Extending the Geometric Ratio Model (GRM)

Applying Fixed-Ratio Logic to Enclosed Non-Circular Shapes

This whitepaper expands GRM beyond circles and spheres. It introduces a structural proportion framework for enclosed non-circular shapes such as ellipses, triangles, rectangles, and composite figures. Each shape is interpreted by its spatial ratio within a bounding square or cube.

The document presents:

GRM-based structural ratio logic across multiple shape families
Classification criteria for enclosed shapes
Dimensional derivations and interpretation rules
Applications in AI, CAD, education, and visual design

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

Published: version 1.0 May 18, 2025 | Language: English | Pages: 27

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