David E. Flesner
Downloadable Figure files
and Power Point files for my paper on Dynamic
Visualization of Planar Hyperbolic Symmetry via the Klein Model.
To realize the full
interactive dynamic effects discussed in the paper, use Cabri to open the Figure (.fig) files in the first link below. However, this requires that the user have a
copy of Cabri Geometry II for Windows
installed on a computer (NOT the “Plus” version) and the Klein model toolbar
(See below) downloaded and opened within Cabri.
Click or ctrl-click (or right-click and open
folder) on the following download
link. For each of the 17 Figure
files, right-click on the file name and Save Link As ...
(or Save Target As ...) the named file in your desired folder.
If
the user does not have the appropriate Cabri software, some of the dynamic (but
not interactive) effects may be viewed via Power Point slide show files in the
next link.
Click or ctrl-click (or right-click and open
folder) on the following download link. For each of the 17 Power Point Figure files,
right-click on the file name and Save Link As ...
(or Save Target As ...) the named file in your desired folder.
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.
Notes:
(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
dflesner@gettysburg.edu
717-334-7714
Locator Information
David E. Flesner
Professor of Mathematics, Emeritus
Gettysburg College
Gettysburg, Pennsylvania
E-mail:
dflesner@gettysburg.edu
URL:
www.gettysburg.edu/~dflesner
Home:
347 West High Street
717-334-7714
This page was last modified on
May 27, 2009.