Whitepaper – Geometric Ratio Model

Geometric Ratio Model (GRM) – A New Metric for Shape and Proportion

The Geometric Ratio Model (GRM), developed by M.C.M. van Kroonenburgh,MSc, introduces a new way to describe geometric forms—not through irrational constants like π, but through fixed, rational proportions relative to the square or cube in which a shape is inscribed.

For example, a circle in GRM is no longer defined by its radius and π, but by its consistent ratio of 0.7854 to the square, both in terms of area and perimeter. This model enables consistent, dimensionally grounded reasoning across education, AI, design, digital geometry, and shape analysis.

GRM works across 1D, 2D, and 3D, offering simplicity, clarity, and precision.

The Geometric Ratio Model – Whitepaper Update (Version 3.0)

We’re proud to announce the release of version 3.0 of the GRM whitepaper:
“The Geometric Ratio Model – A New Metric for Proportion, Shape, and Dimension.”

This latest version builds on the foundational ideas introduced in version 2.0 and brings major improvements in clarity, structure, and visual illustration.

What’s new in version 3.0?

✅ Clearer narrative and dimensional logic (1D–2D–3D)
✅ Rewritten sections with updated examples and terminology
✅ New illustrations based fully on GRM ratios (SPU, SAU, SVU)
✅ Four fully developed application domains:
Design & CAD, AI & Shape Recognition, Education, and Measurement
✅ Updated appendices and classification diagrams
✅ Integrated table of domain applications with new use cases

Open for Peer Review

Version 3.1 is now open for academic, technical, and design-oriented peer review.
If you would like to contribute a critical reading or join the validation process, we invite you to review the document and share your feedback.

Contact: info@inratios.com
More info: inratios.com/peerreview (page in development)

Download the current version (v3.1, June 2025)

White paper GRM_v31_peer review Downloaden

Older versions remain available on request for comparison and documentation.

Published:

Version 1.0 May 4, 2025 | Language: English | Pages: 22
Version 2.0 May 17, 2025 | Language: English | Pages: 26
Version 3.0 June 1, 2025 | Language: English | Pages: 29
Version 3.0 June 12, 2025 | Language: English | Pages: 29

^{This work is officially registered via i-Depot (BOIP). Reference no. 151927 – May 10, 2025.}