David E. Flesner
Professor of Mathematics, Emeritus
347 West High Street
Hyperbolic Geometry -- Klein Model
Downloading the Toolbar:
To download a Cabri Geometry II for Windows (NOT the new Plus version) toolbar that implements the Klein model of hyperbolic geometry: Right-click on the following download link and Save Link As ... (or Save Target As ...) the File name you desire in your desired folder. Alternately, you may wish to download a zipped file. Right-click on this download zipped file link and Save Link As ... (or Save Target As ...) the file HGKM7-04H.zip in your download file folder. Be sure to unzip the file before using it with Cabri. The file will unzip with the name Hyperbolic Geometry – Klein Model 7-04 Horizon.men.
(1) Unfortunately, the toolbar does NOT work with the recent Plus version of Cabri Geometry II. The toolbar was developed with Cabri Geometry II Version 1.0 MS Windows, and there are some yet-to-be-determined incompatibilities with the Plus version.
Using the Toolbar:
Start Cabri Geometry II for Windows. Select File and Open. Under Files of Type, select Menu Files (*.MEN), and open the Hyperbolic Geometry - Klein Model 7-04 Horizon.men file that you have just downloaded. Be patient. The file is very large and takes 2-3 minutes to load. When the File Open process is complete, press the F1 key to show the Help window at the bottom of the screen.
Pull down the Pointer toolbox and select the Horizon tool. Take a moment to scroll through and read the Help window comments at the bottom of the screen. Then click on a center point and radius point for the absolute circle for the Klein model within which you wish to work. Click on a blank spot on the right of the Toolbar to return to the default Pointer tool. All of the hyperbolic tools require you to click on the absolute circle that you are using. For each tool, the other objects that you need to select are described in the Help window using a style similar to the normal Cabri Help comments.
Notice that the toolbar and its toolboxes look similar to those in the ordinary Cabri, but the hyperbolic tools have actually replaced the Euclidean tools. Once you have drawn the absolute circle, you are working within a hyperbolic plane and doing hyperbolic geometry, not Euclidean geometry. Explore, experiment, and discover interesting relationships within this "strange new universe" of János Bolyai.
Feedback about the Toolbar:
Please send questions, comments, and suggestions to:
David E. Flesner
347 W. High St.
Gettysburg, PA 17325
This page was last modified on
April 1, 2010.