Whitepapers GRM Foundations

GRM Foundations

Whitepapers on the Theoretical Core of the Geometric Ratio Model

The Geometric Ratio Model (GRM) is more than a measurement technique, it is a new way of thinking about proportion, dimension, and structure across physical and digital systems. The foundation of this model lies in a set of clear, rational ratios that apply across 1D, 2D, and 3D spaces, enabling scalable, dimensionally consistent logic.

This series of foundational whitepapers introduces the core logic, the underlying geometry, and the dimensional principles of GRM. These papers build the theoretical scaffolding for all further applications in design, AI, education, architecture, and beyond.

What this section includes:

• Whitepaper I – The Geometric Ratio Model
  (Introducing a unified system of rational proportions across 1D, 2D, and 3D)
• Whitepaper II – The role of the radius in the Geometric Ratio Model (GRM)
  (Exploring the reciprocal relationship between shape and container)
• Whitepaper III – GRM as a Digital Geometry Paradigm
  (Framing GRM as a logic-first alternative to π in digital design systems)
• Whitepaper IV – Applying Fixed-Ratio Logic to Enclosed Non-Cicular Shapes
• (Extending GRM to triangles, hexagons, and complex forms within squares)
• Whitepaper V – Volume Estimation Without Displacement
  (Using cube-based GRM ratios for intuitive, non-fluid-based volume logic)

Access & Licensing

All whitepapers in the GRM Foundations Series are available for direct download on their respective pages.

They are published under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) license.
This means you are free to:

• Share — copy and redistribute the material in any medium or format
• Adapt — remix, transform, and build upon the material

…as long as you:

• Credit the original author
• Do not use the material for commercial purposes
• Distribute any derivative works under the same license

You can find the full license terms here: creativecommons.org/licenses/by-nc-sa/4.0

🛈 For commercial or extended academic use, please contact: info@inratios.com