Repeatedly Subdividing Triangles through Special Points
Repeatedly Subdividing Triangles through Special Points
Associated with every triangle are a number of special points called "triangle centers". Some of the best known of these include the centroid, incenter, and circumcenter; many more have been named and studied. Not all triangle centers, in fact, fall in the interior of a given triangle, but some always do. We can draw segments from the vertices to one of these interior triangle centers to subdivide the triangle into three new ones. Iterating this process can produce some beautiful figures. This Demonstration shows the centers of all the subtriangles up to the iteration.
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