A New Mathematical Constant: The Sigma Spiral/Introduction

Introduction

The Sigma Spiral Constant is a proposed mathematical constant that emerges from studying the geometry of logarithmic spirals. Whereas π governs the relationship between radius and circumference in circles, the Sigma Spiral Constant is inspired by π and is explored as a way to describe the relationship between radius and arc length in spirals over one radian.

The motivation for introducing this constant is the search for a natural invariant that might capture the scaling behavior of spirals. Spirals are ubiquitous in nature (shells, galaxies, hurricanes), yet unlike circles, there is no widely recognized constant that encodes their fundamental geometry. The Sigma Spiral Constant is presented here as an exploratory idea, intended to encourage discussion and experimentation rather than to claim a fully established law.

In this Wikibook, we will:

  • Define the constant as it has been proposed.
  • Provide examples of its tentative computation.
  • Explore its relation to other well-known constants.
  • Suggest directions for further study, noting current limitations.
This article is issued from Wikibooks. The text is available under Creative Commons Attribution-Share Alike 4.0 unless otherwise noted. Additional terms may apply for the media files.