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X₁₉₇₃¶

TRILINEAR PRODUCT OF PU(39)

X₁₉₇₃ = barycentric product of PU(18)

X₁₉₇₃ (TRILINEAR PRODUCT OF PU(39)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1973 = TRILINEAR PRODUCT OF PU(39)."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01973(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1973 = TRILINEAR PRODUCT OF PU(39) on reference triangle ABC."""
            X_304 = eval_trilinear_point(model, A, B, C, '(cot(A))*(csc(A))**(2)', ID="X_304", classes=["center"])
            X_1973 = isogonal_conjugate(model, A, B, C, X_304, ID="X_1973", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            central_line(model, X_1, X_19, 1, 19, incident=True)
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_41 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b + c - a)', ID="X_41", classes=["center", "incident"])
            central_line(model, X_25, X_41, 25, 41, incident=True)
            X_47 = eval_trilinear_point(model, A, B, C, 'cos(2*A)', ID="X_47", classes=["center", "incident"])
            X_163 = eval_trilinear_point(model, A, B, C, '(sin(2*A))/(sin(2*B) - sin(2*C))', ID="X_163", classes=["center", "incident"])
            central_line(model, X_47, X_163, 47, 163, incident=True)
            return promote_point_to_top(model, X_1973)


        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_1973 on the given reference triangle."""
            model = create_model('X_1973 = TRILINEAR PRODUCT OF PU(39)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01973(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-01973.json"))
            write_center_svg(
                model_acute,
                here / "x-01973.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1973¶

X₁₉₇₃¶