Unit VII Summary: Complementarity of the Three Euclidean Formalisms

Synthesis of Textual, Chromatic & Symbolic Representations

Architectural Comparison Across the GEOMETOR Triad

Dimension	Heath / geometor/euclid	Byrne 1847 / geometor/byrne	geometor/elements & model
Binding Model	Pass-by-reference (A, B, C)	Pass-by-value (, )	Typed Symbolic DAG (Point, Circle, Polygon)
Cognitive Strength	Unbounded variable namespace	Zero eye-lookup latency; instant symmetry	Deterministic machine constructibility
Scaling Limit	High working-memory indirection	4-color register pressure	Requires explicit orientation selectors (side_of)
Proof Verification	Natural-language syllogism	Visual equational inspection	Exact SymPy polynomial/radical simplification