What Is Dynamic Geometry?

The term "dynamic" in mathematics refers to the ideas of motion and change. Dynamic Geometry is a new term coined in response to the new software packages such as Sketchpad and Cabri. These products act as a sort of electronic ruler and compass.

What really sets a Sketchpad sketch apart from one that you might have made on a sheet of paper with the good old tools of our high school days is not just the accuracy of the constructions. It is the fact that the software remembers relationships among the various components of a construction --- that point P is the midpoint of the segment AB, that circle (C) has center O and goes through point X etc.

So, for instance, when you construct the circumcircle of a triangle, you can move any of the vertices of the triangle and see that the circle still circumscribes the triangle. Try this by clicking on a vertex, holding down the mouse, and dragging the vertex around. Notice that you can make the center, O of the circumcircle either inside, outside, or on an edge of the triangle. Can you find a triangle where the circumcenter is at a vertex? What can you say about the triangles where the circumcenter is on one of the edges? These are the kinds of questions you can have students explore when they can see different instances of the same construction just by moving the initial objects (in this case the three vertices of the triangle).