A regular $n$-gon spiral

TL;DR

This paper introduces a flexible method for constructing polygonal spirals using regular n-gons, allowing various analytical and asymptotic behaviors based on size arrangements.

Contribution

It presents a novel construction of polygonal spirals with adjustable sizes, enabling diverse analytical and asymptotic properties.

Findings

Different size configurations lead to varied spiral behaviors.

The construction allows for both analytical and asymptotic analysis.

Flexible design enables exploration of geometric properties.

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.