In 1913, George Polya described an iterative construction P, that maps an arbitrary t in [0, 1] to P(t) onto a non-isosceles right triangle, T. This mapping constructs P(t) by producing a sequence of nested subtriangles by drawing the altitude of the current triangle at each step. This sequence has only one point in common, P(t). Polya proved that this mapping P is continuous and surjective. In this project, we built upon this and other research to analytically prove that the trajectory of Polya's function in T is self-similar. In doing so, we constructed a parametric equation for P. We plan to develop this study further and submit a paper with our own contributions to an appropriate journal.
Worcester Polytechnic Institute
Major Qualifying Project
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