One of the things that I've noticed geometry students could use some help with is visualizing the concepts they're studying. Computers make a valuable resource for this, because students can create points, construct figures from them, and even drag the points about to see how their constructed figures change, thus giving them a better idea of the behavior of geometric objects. However, most students probably aren't aware of their options for geometry software, or they expect that they have to pay for software packages.

To correct this, I thought it would be helpful to compile a list of open-source software packages students can install. “Open-Source” means that anybody can download a copy of the source code and compile it. Open-Source software has three advantages over closed-source software. First, it's completely free to run, and always will be; they won't even bug you about registering after 30 days or some similar nuisance. The most you'll have to put up with is a widget asking for a donation, and even these are usually unobtrusive. Second, open-source software is extremely unlikely to have malware or viruses in it; after all, anybody can look at the code that makes it up, so if somebody put something malicious in it, they wouldn't be able to hide it. Finally, open-source software tends to be available for more operating systems than closed-source software, because it's a lot easier for people with minority operating systems to create versions of the program compatible with their system if they have access to the complete source code. In particular, both of the packages I found could be installed on Windows, MacOSX, as well as real operating systems like Linux.

The package I recommend is GeoGebra. It has all of the basic qualities one would expect to find in a software package for teaching elementary geometry:

[1] It can create points at arbitrary locations

[2] You can drag around arbitrarily chosen points freely

[3] It can draw lines, circles, and derived points (i.e. midpoint between two points, intersection of two lines) based on the arbitrary points

[4] The figures drawn by the software will be updated based on how you've dragged your arbitrary points

Naturally, it has many more features. You have the option to change the color, thickness, or label of points and figures so you can tell which one is which. It supports more curves than just lines and circles as well, which is fun to play with even though most high-school geometry courses don't go much further than lines & circles.

You can download GeoGebra from its homepage, found here:

If you can't get GeoGebra to work for you, another alternative is called CaRMetal. CaRMetal boasts most of the features of GeoGebra and a similar interface; I prefer GeoGebra's interface, but you might prefer CaRMetal's. The primary reason I recommend GeoGebra over CaRMetal is because I could tell there was still ongoing work on GeoGebra -- adding features and porting to new platforms -- whereas I wasn't sure that there were still people working on CaRMetal.

You can download CaRMetal from its homepage, found here:

There are many other geometry packages out there, such as Geomview. Some of these I omitted because they're more suited for things like three-dimensional analysis or other higher-level concepts, and as such have a steep learning curve that would get in the way of learning the basics of geometry. Most of these I omitted simply because I haven't found them yet. If you know of other open-source geometry applications out there, by all means post a link in the comments section.