The Hyperbolic Toolbox:
Non-Euclidean Constructions in Geometer's Sketchpad

Stephen Szydlik (e-mail)

University of Wisconsin Oshkosh

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


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