  Starting with any nondegenerate triangle we can use a well defined interior
point of the triangle to subdivide it into six smaller triangles. We can repeat
this process with each new triangle, and continue doing so over and over. We
show that starting with any arbitrary triangle, the resulting set of triangles
formed by this process contains triangles arbitrarily close (up to similarity)
any given triangle when the point that we use to subdivide is the incenter. We
also show that the smallest angle in a "typical" triangle after repeated
subdivision for many generations does not have the smallest angle going to
zero.

Combinatorics