A dynamic setup for elementary geometry

TitelA dynamic setup for elementary geometry
Publication TypeConference Paper
Year of Publication2001
AuthorsRichter-Gebert, J., & Kortenkamp U.
Conference NameProceedings of MTCM 2000

In this article we survey the theoretical background that is required to build a consistent and continuous setup of dynamic elementary geometry. Unlike in static elementary geometry in dynamic elementary geometry the elements of a construction are allowed to move around as long as the geometric constraints intended by the construction are not violated. A typical problem in such a scenario is to resolve ambiguous situations that arise from geometric operations like intersecting a circle and a line. After introducing a formal framework for dealing with dynamic geometric constructions, we will demonstrate that a suitable resolution of these ambiguities requires the consideration of complex projective spaces. We will discuss several aspects where one can benefit from such a rather general approach. Finally, we will sketch some proofs that show that several fundamental algorithmic problems arising in such a context are NP-hard or even harder.

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