Inratios

Whitepaper – Geometric Ratio Model

A new metric for shape and proportion

The Geometric Ratio Model (GRM), developed by M.C.M. van Kroonenburgh, MSc, introduces a structural way to describe geometric forms through fixed proportional occupation of a square or cube. Rather than starting from internal parameters, GRM begins with the container and interprets form through ratio.

For example, a perfectly inscribed circle is described through a canonical proportional relation to its square reference frame. This enables consistent reasoning across education, AI, design, digital geometry, and shape analysis, while remaining scalable across 1D, 2D, and 3D.

Whitepaper update (Version 3.0)

Version 3.0 of the GRM whitepaper is now available:

“The Geometric Ratio Model (GRM): A New Metric for Proportion, Shape, and Dimension.”

This release builds on earlier versions and introduces a clearer structure, improved terminology, and fully GRM-based illustrations.

What’s new in Version 3.0

  • clearer narrative and dimensional logic across 1D to 3D
  • rewritten sections with updated examples and terminology
  • new illustrations based on GRM units (SPU, SAU, SVU)
  • four expanded application domains:
    Design and CAD, AI and Shape Recognition, Education, Measurement
  • updated appendices and classification diagrams
  • integrated table of domain applications with new use cases

Open for peer review (v3.1)

Version 3.1 is currently open for academic, technical, and design-oriented peer review.

If you would like to contribute a critical reading or join the validation process, you are invited to review the document and share feedback.

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

Download

Current version: v3.1 (June 2025)

White paper GRM_v31_peer reviewDownloaden

Older versions remain available upon request for comparison and documentation.

Publication history

  • v1.0 (May 4, 2025) | English | 22 pages
  • v2.0 (May 17, 2025) | English | 26 pages
  • v3.0 (June 1, 2025) | English | 29 pages
  • v3.1 (June 12, 2025) | English | 29 pages

Registration

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

© 2026 M.C.M. van Kroonenburgh, MSc (Inratios). Registered under i-Depot 157326. This framework forms part of the Geometric Integrity framework