**This package is no longer being maintained.
The only part of this project of value to those who want to explore conic sections in hyperbolic geometry are the
core drawing routines, but getting them into a useful form will be quite
a bit of work. I would be willing to license the core algorithms
under a BSD-like license.**

**David Royster has a page of links that might interest you. NonEuclid
should be of particular interest (if it is still being maintained...).**

This is the home of GPLconx, a tool for visualizing points, lines, circles,
ellipses, hyperbolas, parabolas, and more in three models of
hyperbolic geometry. Hyperbolic geometry is the geometry that results when
you deny Euclid his
fifth postulate, which basically states ``Given a line *L* and a point *P* not on *L*, there exists a unique line containing *P* that is parallel to *L*.'' and instead proffer ``Given a line *L* and a point *P* not on *L*, there exist at least two unique lines containing *P* that are parallel to *L*.'' In geometry, changing an
assumption can lead to a contradiction, and this is very useful as a means
of showing that the assumption is false. If you look for the
contradiction that is implied by the second statement, you will instead
end up proving that Euclidean geometry is exactly as ``true'', as ``correct''
as hyperbolic geometry.

The obvious next step after changing an underlying assumption (they go by the names ``axiom'' and ``postulate'' in geometry) is to explore the resulting system. For many people, the best way to get geometric intuition, i.e. a ``feel'' for geometry, is to look at it. GPLconx is a free (as in ``free speech'' as well as ``free soymilk'') computer program that lets you see 2-D hyperbolic geometry and manipulate it with your mouse and a special scripting language.

GPLconx is currently in an early stage of development. There are upwards of 23,000 lines of C, C++, and Tcl source code, but the user experience is still up in the air. In short, that means that you should not plan a curriculum around the current user interface (though once GPLconx is mature, it will most likely be used for no more than a week in a course on geometry). A release is out, but it's not ready for the alpha testers, so stay far away and check back here often or subscribe to the mailing list. For now, this page is not good for much except pointing you to the GPLconx project page and the optional downloads area, which has packages that you'll need if you want to build or hack GPLconx.

Here is the README for the latest release of GPLconx. It points to some other documents that are found in the source distribution.

Release 0.147's documentation is here, but don't bother.

Since GPLconx's documentation is so rough, maybe you should just read Edwin
A. Abbot's
*Flatland* instead. It is here for free thanks to
Project Gutenberg(TM).

David L. Chandler

Project graciously hosted by: