What is GeoGebra?
From Markus Hohenwarter, the creator of GeoGebra:
"GeoGebra is dynamic mathematics software for all levels of education that joins arithmetic, geometry, algebra and calculus. On the one hand, GeoGebra is an interactive geometry system. You can do constructions with points, vectors, segments, lines, conic sections as well as functions and change them dynamically afterwards. On the other hand, equations and coordinates can be entered directly. Thus, GeoGebra has the ability to deal with variables for numbers, vectors and points, finds derivatives and integrals of functions and offers commands like Root or Extremum. These two views are characteristic of GeoGebra: an expression in the algebra view corresponds to an object in the graphics view and vice versa."
The best way to see what it is, is to play with an applet yourself.
Click on this link, or the picture below. You may get an "error" message, depending on your security settings. If you do, go up to the top yellow bar, and right-click, and "allow" content.
Sample Applet, just for fun.
(The newest version of GeoGebra, version 3.2, now has statistics and spreadsheet capabilities. I haven't had a chance to play much with it yet, but it looks fantastic.)
Since GeoGebra is Java-based, it can be used from any computer, by anyone, free of charge. Just go to the GeoGebra web site, and click on "web start." If you don't have proper administrative privileges, or don't want to download GeoGebra onto the computer you're using, click on "applet start."
This way, any student can also play with GeoGebra.
To see more of what GeoGebra can do, as well as how you can do it, see the tutorial videos.