Geometry Explorer Help
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History:

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In the fall of 1995, while on leave at the University of Edinburgh, I spent considerable time thinking about teaching and education. As a teacher of mathematics at Gustavus Adolphus College, I had taught the usual math courses in the usual way - lecture and discussion - for many years. However, it seemed to me that the teaching style I was using was getting "out of date" with the times. In particular, one of the most exciting developments - that of computational mathematics - was not being used in a significant way in any of the math courses that I was teaching. On the other hand, the introductory computer science course that I was teaching was using many mathematical ideas to illustrate programming concepts, and these programming assignments were incredibly exciting to the students taking the course. Why didn't we mathematicians, who actually discovered these ideas, use them in the same computational way in our math courses?

After reviewing the math courses in our department, it seemed to me that our geometry course would be the ideal course to re-structure in this way. The only question was what software would I use in the new course. There were (and still are) two widely used programs for doing geometry on the computer -- Geometer's Sketchpad and Cabri. These are both excellent programs.  However, I chose to write my own geometry exploration software for several reasons. First, I wished to have a program that would be relatively inexpensive so that it would be widely used in the public schools.  Second, I wished to work in an environment that was fully integrated with the Internet and the World-Wide Web. Third, I wanted the program to be usable on any computer from Mac's to PC's to UNIX machines.

It was a fortunate coincidence that the Java language was just becoming widely available during the time that I was designing the new geometry software.  Java is a programming language that allows one to write an application that can be used on any machine that has a Java Virtual Machine (JVM). It is also comes with Internet and networking capabilities.  Thus, a geometry program in Java would be an ideal way to accomplish the three goals listed above.

After settling on a design for the new program in the fall of 1996, I started serious work on the coding in the spring of 1997. In the summer of 1997, Alicia Sutphen, then a senior at Gustavus, helped in the design and coding of the Non-Euclidean (Hyperbolic Geometry) part of the project. A major feature of Geometry Explorer is the ability to switch between Euclidean and Non-Euclidean environments easily. The Non-Euclidean environments consist of three models of hyperbolic geometry (Poincare disk, Klein disk, and Half-Plane) as well as a model for elliptic geometry.  I wished to add these geometries to the program because of my experience with teaching Non-Euclidean geometry at the college level. Traditionally, the material has been presented in an axiomatic fashion using diagrams that are confusing at best. Using a computer model,  students can gain intuition for how Non-Euclidean geometry works. This intuition then clarifies the theoretical models of the classroom.

In the fall of 1997, students in my geometry class at Gustavus (mainly secondary math education majors) used a beta version of the program to explore the Poincare model of hyperbolic geometry.  In January of 1998, students in my January-term course, Geometry and the Imagination, used the program almost daily to explore topics in Euclidean and non-Euclidean geometry, fractal geometry, perspective drawing, Escher prints, LindenMeyer systems, and analytic geometry.  The program was used again in the fall of 1998 for the department's geometry course. and has been used every fall since that time in geometry courses at Gustavus, as well as many other institutions.