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X₁₉₃₄¶

TRILINEAR POLE OF PU(14)

X₁₉₃₄ (TRILINEAR POLE OF PU(14)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1934 = TRILINEAR POLE OF PU(14)."""

        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,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01934(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1934 = TRILINEAR POLE OF PU(14) on reference triangle ABC."""
            X_1933 = eval_trilinear_point(model, A, B, C, '(a**(2)*(a**(4) - b**(2)*c**(2)))', ID="X_1933", classes=["center"])
            X_1934 = isogonal_conjugate(model, A, B, C, X_1933, ID="X_1934", classes=["selected", "target"])
            X_257 = eval_trilinear_point(model, A, B, C, '1/(a**(3) + a*b*c)', ID="X_257", classes=["center", "incident"])
            X_335 = eval_trilinear_point(model, A, B, C, 'b*c/(a**(2) - b*c)', ID="X_335", classes=["center", "incident"])
            central_line(model, X_257, X_335, 257, 335, incident=True)
            X_38 = eval_trilinear_point(model, A, B, C, 'b**(2) + c**(2)', ID="X_38", classes=["center", "incident"])
            X_799 = eval_trilinear_point(model, A, B, C, '(csc(A))**(2)/((cos(B))**(2) - (cos(C))**(2))', ID="X_799", classes=["center", "incident"])
            central_line(model, X_38, X_799, 38, 799, incident=True)
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            X_1581 = eval_trilinear_point(model, A, B, C, '1/(a**(4) - b**(2)*c**(2))', ID="X_1581", classes=["center", "incident"])
            central_line(model, X_75, X_1581, 75, 1581, incident=True)
            return promote_point_to_top(model, X_1934)


        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_1934 on the given reference triangle."""
            model = create_model('X_1934 = TRILINEAR POLE OF PU(14)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01934(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-01934.json"))
            write_center_svg(
                model_acute,
                here / "x-01934.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1934¶

X₁₉₃₄¶