Basic geometry as work. Circles with radii 1, 3, and 6, centered at the origin and 3 units below. Two points rotating counterclockwise at the same rotational speed, one clockwise at twice that speed. Those points are connected to form a triangle, and two angle bisectors shown. The trace shows the path of the point of intersection of those medians, the incenter.
There is a lot of mathematics in this diagram. I believe that creations such as these can be used with young students to "hook" them into mathematics long before they know the math needed to write equations for such graphs. Although the equation would be heavy into trig, the creation of the graph requires no trig at all. Basic geometric concepts such as circle, line, bisection, rotation are just about all that is needed.
A tremendous amount of mathematics can be learned by setting kids loose with GeoGebra and a basic knowledge of the GeoGebra toolbar. In many respects, kids would probably learn GeoGebra faster than adults.
Animations and GeoGebra will be the topic of my session at the AMTNYS (Association of Mathematics Teachers of New York State) annual conference in Syracuse next Monday.
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