Faculty Advisor

Mosco, Umberto

Abstract

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.

Publisher

Worcester Polytechnic Institute

Date Accepted

April 2010

Major

Mathematical Sciences

Project Type

Major Qualifying Project

Accessibility

Unrestricted

Advisor Department

Mathematical Sciences

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