Foundations of dynamic geometry
Ulrich Kortenkamp · 1999
Although it is known that Calvin and Hobbes tell the truth about life, I was surprised that Bill Watterson knew in 1988 what Jürgen Richter-Gebert and I had to learn ten years later: Sometimes it is necessary to use imaginary numbers even for seemingly trivial tasks. This thesis shall explain the details of a method called complex tracing, and lay the foundations of Dynamic Geometry, a new field of research that opened up after we solved the continuity problem for interactive geometry software. I came into this project right after I decided not to write my thesis on Cinderella, the interactive geometry software which at that time was a project of Jürgen Richter-Gebert and Henry Crapo, but on neighborly polytopes. After the first few weeks of implementing the new version of Cinderella in Java I understood why it is really hard to write “just another geometry software. ” I had to try to implement a dynamic geometry software in order to understand why it is difficult to create a software that “behaves as expected. ” It needs a mathematical theory, and it was not clear to us what to do three years ago. It was in early 1998 when we had our “ultimate break-through. ” The time since then was spent for the implementation of the theory, and it is nice to see that this implementation