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 structural way of thinking about proportion, dimension, and geometric meaning across physical and digital systems.

The foundation of GRM lies in a set of clear proportional ratios that remain consistent across 1D, 2D, and 3D, enabling scalable and dimensionally coherent reasoning.

This series introduces the core logic, structural geometry, and dimensional principles of GRM. Together, these papers form the theoretical foundation for all GRM applications in design, AI, education, architecture, and digital measurement systems.

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 container-first logic and reciprocal relation between form and frame.

Whitepaper III – GRM as a Digital Geometry Paradigm
Positioning GRM as a logic-first framework for digital geometry and proportional design.

Whitepaper IV – Applying Fixed-Ratio Logic to Enclosed Non-Circular Shapes
Extending GRM beyond circles toward triangles, hexagons, and composite enclosed forms.

Whitepaper V – Volume Estimation Without Displacement
Introducing cube-based proportional volume logic for intuitive and non-invasive estimation.

Access and licensing

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

License: Creative Commons Attribution–NonCommercial–NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)

You are free to:

Share: copy and redistribute the material in any medium or format

As long as you:

provide appropriate attribution
do not use the material for commercial purposes
do not remix, transform, or redistribute modified versions

For commercial licensing, implementation partnerships, or AI training/integration requests, contact: info@inratios.com