Whitepaper – The role of the radius in the Geometric Ratio Model (GRM)

From Classical Dependency to Derived Proportion

This second whitepaper in the GRM series by M.C.M. van Kroonenburgh presents a fundamental reformulation of circular geometry. While classical geometry defines circles based on their internal radius and relies on the irrational constant π, the Geometric Ratio Model (GRM) reverses this logic: it starts from the square that bounds the circle. From this reference structure, the radius becomes a derived system constant (expressed in SPU).

What you’ll find inside:

A consistent geometric framework for deriving the radius from the bounding square
A side-by-side comparison between classical and GRM logic
Applications in CAD, AI, education, and interface design
Includes examples, derivations, and visualizations
A practical and theoretical foundation for dimensionally grounded design

Why it matters:

This whitepaper makes geometry more intuitive, more visual, and more applicable in digital systems—without sacrificing mathematical rigor. Whether you’re a designer, educator, developer, or theorist, GRM provides a scalable and rational way to define and analyze geometric forms.

What’s New in Version 2.0?

The whitepaper “The Role of the Radius in the Geometric Ratio Model (GRM)” has been completely revised and expanded.

While version 1.1 introduced the basic idea of the radius as a derived quantity, version 2.0 goes further, offering a full narrative structure, deeper theoretical logic, and broader practical applications. It is part of the GRM Foundation Series, and builds directly on new insights developed since the original release.

Here’s what’s new:

✅ Structured narrative

The new version takes the reader step-by-step:

From classical geometry (radius as fixed input),
To derived radius (from the frame outward),
And into a full ratio-based system that works across dimensions.

✅ Radius as a system constant

Rather than being measured or assumed, the radius is now treated as a derived constant, a fixed outcome of a square (or cube) that a shape fills.
The radius becomes a derived system constant (expressed in SPU).
This leads to consistent scaling across all levels of form.

✅ Dimensional consistency

The paper shows how GRM remains dimensionally consistent across 2D and 3D, deriving surface and volume proportions directly from the square or cube—without relying on π. This enables scalable geometric reasoning grounded in visual structure.