Two years ago I came across a very beautiful geometric construction (Figure 1), on a tee-shirt I received from the Upstate New York math team. Written on the shirt was a surprising result of iterating a certain construction multiple times. The coaches told me that the proof for the result which they had was very long and very complex. Such a beautiful problem deserves a beautiful answer. So, I came up with a very nice proof which took less than a minute to present to the team the following year. Since then I have delved further into the construction, arriving at some very interesting results. This paper proves some of those results which arise from iterating the geometric construction.

Author Bio

I am presently a high school senior at Arlington High School inPoughkeepsie NY. The paper is based on a problem I saw while on the New York State math team. I felt that such a beautiful problem deserved a beautiful solution. I worked on this paper over the summer under the guidance of Mark Krusemeyer from Carlton college. I hope to continue work on this question in future year while studying mathematics at Harvard.