Iterated Partitions of Triangles

03/31/2009 - 12:15pm
03/31/2009 - 1:10pm
Ronald Graham (University of California San Diego)

For a given triangle there are many points associated with the triangle that lie in its interior; examples include the incenter (which can be found by the intersection of the angle bisectors) and the centroid (which can be found by the intersection of the medians). Using this point, one can naturally subdivide the triangle into six “daughter" triangles. We can then repeat the same process on each of the six daughter triangles, and then repeat it on each of 36 resulting triangles, and so on. A natural question is to ask what the typical nth generation daughter triangle looks like after some large number of steps. In this talk we examine this problem for both the incenter and the centroid and show that they result in very different behavior as n gets large. We will also look at this process for a number of other lesser known points, such as the Gergonne point and the Lemoine point.

ML 134 (note room change!)
Misc. Information: 

The speaker will also be giving a talk at the Athenaeum in the evening.