November 20

The NonEuclid Simulation
with Angles, Parallel Lines, and Triangles

NonEuclid

NonEuclid is a Java Software Simulation offering Ruler and Compass Constructions in both the Poincaré Disk and the Upper Half-Plane Models of Hyperbolic Geometry (a geometry of Einstein's General Relativity Theory and Curved Hyperspace) for use in High School and Undergraduate Education.

NonEuclid uses a bounded, two-dimensional, model (the Poincaré Model) of a particular Non-Euclidean Geometry called Hyperbolic Geometry. The large empty circle that appears when you first start NonEuclid is called the "Boundary Circle". This boundary circle is the graphing area of the screen and it contains the entire, infinite, two-dimensional Hyperbolic Space.

NonEuclid Applet | Download Applet | Required Exercises | More Concepts

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
3) you have Java deactivated in the preferences of your browser.
Both Netscape Communicator 4.7 and Microsoft Internet Explorer 5.0 include Java 1.1.6.

NonEuclid Stand-Alone Application and Applet:

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.

NOTE: If you are on a Mac platform, you can still download the zipped file. Expand it with Stuffit Expander™ and then use the Apple Applet Runner which ought to be in your Apple Extras folder. Open the Applet Runner and then open the file NonEuclid.html. If you have any trouble, please post me a note at beva@igc.org.

Required Exercises:

Using NonEuclid - My First Triangle

Activities: Adjacent Angles, Angles, Parallel Lines, General Triangles,
Isosceles Triangles, Equilateral Triangle, Right Triangles, Congruent Triangles,
Rectangles & Squares, Parallelograms, Rhombus, Polygons, Circles, Tessellations of the Plane.

More Concepts:

Axioms and Theorems: - Euclid's Postulates, Hyperbolic Parallel Postulate,
SAS Postulate, Hyperbolic Geometry Proofs.
Area: - A=1/2bh, Altitudes of a Hyperbolic Triangle, 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.