NonEuclid

NonEuclid is a Java Software Simulation offering Straightedge 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.

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
Elliot Anshelevich - Undergraduate, Rice University

NonEuclid is Supported by the
     Institute for Advanced Study / Park City Mathematics Institute

Run NonEuclid Applet:

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  Click Button  on Right ------->

  If you do not see a button above, it means that your browser is not Java 1.1.6 enabled.  This may be because:
  1) you are running an older version of a browser,
  2) there is a firewall around your Internet access, or
  3) you have Java deactivated in the preferences of your browser.
  Both Netscape Communicator 4.6 and Microsoft Internet Explorer 5.0 include Java 1.1.6.

• There are two reasons why you may prefer to run NonEuclid as a Stand-alone application:
  1. The Java Security Manager does not allow applets to read or write to your local drive.  Therefore, when you run NonEuclid as an applet, you can not save your work.   However, when you install and run NonEuclid as an application, you can save and open files on your local drive.
  2. You may want to run NonEuclid from computers that are not connected to the Internet.

  The link below will download a .zip archive file that contains all of the NonEuclid program files (*.class) and the NonEuclid help files (*.html and *.gif).  The archive can be expanded with WinZip.  All files in the archive should be placed in the same directory.  In spite of the fact that this is called a "Stand-Alone" Application, you will need either a Java enabled browser or the JAVA Runtime Environment (JRE) to run the application.

  Running the NonEuclid Applet from a computer without an Internet connection: Install a Java enabled browser on the computer, and use it to open the file NonEuclid.html from the archive.  The page will look just like this one, except that when you click on a link or on the NonEuclid applet button, the information will come from the local archive (not from the Internet).

  Running the NonEuclid Application from a computer with or without an Internet connection:  Install a Java Interpreter on the computer.  Also install a browser on the computer.  The browser does NOT need to be Java enabled.  The browser will only be used to display the NonEuclid help files (html and gif).  To run the NonEuclid application, use the JAVA Runtime Environment (JRE).  Once you have installed JRE on your computer, open a command prompt window and enter the following command:
          jre -cp "c:\Program Files\NonEuclid" StartNonEuclid
  Where "c:\Program Files\NonEuclid" is the path of directory where you have installed the NonEuclid class files.  To read the NonEuclid help files, use a browser or html reader to open "NonEuclid.html".

  Download NonEuclid Archive Applet/Application and Documentation (if the .zip file loads into your browser, then click with the RIGHT mouse button and select the option "save to disk", or reconfigure your browser to save ZIP files to disk).  This archive includes all NonEuclid .class files and .html files.

• 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.
   

What-to-do:

• 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.
   

More Concepts:

• Postulates and Proofs: - Euclid's Postulates, Hyperbolic Parallel Postulate, SAS Postulate, Hyperbolic Geometry Proofs.
  Area: - A=½bh, Altitudes of a Hyperbolic Triangle, A=s², 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 Model: - This includes the definitions of points, lines, angles and a distance function in each model.

   

For The Teacher:

Why is it Important for Students to Study Hyperbolic Geometry?

References & Further Reading.