COURSE BACKGROUND: POINCARE is a prototype web-based module for a third year geometry course on the topic of the geometry of the Euclidean/Möbius plane, as described through complex numbers. The course is mainly lecture-based, at least at present, but the students also work extensively in computer labs with the software package "Geometer's Sketchpad" (GSP) for visualization and experimentation.
In the final section of the course, the Poincaré universe is modeled as the interior of a Möbius circle, and its properties explored and discussed in terms of Möbius geometry.
TECHNOLOGY: For interactivity, POINCARE uses Geometer's Sketchpad (GSP) as a helper application.
GIFs were used to create the mathematical text of the demo.
PEDAGOGY: The main intent of the project was to encourage the students to develop a intuitive, visual and kinesthetic understanding of Poincaré geometry through interaction and experimentation with live sketches, and to enable them to understand the analytic reasons behind these intuitions.