Reflection

What follows is a direct result of the work I have been doing over the past five years on a National Science Foundation project, grant number ESI9618029. The project, known as CAS-Intensive Mathematics, was based at Penn State and the University of Iowa and was headed by Dr. M. Kathleen Heid, and Dr. Rose Mary Zbiek.The goal of the project was to create materials for the secondary school curriculum that took full advantage of the latest technologies. We ended up making extensive use of Geometer's Sketchpad and the computer algebra system found on the TI-92 and more recently on the TI-89. We found that given these technologies we could have students work with geometric transformations in new and exciting ways. Because of this I found myself becoming more and more interested in computer graphics and their underlying mathematics.

The study of transformations is greatly enhanced by the use of geometric construction packages such as Cabri and Geometer's Sketchpad, but there has been a lot written about that. So, this issue's column will focus on how you can use a computer algebra system, Mathematica, to study a particular geometric transformation, or reflection, in new and rewarding ways. Almost all that follows can be done using the computer algebra systems now available on handheld calculators such as the TI-89 and is in no way dependent on using Mathematica.