Hyperbolic Geometry Article and Javascript Software (original) (raw)

If our browser supported the HTML5 canvas and WebGL, there would be a nice animation here :(

NonEuclid allows the curious explorer to gain experience in Hyperbolic Geometry and to empirically investigate questions such as: "Does the Euclidean geometry method for constructing an equilateral triangle work in Hyperbolic geometry?" or "In Hyperbolic Geometry, are the base angles of an isosceles triangle congruent?"

Aside from being interesting in itself, a study of hyperbolic geometry can, through its novelty, be helpful to high school geometry students. For example, when asked to prove that the opposite sides of a rectangle have the same length, many beginning geometry students will be confused about what to do. Students sometimes think: "Why I am being told to prove what I learned in kindergarten is just part of the definition of what it means for a figure to be a rectangle." The strangeness of hyperbolic geometry helps such students think about and understand the difference between what is part of an object's definition and what is a theorem about an object.

Hyperbolic Geometry also has practical aspects such as orbit prediction of objects within intense gravitational 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

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

Polar Coordinates:(-.---, --.-)

The above new Javascript version is still under development. The older Java version is:<NonEuclid.jar> To run this, download, and either double-click or use the command:
java" -jar NonEuclid.jar