NonEuclid

NonEuclid is Interactive Java Software
for Creating Ruler and Compass Constructions
in both the Poincaré Disk and the Upper Half-Plane Models
of Hyperbolic Geometry.


Copyright©: Joel Castellanos, 1994-2007

NonEuclid allows the curious explorer to gain experience in Hyperbolic Geometry and to empirically investigate questions such as: "In Hyperbolic Geometry, are the base angles of an isosceles triangle congruent?"

The NonEuclid software and documentation are accessible to anyone with high school level geometry.

Aside from being interesting in itself, a study of Hyperbolic geometry can, through its novelty, enable a deeper understanding of a formal proof.

Hyperbolic Geometry also has practical aspects such as orbit prediction of objects within intense gradational fields. Hyperbolic Geometry is used in Einstein's General Theory of Relativity and Curved Hyperspace.


Authors:
Joel Castellanos, Dept. of Computer Science, University of New Mexico
Joe Dan Austin, Dept. of Education, Rice University
Ervan Darnell, Dept. of Computer Science, Rice University

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

Funding for NonEuclid has been provided by:
The Center for High Performance Software Research (HiPerSoft), Rice University, and
The Institute for Advanced Study / Park City Mathematics Institute


Run NonEuclid using Java Web Start WITHOUT Save and Print Permissions
Run NonEuclid using Java Web Start WITH Save and Print Permissions

Some firewalls prevent downloading of jar files. This will result in the error message:
Unable to load resource: http://cs.unm.edu/~joel/NonEuclid/NonEuclid.jar

If Java Web Start is not installed on your machine, then it can be downloaded from the grahpic link below.

Get Java Web Start NOW!
NonEuclid can also be downloaded and run locally on your machine. Running NonEuclid locally does not require any instlation of NonEuclid: just download NonEuclid.jar and run it with Java 1.5 or newer. If java is installed on your system, but not in your system's default path, then, to run NonEuclid locally, you will need to give the full Java path. For example, on a Microsoft Windows XP machine, the full-path command for starting NonEuclid from the command prompt while in the directory where NonEuclid.jar was downloaded might be:

"C:\Program Files\Java\jdk1.5.0_09\bin\java" -jar NonEuclid.jar

This command assumse that Java has been installed in the directory
"C:\Program Files\Java\jdk1.5.0_09\bin\java".
The quotation marks are needed around the java path to tell Windows that the space in "Program Files" is part of the directory name.

Download NonEuclid.jar


Contents:

1) What is Non-Euclidean Geometry: - Euclidean Geometry, Spherical Geometry, Hyperbolic Geometry, and others.
2) Using NonEuclid - My First Triangle:
3) Activities: - Exploring properties in Hyperbolic Geometry of Adjacent Angles, General Triangles, Isosceles Triangles, Equilateral Triangle, Right Triangles, Congruent Triangles, Rectangles, Squares, Parallelograms, Rhombuses, Polygons, Circles, and Tessellations of the Plane.
4) The Shape of Space: - Curved Space, Flatland, Ourland, and Mercury's Orbit.
5) The Pseudosphere: - A description of the space of which NonEuclid is a model.
6) Parallel Lines: - In Hyperbolic Geometry, a pair of intersecting lines can both be parallel to a third line.
7) Axioms and Theorems: - Euclid's Postulates, Hyperbolic Parallel Postulate, SAS Postulate, Hyperbolic Geometry Proofs.
8) 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.
9) X-Y Coordinate System: - A description of how an x-y coordinate system can be set up in Hyperbolic Geometry.
10) 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 joel@cs.unm.edu

Copyright©: Joel Castellanos, 1994-2007
        hit counter (11/29/2005)
Updated April, 4, 2007