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X₁₂₃₄¶

ISOTOMIC CONJUGATE OF X₁₁₇₅

X₁₂₃₄ is the isotomic conjugate of X₁₁₇₅.

X₁₂₃₄ (ISOTOMIC CONJUGATE OF X₁₁₇₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1234 = ISOTOMIC CONJUGATE OF X_1175."""

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


        def construct_x_01234(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1234 = ISOTOMIC CONJUGATE OF X_1175 on reference triangle ABC."""
            X_1175 = point_from_barycentrics(model, A, B, C, 0.23759272, 0.33745259, 0.42495468, ID="X_1175", classes=["center"])
            X_1234 = isotomic_conjugate(model, A, B, C, X_1175, ID="X_1234", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            central_line(model, X_4, X_69, 4, 69, incident=True)
            X_12 = eval_trilinear_point(model, A, B, C, '1 + cos(B - C)', ID="X_12", classes=["center", "incident"])
            X_313 = eval_trilinear_point(model, A, B, C, '(b + c)*b**(3)*c**(3)', ID="X_313", classes=["center", "incident"])
            central_line(model, X_12, X_313, 12, 313, incident=True)
            X_312 = eval_trilinear_point(model, A, B, C, '(b + c - a)*b**(2)*c**(2)', ID="X_312", classes=["center", "incident"])
            X_1230 = eval_trilinear_point(model, A, B, C, '(b**(3)*c**(3)*(b + c)*(2*a + b + c))', ID="X_1230", classes=["center", "incident"])
            central_line(model, X_312, X_1230, 312, 1230, incident=True)
            return promote_point_to_top(model, X_1234)


        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_1234 on the given reference triangle."""
            model = create_model('X_1234 = ISOTOMIC CONJUGATE OF X_1175')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01234(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-01234.json"))
            write_center_svg(
                model_acute,
                here / "x-01234.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1234¶

X₁₂₃₄¶