KSEG is a free interactive geometry program for exploring Euclidean geometry. It runs on Unix-based platforms (according to users, it also compiles and runs on Mac OS X and should run on anything that Qt supports). You create a construction, such as a triangle with a circumcenter, and then, as you drag verteces of the triangle, you can see the circumcenter moving in real time. Of course, you can do a lot more than that--see the feature list below.
KSEG can be used in the classroom, for personal exploration of geometry, or for making high-quality figures for LaTeX. It is very fast, stable, and the UI has been designed for efficiency and consistency. I can usually make a construction in KSEG in less than half the time it takes me to do it with similar programs. Despite the name, it is Qt based and does not require KDE to run. More Info »
KSEG was inspired by The Geometer's Sketchpad , but it goes beyond the functionality that Sketchpad provides.
Fast core which can support large constructions
Free/GPL-runs on Linux (and probably most other systems which support Qt)
Supports multiple languages
Construction of points, segments, rays, lines, circles, and arcs
Transformations (rotation, translation, scaling, reflection)
Construction of adaptively sampled loci for better quality and speed
Ability to easily redefine points to "edit" drawings
Easy to use editable scripting/macro with support for recursion
Pretty formulas for calculations-with my libkformula
Pretty colors, fonts, etc.
View panning/zooming and multiple simultaneous views
Export view to image file, including antialiased option
Selection Groups--group a bunch of objects, then select them later with two clicks