Applying Fixed-Ratio Logic to Enclosed Non-Circular Shapes

This third whitepaper in the GRM series expands the scope of the Geometric Ratio Model beyond circles and spheres. It introduces a proportional logic framework for enclosed non-circular shapes such as ellipses, triangles, rectangles, and composite figures—each analyzed in terms of their fixed spatial ratio within a bounding square or cube.

The document presents:

Canonical and parameterized GRM ratios (SAU, SPU, SVU),
Structural criteria for valid classification,
Mathematical derivations and dimensional logic,
Real-world applications in AI, CAD, education, and visual design,
A comprehensive matrix of GRM ratios across shape types.

It also includes strategies for robust implementation and outlines how this logic can inform future software tools, shape libraries, and educational frameworks.

This paper marks a key step in transforming geometry from formula-based calculation into scalable, visual reasoning—anchored in structure and powered by proportion.

Whitepaper – Extending the Geometric Ratio Model Downloaden

Published:

version 1.0 May 17, 2025 | Language: English | Pages: 27