Subdivision by bisectors is dense in the space of all triangles

Details Subdivision by bisectors is dense in the space of all triangles Subdivision by bisectors is dense in the space of all triangles

2010-07-14

arxiv.org/abs/1007.2301v1

Mathematics

Combinatorics

8 pages, lots of figures

Scientific paper

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.

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