The drag mode
The most prominent feature of "dynamic geometry systems" is the "drag mode". The following construction shows what is meant by this. The drawing shows a triangle together with its circumcircle and its incircle. The details of the construction are hidden:
To "drag" the drawing, just do the following:
Whenever you move one of the points A, B or C, the whole drawing is immediately updated as if it had been constructed with the dragged point in the new position. So the geometric dependencies between the objects of the drawing are preserved: the circumcircle always runs through A, B and C, and the incircle always has the triangles' sides as tangent lines, no matter where you drag these points to!
- Move the mouse to one of the points A, B or C.
- When the mouse cursor changes to a pair of pliers press the left mouse button and hold it down.
- Move the mouse!
Such a dynamic drawing is a much better representation of a "construction" as a single static picture could ever be, because the dynamic drawing allows to browse through a great number of examples that belong to the same construction plan. So the dynamic drawing is in a certain sense a whole class of pictures.