I. The Symbolic Core & Discovery Engine

Exact Algebraic Modeling, Interactive Visualization & Automated Discovery

The symbolic core provides the mathematical substrate on which every GEOMETOR construction, verification script, and studio broadcast runs.

model — The Symbolic Construction Engine

geometor.model implements compass-and-straightedge geometry in pure symbolic algebra (SymPy):

  • Exact Primitives & Closed-Form 2D Intersections: Points, infinite lines [ A B ], circles ( A B ), segments / A B /, polygons < A B C >, wedges, and polynomial loci—with fast closed-form algebraic intersection deduplication and scoped subconstructions.

  • Rational & Projective Invariants (`invariants.py`): Exact symbolic quadrance, line_spread, vertex_spread, cross, cross_ratio, and is_harmonic verification without transcendental rounding error.

  • Constructive Proof & Ancestral DAGs (`proof.py`, `ancestors.py`): Every derived point records the exact ancestral chain of givens, lines, and circles required to construct it, plus JSON serialization for downstream rendering and analysis.

explorer — Interactive SVG Workbench

geometor.explorer unifies visual inspection, interactive construction, and print/video SVG export (superseding the earlier standalone render prototype):

  • Web Canvas & Symbolic CLI: Construct and inspect geometor.model figures interactively in the browser with pan/zoom SVG viewports, KaTeX algebraic coordinate inspection, and ancestral highlighting.

  • Step-by-Step Timeline & Sheet Export: Scrub through construction history step by step or export publication-grade vector figures for Sphinx Book Codices and QHD broadcasts.

divine — Golden Ratio & Harmonic Discovery

Once a model is constructed, geometor.divine scans every collinear point set on every line in the field to uncover emergent proportional structures:

  • Exact Golden Sections: Identifies collinear triples \((A, B, C)\) whose segment ratios simplify algebraically to \(\phi = \frac{1 + \sqrt{5}}{2}\) or \(\frac{1}{\phi} = \phi - 1\).

  • Golden Chains & Harmonic Ranges: Groups contiguous golden sections into self-similar geometric progressions (golden chains) and detects projective harmonic quadruples \((A, B; C, D) = -1\).

trees — Monotone Planar Tree Drawings

Investigates straight-line monotone planar drawings of arbitrary rooted trees on compact integer grids using Stern–Brocot mediant trees and Farey rational sequences—connecting discrete number-theoretic mediants directly to crossing-free geometric graph layouts.