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X₃₀₀₅¶

(DE LONGCHAMPS LINE)∩(LEMOINE AXIS)

Let L denote the line at infinity. Then (Lemoine axis) = (isogonal conjugate of isotomic conjugate of L) and (de Longchamps line) = (isotomic conjugate of isogonal conjugate of L), and X₃₀₀₅ = (Lemoine axis)∩(de Longchamps line). (Randy Hutson, February 10, 2016)

X₃₀₀₅ ((DE LONGCHAMPS LINE)∩(LEMOINE AXIS)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3005 = (DE LONGCHAMPS LINE)∩(LEMOINE AXIS)."""

        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,
            isotomic_conjugate,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03005(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3005 = (DE LONGCHAMPS LINE)∩(LEMOINE AXIS) on reference triangle ABC."""
            X_689 = eval_trilinear_point(model, A, B, C, '1/(a**(3)*(b**(4) - c**(4)))', ID="X_689", classes=["center"])
            X_3005 = isotomic_conjugate(model, A, B, C, X_689, ID="X_3005", classes=["selected", "target"])
            X_187 = eval_trilinear_point(model, A, B, C, 'a*(2*a**(2) - b**(2) - c**(2))', ID="X_187", classes=["center", "incident"])
            X_237 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A +  omega  )', ID="X_237", classes=["center", "incident"])
            central_line(model, X_187, X_237, 187, 237, incident=True)
            X_325 = eval_trilinear_point(model, A, B, C, '(csc(A))**(2)', ID="X_325", classes=["center", "incident"])
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center", "incident"])
            central_line(model, X_325, X_523, 325, 523, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_881 = point_from_barycentrics(model, A, B, C, 0.016681659, 1.0244659, -0.041147528, ID="X_881", classes=["center", "incident"])
            central_line(model, X_2, X_881, 2, 881, incident=True)
            return promote_point_to_top(model, X_3005)


        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_3005 on the given reference triangle."""
            model = create_model('X_3005 = (DE LONGCHAMPS LINE)∩(LEMOINE AXIS)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03005(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-03005.json"))
            write_center_svg(
                model_acute,
                here / "x-03005.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3005¶

X₃₀₀₅¶