A regular $n$-gon spiral

Abstract

We construct a polygonal spiral by arranging a sequence of regular $n$-gons such that each $n$-gon shares a specified side and vertex with the $(n+1)$-gon in the construction. By offering flexibility for determining the size of each $n$-gon in the spiral, we show that a number of different analytical and asymptotic behaviors can be achieved.

12 pages, 5 figures. Improved presentation. This version to appear in Rocky Mt. J. Math