This page introduces the concept of a proposed mathematical constant related to logarithmic spirals, as part of a broader study of special constants like π, e, and φ. The goal is educational: to show how new constants might be defined, studied, and compared.

This Wikibook introduces and explores the Sigma Spiral Constant, a hypothetical constant that appears in the geometry of logarithmic spirals. The idea is inspired by π: while π governs circular geometry, the Sigma Spiral Constant is explored as potentially describing the length–radius relation in one radian of a spiral.

Importantly, this idea is still exploratory. Unlike classical constants such as π, e, or φ, the Sigma Spiral Constant has not yet been established as universal or fundamental. Its presentation here is intended mainly for educational purposes, to illustrate how mathematicians might investigate new constants and compare them with well-known ones.

• Introduction
• Definition and Properties
• Computation and Examples
• Relation to Other Constants
• Open Problems
• References

The goal of this book is to:

• Provide a clear introduction to the Sigma Spiral Constant as a proposal.
• Explore its tentative definition, basic properties, and possible applications.
• Compare it with other well-known constants such as π and e, while noting the differences in status.
• Present open questions for further research.

This is an open textbook. Contributions, critiques, and improvements are welcome. Readers should keep in mind that this constant is not yet formally established, and its study here is primarily educational and exploratory.