Geometry Explorer Help

Windows, Tools, etc.:

Working in the Poincare model with Geometry Explorer is essentially no different than working with the Euclidean model.  Almost all of the tools work in both environments, with a couple of notable exceptions which are described below.  Even recordings made in one environment can be played back in the other environment. Thus, for example, the Koch snowflake example can be recorded in a Euclidean canvas and played back on a hyperbolic triangle, or vice-versa. This flexibility was deliberately designed to give the user the maximum opportunity to explore and contrast different geometric "universes" and thus to develop an intuition for how it "feels' to live in one geometry versus another.

There are four main differences between the two environments:
•  In the Euclidean canvas the parallel button in the tool panel will result in the unique parallel being created, once a linear object (segment, ray, or line) and a point have been selected.  In the Poincare (Hyperbolic) model, using this tool (with the same selection of a linear object and a point) will result in the creation of the two unique ultraparallels to the given linear object and point.  Thus, recordings made using parallels in either environment will not be playable in the other environment.
• In the Euclidean canvas, circles and arcs can be defined using three points. This construction depends on the Euclidean parallel postulate, and thus is not available in the Hyperbolic canvas.
• There is no graph option available in the Poincare model.
• Transformations cannot be defined in terms of measurements in the Poincare model.  (At least not yet!)