W.08 Law III: The Spread Law & Extended Circumquadrance Law — Code

In any non-null triangle A_1 A_2 A_3 with side quadrances Q_1, Q_2, Q_3, vertex spreads s_1, s_2, s_3, quadrea A, and circumquadrance K, the ratios of spread to opposite quadrance are equal: s_1 / Q_1 = s_2 / Q_2 = s_3 / Q_3 = A / (4 * Q_1 * Q_2 * Q_3) = 1 / (4 * K).
t c (Q = 4225/64) / A_1 F_1 / (Q = 3136/25) / A_2 F_2 / (Q = 28224/169) A_1 = [0, 0] A_2 = [14, 0] A_3 = [5, 12] F_1 = [224/25, 168/25] F_2 = [350/169, 840/169] C = [7, 33/8] s_i / Q_i = 16/4225 = 1/(4K) K = 4225/64 A1A1 A2A2 A3A3 F1F1 F2F2 CC + − ⟲ Lbl Gde

Exact geometor.model SVG output of model.py for W.08 (Law III: The Spread Law & Extended Circumquadrance Law).

Symbolic Construction & Verification Script (model.py)

"""GEOMETOR Wildberger symbolic model and proof script for W.08: Law III: The Spread Law & Extended Circumquadrance Law.

        Enunciation: In any non-null triangle A_1 A_2 A_3 with side quadrances Q_1, Q_2, Q_3, vertex spreads s_1, s_2, s_3, quadrea A, and circumquadrance K, the ratios of spread to opposite quadrance are equal: s_1 / Q_1 = s_2 / Q_2 = s_3 / Q_3 = A / (4 * Q_1 * Q_2 * Q_3) = 1 / (4 * K).
        """

        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_08() -> TopicBuildResult:
            """Construct the exact symbolic model and verifications for W.08.

            Returns:
                Populated `TopicBuildResult` for W.08 (Law III: The Spread Law & Extended Circumquadrance Law).
            """
            result = build_principle_model("W.08")
            assert_zero_floats(result.model)
            return result


        def main() -> None:
            """Execute W.08 symbolic construction, render `w-08.svg`, and print invariants."""
            here = Path(__file__).resolve().parent
            bundle = construct_w_08()
            svg_out = render_svg(
                bundle.model,
                here / "w-08.svg",
                extra_curves=bundle.extra_curves,
                annotations=bundle.annotations,
            )
            print("W.08: Law III: The Spread Law & Extended Circumquadrance Law")
            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()