W.24 Exact Triangle Solvers & Surveying Triangulation — Code

Every classical triangle specification (QQQ, QQS, QSS, SQQ, and SSS up to scaling) reduces to linear or quadratic equations in quadrances and spreads with exact discriminant branching; applied to surveying, inaccessible heights and Regiomontanus’ maximum-spread viewing problem resolve by pure rational algebra without trigonometric tables.

Exact geometor.model SVG output of model.py for W.24 (Exact Triangle Solvers & Surveying Triangulation).

Symbolic Construction & Verification Script (model.py)

"""GEOMETOR Wildberger symbolic model and proof script for W.24: Exact Triangle Solvers & Surveying Triangulation.

        Enunciation: Every classical triangle specification (QQQ, QQS, QSS, SQQ, and SSS up to scaling) reduces to linear or quadratic equations in quadrances and spreads with exact discriminant branching; applied to surveying, inaccessible heights and Regiomontanus' maximum-spread viewing problem resolve by pure rational algebra without trigonometric tables.
        """

        from __future__ import annotations

        import sys
        from pathlib import Path

        _ROOT_SRC = Path(__file__).resolve().parents[3] / "src"
        if str(_ROOT_SRC) not in sys.path:
            sys.path.insert(0, str(_ROOT_SRC))

        from geometor.wildberger.models import (  # noqa: E402
            TopicBuildResult,
            assert_zero_floats,
            build_principle_model,
        )
        from geometor.wildberger.render import render_svg  # noqa: E402


        def construct_w_24() -> TopicBuildResult:
            """Construct the exact symbolic model and verifications for W.24.

            Returns:
                Populated `TopicBuildResult` for W.24 (Exact Triangle Solvers & Surveying Triangulation).
            """
            result = build_principle_model("W.24")
            assert_zero_floats(result.model)
            return result


        def main() -> None:
            """Execute W.24 symbolic construction, render `w-24.svg`, and print invariants."""
            here = Path(__file__).resolve().parent
            bundle = construct_w_24()
            svg_out = render_svg(
                bundle.model,
                here / "w-24.svg",
                extra_curves=bundle.extra_curves,
                annotations=bundle.annotations,
            )
            print("W.24: Exact Triangle Solvers & Surveying Triangulation")
            print(f"  Elements in model: {len(bundle.model)}")
            print(f"  Rendered SVG:      {svg_out.name}")
            for label, val, status in bundle.verifications:
                print(f"  [OK] {label}: {val} ({status})")


        if __name__ == "__main__":
            main()