W.03 Quadrance, Midpoints & Point-to-Line Separation — Code

The quadrance between A_1 = [x_1, y_1] and A_2 = [x_2, y_2] is the quadratic form Q(A_1, A_2) = (x_2 - x_1)^2 + (y_2 - y_1)^2; midpoint M divides the quadrance by 4, the locus Q(X, A_1) = Q(X, A_2) is the linear perpendicular bisector, and the quadrance from A_0 to a non-null line l = <a : b : c> is (a*x_0 + b*y_0 + c)^2 / (a^2 + b^2).

Exact geometor.model SVG output of model.py for W.03 (Quadrance, Midpoints & Point-to-Line Separation).

Symbolic Construction & Verification Script (model.py)

"""GEOMETOR Wildberger symbolic model and proof script for W.03: Quadrance, Midpoints & Point-to-Line Separation.

        Enunciation: The quadrance between A_1 = [x_1, y_1] and A_2 = [x_2, y_2] is the quadratic form Q(A_1, A_2) = (x_2 - x_1)^2 + (y_2 - y_1)^2; midpoint M divides the quadrance by 4, the locus Q(X, A_1) = Q(X, A_2) is the linear perpendicular bisector, and the quadrance from A_0 to a non-null line l = <a : b : c> is (a*x_0 + b*y_0 + c)^2 / (a^2 + b^2).
        """

        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_03() -> TopicBuildResult:
            """Construct the exact symbolic model and verifications for W.03.

            Returns:
                Populated `TopicBuildResult` for W.03 (Quadrance, Midpoints & Point-to-Line Separation).
            """
            result = build_principle_model("W.03")
            assert_zero_floats(result.model)
            return result


        def main() -> None:
            """Execute W.03 symbolic construction, render `w-03.svg`, and print invariants."""
            here = Path(__file__).resolve().parent
            bundle = construct_w_03()
            svg_out = render_svg(
                bundle.model,
                here / "w-03.svg",
                extra_curves=bundle.extra_curves,
                annotations=bundle.annotations,
            )
            print("W.03: Quadrance, Midpoints & Point-to-Line Separation")
            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()