Medial Triangles

In triangle ABC pictured below, we know that segment AA', segment BB', and segment CC' are medians. Thus triangle A'B'C' is a medial triangle. The next triangle interior to triangle A'B'C' is the medial triangle of A'B'C'. This pattern continues.

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First, what is point G called?
Move the vertices of triangle ABC. What do you notice about point G and the medial triangles?
Based on this, what hypothesis can you make about point G and the repeated construction of the medial triangles?

Jackie Southard, June 26, 2008, Created with GeoGebra