NonEuclid

Authors:
Joel Castellanos - Research Staff, Dept. of Mathematics, Rice University
Joe Dan Austin - Associate Professor, Dept. of Education, Rice University
Ervan Darnell - Graduate Student, Dept. of Computer Science, Rice University

Funding for NonEuclid has been provided by:
CRPC, Rice University
     Institute for Advanced Study / Park City Mathematics Institute

Run NonEuclid Applet (click button below):

If you do not see the button above, it means that your browser is not Java 1.1.6 enabled.  This may be because:
1) you are running a browser that does not support Java 1.1.6,
2) there is a firewall around your Internet access, or
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Both Netscape Communicator 4.7 and Microsoft Internet Explorer 5.0 include Java 1.1.6.

Download

Click on the link above to download the NonEuclid archive (noneuclid.zip).  If the file loads into your browser, then click the above link with the RIGHT mouse button and select the option "save to disk", or reconfigure your browser to save ZIP files to disk.

This archive contains the NonEuclid applet and application files (*.class).  It also contains the NonEuclid help files (*.html and *.gif).  Therefore, once downloaded, both the applet and the application can be run without an internet connection.  The archive can be expanded with WinZip.  All files in the archive should be placed in the same directory.

The Java Security Manager does not allow applets to read or write to a local drive.  Nor are applets allowed to access local printers.  The NonEuclid application, however, can save and open files on your local drive and print on your local printer.

In spite of the fact that this is called a "Stand-Alone" Application, Java applications need to run within the JAVA Runtime Environment (JRE) which is available free of charge from Sun Microsystems.  Once you have installed JRE on your computer, you should find a file called "java.exe".  In windows, the default location for this file is "C:\Program Files\JavaSoft\JRE\1.2\bin".  This default path is used in the example below.

When both JRE and NonEuclid have been installed, open a command prompt window, and enter the following, CASE SENSITIVE,  commands:
        cd "C:\Program Files\JavaSoft\JRE\1.2\bin"
        java -cp "C:\Program Files\NonEuclid" StartNonEuclid
Where "C:\Program Files\NonEuclid" is the path of directory where you have installed NonEuclid.  To read the help files, use a browser or html reader to open "NonEuclid.html".

Non-Euclidean Geometry: - Euclidean Geometry, Spherical Geometry, Hyperbolic Geometry, and others.
The Shape of Space: - Curved Space, Flatland, Ourland, and Mercury's Orbit.
The Pseudosphere: - A description of the space of which NonEuclid is a model.
Parallel Lines: - In Hyperbolic Geometry, a pair of intersecting lines can both be parallel to a third line.

Using NonEuclid - My First Triangl
Activities - How to get started Exploring: - Adjacent Angles, Angles, General Triangles, Isosceles Triangles, Equilateral Triangle, Right Triangles, Congruent Triangles, Rectangles & Squares, Parallelograms, Rhombus, Polygons, Circles, Tessellations of the Plane.

Axioms and Theorems: - Euclid's Postulates, Hyperbolic Parallel Postulate, SAS Postulate, Hyperbolic Geometry Proofs.
Area: - A=½bh, Altitudes of a Hyperbolic Triangle, A=s², Defect of a Triangle, Defect of a Polygon, Properties Necessary for an Area Function, Upper Bound to Area.
X-Y Coordinate System -  A description of how an x-y coordinate system can be set up in Hyperbolic Geometry.
Disk and Upper Half-Plane Models: - A semiformal development of each model.

For The Teacher:Why is it Important for Students to Study Hyperbolic Geometry?
Non-Euclidean Themes by Artist/Mathematician, Clifford Singer.

References & Further Reading.