GeoGebra, the free, open-source mathematics software is designed for math classrooms in secondary schools, but anyone who uses geometry, algebra, or calculus should check it out. It combines a flexible, easy-to-use geometry tool with direct input of equations and coordinates. It can create points, vectors, lines, segments, conic sections, and more using preconfigured tools and handle variables for vectors, numbers, and points. It's available in many languages and is supported by a community of users and developers as well as a useful Web-based Help file, a forum, and a wiki. It requires the Java Runtime Environment.
GeoGebra's default interface displays a toolbar full of unique icons for adding a range of objects, including Points, Lines Through Two Points, Polygons, Ellipses, Angles, Reflect Objects, and Sliders. Clicking any object and then clicking on the main two-axis view opened small properties boxes that let us customize and configure each item. As we clicked to add points or other objects, the program added them to either the Free Objects or Dependent Objects lists. Once we'd placed an object, we could easily move it around. For example, we clicked the tool to add a Circle Through Three Points. We added the first two points, which drew the circle. As we moved the cursor around for the third point, the circle moved position, expanded, and contracted to follow, with the changing value displayed in the Free Objects list in the left-hand navigation console as well as in small parentheses next to the cursor. We entered some simple equations in the Input field, and GeoGebra displayed them in the main view. We could also customize much of the program's look and functions on the Options menu. The Tools menu let us create and manage new tools via a simple wizard, a great extra.
We barely scratched the surface of the many ways users can customize GeoGebra and use it to teach, learn, and perform math. It's flexible, very easy to use, and very well supported, too. For anyone who can use it, we recommend it.