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X₁₉₇₈¶

TRILINEAR PRODUCT OF PU(41)

As the trilinear product of Steiner circumellipse antipodes, X₁₉₇₈ lies on conic {{A, B, C,X₆₆₈,X₇₈₉}} with center X₆₃₇₆ and perspector X₇₅. (Randy Hutson, July 11, 2019)

X₁₉₇₈ (TRILINEAR PRODUCT OF PU(41)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1978 = TRILINEAR PRODUCT OF PU(41)."""

        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_01978(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1978 = TRILINEAR PRODUCT OF PU(41) on reference triangle ABC."""
            X_1919 = eval_trilinear_point(model, A, B, C, '(a**(3)*(b - c))', ID="X_1919", classes=["center"])
            X_1978 = isogonal_conjugate(model, A, B, C, X_1919, ID="X_1978", classes=["selected", "target"])
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            X_244 = eval_trilinear_point(model, A, B, C, '(b - c)**(2)', ID="X_244", classes=["center", "incident"])
            central_line(model, X_75, X_244, 75, 244, incident=True)
            X_310 = eval_trilinear_point(model, A, B, C, 'b**(3)*c**(3)/(b + c)', ID="X_310", classes=["center", "incident"])
            X_321 = eval_trilinear_point(model, A, B, C, '(b + c)*b**(2)*c**(2)', ID="X_321", classes=["center", "incident"])
            central_line(model, X_310, X_321, 310, 321, incident=True)
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            X_689 = eval_trilinear_point(model, A, B, C, '1/(a**(3)*(b**(4) - c**(4)))', ID="X_689", classes=["center", "incident"])
            central_line(model, X_101, X_689, 101, 689, incident=True)
            return promote_point_to_top(model, X_1978)


        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_1978 on the given reference triangle."""
            model = create_model('X_1978 = TRILINEAR PRODUCT OF PU(41)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01978(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-01978.json"))
            write_center_svg(
                model_acute,
                here / "x-01978.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1978¶

X₁₉₇₈¶