?
- Filling your Toolbox: Obtaining, Installing
and Using the Hyperbolic Tools
- Teaching Examples
- References and Acknowledgements

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Abstract

In this document, I describe and examine some software tools that have been
developed to aid in constructions in non-Euclidean geometry. The tools consist
of *Geometer's Sketchpad* scripts that automate hyperbolic "straightedge
and compass" constructions in each of three models of hyperbolic geometry. These
scripts, based on the earlier work of Alexander and Finzer in the Poincaré
disk, automate ten "standard" constructions, including constructing hyperbolic
lines and circles in the models, and dropping and raising perpendiculars. The
tools can be used to enhance student understanding of hyperbolic geometry in
several ways, and I give numerous examples of how they can be effectively used
in the classroom.

Mathematics Department

University of Wisconsin Oshkosh

Oshkosh, WI 54901