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X₁₂₃₉¶

ISOTOMIC CONJUGATE OF X₁₁₈₀

X₁₂₃₉ is the isotomic conjugate of X₁₁₈₀.

X₁₂₃₉ (ISOTOMIC CONJUGATE OF X₁₁₈₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1239 = ISOTOMIC CONJUGATE OF X_1180."""

        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_barycentric_point,
            eval_trilinear_point,
            isotomic_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01239(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1239 = ISOTOMIC CONJUGATE OF X_1180 on reference triangle ABC."""
            X_1180 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) + b**(2)*c**(2) + c**(2)*a**(2) + a**(2)*b**(2))', ID="X_1180", classes=["center"])
            X_1239 = isotomic_conjugate(model, A, B, C, X_1180, ID="X_1239", classes=["selected", "target"])
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            X_251 = eval_trilinear_point(model, A, B, C, 'a**(2)*csc(A +  omega  )', ID="X_251", classes=["center", "incident"])
            central_line(model, X_76, X_251, 76, 251, incident=True)
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_1235 = eval_barycentric_point(model, A, B, C, '(csc(A))*(csc(2*A))*sin(A +  omega  )', ID="X_1235", classes=["center", "incident"])
            central_line(model, X_25, X_1235, 25, 1235, incident=True)
            return promote_point_to_top(model, X_1239)


        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_1239 on the given reference triangle."""
            model = create_model('X_1239 = ISOTOMIC CONJUGATE OF X_1180')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01239(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-01239.json"))
            write_center_svg(
                model_acute,
                here / "x-01239.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1239¶

X₁₂₃₉¶