This is a game trying to help you understand the Poincare Disk. Your goal is to "bounce" a ball off the (geodesic) walls so that your ball will hit the boundary drawn in red, and to use the fewest "bounces" possible. The ball will move along a "geodesic line", which is determined by the "Poincare distance". It is not a straight line, but rather a part of a circle. Try it, you'll quickly get the hang of it.
- Your "ball" will follow geodesic trajectories. The starting trajectory will be the shortest distance (in the Poincare metric) between the red dot and the point where you click your mouse. After that, trajectories are reflected around the boundary circles when the ball hits a boundary.
- You must first bounce off a blue bumper before hitting the red bumper.
- Sometimes the ball gets stuck ... I think that is (mathematically) correct, so it's not a bug (proof ?) ... hit [Start over] to start over in that case.
- Click the mouse somewhere "inside" the pool table to start. - there may be a small delay the first time while one last class is loaded after you click the mouse - wait a few seconds!
For more information:
- NonEuclid: Java Software Simulation offering Straightedge and Compass Constructions in both the Poincar Disk and the Upper Half-Plane Models of Hyperbolic Geometry for use in High School and Undergraduate Education
- Relationships between Euclidian and Non-Euclidian Geometry: describes some relationships between Euclidean geometry and the Poincare disk.