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X₂₁₂₈¶

EIGENTRANSFORM OF X₁₉

X₂₁₂₈ (EIGENTRANSFORM OF X₁₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2128 = EIGENTRANSFORM OF X_19."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02128(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2128 = EIGENTRANSFORM OF X_19 on reference triangle ABC."""
            X_2128 = eval_trilinear_point(model, A, B, C, '((b**(2) + c**(2) - a**(2))*((a**(2) + b**(2) + c**(2))**(2) - 8*b**(2)*c**(2)))', ID="X_2128", classes=["selected", "target"])
            X_63 = eval_trilinear_point(model, A, B, C, 'cot(A)', ID="X_63", classes=["center", "incident"])
            X_304 = eval_trilinear_point(model, A, B, C, '(cot(A))*(csc(A))**(2)', ID="X_304", classes=["center", "incident"])
            central_line(model, X_63, X_304, 63, 304, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_1958 = eval_trilinear_point(model, A, B, C, '((cot(A))**(2) + cot(B)*cot(C))', ID="X_1958", classes=["center", "incident"])
            central_line(model, X_1, X_1958, 1, 1958, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_2082 = eval_trilinear_point(model, A, B, C, '(b + c - a)*(a**(2) + (b - c)**(2))', ID="X_2082", classes=["center", "incident"])
            central_line(model, X_2, X_2082, 2, 2082, incident=True)
            return promote_point_to_top(model, X_2128)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_2128 on the given reference triangle."""
            model = create_model('X_2128 = EIGENTRANSFORM OF X_19')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02128(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-02128.json"))
            write_center_svg(
                model_acute,
                here / "x-02128.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2128¶

X₂₁₂₈¶