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Steve's Hyperbolic Tools Page

 

There are many models of hyperbolic geometry. Three common models are the Poincaré disk model, the the Poincaré half-plane model, and the Beltrami-Klein model. Within those models, we often want to perform standard constructions, such as bisecting angles, dropping perpendiculars, or drawing circles. However, in the non-Euclidean models, the constructions are not the same constructions as in Euclidean geometry. For example, in the Poincaré models, "lines" are defined to be arcs of certain circles.

On this and other linked pages can be found dynamic geometry tools that automate 10 "standard" non-Euclidean constructions in the three models:

 

The two most popular dynamic geometry software packages are the commercial software Geometer's Sketchpad and the open-source software GeoGebra.Tools for both packages are available here.  Unfortunately, I do not have access to the most recent versions of Geometer's Sketchpad, and the tools are only updated through version 4 of that software.


 

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Links to Others Work - Good Stuff!

 

Many others have created tools for hyperbolic constructions using dynamic geometry software.  Here are links (last checked in April 2009) to some of their work.

As GeoGebra has grown in popularity, the number and diversity of tools for hyperbolic geometry has increased dramatically.  A simple web search or on the GeoGebra Tube will yield many other examples of hyperbolic geometry construction tools and sketches.