GRM as a Digital Geometry Paradigm

A rational system for visual, scalable, and data-oriented geometry

In an age where digital systems increasingly shape design, simulation, education, and AI workflows, classical geometric reasoning does not always map cleanly onto how machines process structure. This whitepaper introduces the Geometric Ratio Model (GRM) as a complementary paradigm for geometry in digital environments.

Rather than relying on parameter-first formulas, GRM defines shapes through fixed rational ratios within bounding squares and cubes. A perfectly inscribed circle, for example, is described by its canonical occupation of the square reference frame: 0.7854 SAU (78.54%). This is a structural ratio that can be interpreted visually and applied consistently across scale.

This whitepaper outlines how GRM supports:

pixel-based measurement and digital geometry
shape classification through proportional structure
explainable AI through ratio-based constraints
scalable design logic grounded in enclosure and reference framing

Grounded in classical mathematics but tailored for computational environments, GRM offers a practical language for proportion, identity, and form in digital systems.

Update: Version 1.1 (June 2025)

This updated release refines structure, layout, and visual clarity while preserving the full conceptual content. It reaffirms GRM as a complementary proportional framework designed for digital, pixel-based, and AI-driven environments.

Whitepaper – GRM as a Digital Geometry Paradigm_v1_1 Downloaden

Published:

version 1.0 May 25, 2025 | Language: English | Pages: 23
version 1.1 June 6, 2025 | Language: English | Pages: 16

Registration and copyright

© 2025 M.C.M. van Kroonenburgh, MSc (Inratios).
Registered via i-Depot (BOIP) Reference no. 151927 (May 10, 2025).
This whitepaper may be shared in unmodified form with attribution. For licensing or commercial use: info@inratios.com.