NonEuclid is Java Software for
Interactively Creating Ruler and Compass Constructions in both the
Poincaré Disk and the Upper Half-Plane Models of Hyperbolic Geometry
for use in High School and Undergraduate Education.

Hyperbolic Geometry is used in Einstein's General Theory of Relativity and Curved Hyperspace.

Copyright©: Joel Castellanos, 1994-2005

Joel Castellanos  - Graduate Student, Dept. of Computer Science, University of New Mexico
Joe Dan Austin - Associate Professor, Dept. of Education, Rice University
Ervan Darnell - Graduate Student, Dept. of Computer Science, Rice University

Italian Translation by Andrea Centomo, Scuola Media "F. Maffei", Vicenza

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 1.3.0 enabled.  This may be because:
1) you are running a browser that does not support Java 1.3.0,
2) there is a firewall around your Internet access, or
3) you have Java deactivated in the preferences of your browser.
Both Netscape 6.2 and Microsoft Internet Explorer 6.0 include Java 1.3.0.

Download NonEuclid to run on computers without an Internet connection:

Click on the link above to download a compressed archive of NonEuclid. This archive can be moved to a computer without an Internet connection, and uncompressed using WinZip. Uncompress the archive into a single directory. Then open the file named "NonEuclid.html" with Netscape, Internet Explorer or some other browser.


Using NonEuclid - My First Triangle
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.

Basic Concepts:

What is 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.
Axioms and Theorems: - Euclid's Postulates, Hyperbolic Parallel Postulate, SAS Postulate, Hyperbolic Geometry Proofs.
Area: - Exaimation of A=½bh and A=s² in Hyperbolic Geometry, Properties Necessary for an Area Function, Altitudes of a Hyperbolic Triangle, Defect of a Triangle, Defect of a Polygon, and an 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: - An informal development of these two models of Hyperbolic Geometry.

References, Appendices, and Supporting Information:

For The Teacher: Why is it Important for Students to Study Hyperbolic Geometry?
Conceptual Mechanics of Expression in Non-Euclidean Fields by Artist/Mathematician, Clifford Singer.
Palm OS Application for Exploring Non-Euclidean Geometry. The package includes two files: MathLib.prc and HypGeom.prc. MathLib is a library that contains mathematical functions missing on the standard palm libraries. HypGeom is the application. This package was written by Felipe Grajales, Faculty, Universidad de los Andes, Colombia.

References & Further Reading.

Change History.

For more information, questions, bug reports, or comments send e-mail to Joel Castellanos
Copyright©: Joel Castellanos, 1994-2005