Copyright©: Joel Castellanos, 1994-2009
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.
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
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
Running NonEuclid in this way does not require an Internet connection. Additionally, the Java security manager will not prevent NonEuclid from saving or printing files.
|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.|
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.|