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X₁₂₃₇¶

ISOTOMIC CONJUGATE OF X₁₁₇₈

X₁₂₃₇ is the isotomic conjugate of X₁₁₇₈.

X₁₂₃₇ (ISOTOMIC CONJUGATE OF X₁₁₇₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1237 = ISOTOMIC CONJUGATE OF X_1178."""

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


        def construct_x_01237(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1237 = ISOTOMIC CONJUGATE OF X_1178 on reference triangle ABC."""
            X_1178 = eval_trilinear_point(model, A, B, C, '(a/((b + c)*(a**(2) + b*c)))', ID="X_1178", classes=["center"])
            X_1237 = isotomic_conjugate(model, A, B, C, X_1178, ID="X_1237", classes=["selected", "target"])
            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_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            X_334 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)/(a**(2) - b*c)', ID="X_334", classes=["center", "incident"])
            central_line(model, X_76, X_334, 76, 334, incident=True)
            X_561 = eval_trilinear_point(model, A, B, C, 'a **(- 4)', ID="X_561", classes=["center", "incident"])
            X_756 = eval_trilinear_point(model, A, B, C, '(b + c)**(2)', ID="X_756", classes=["center", "incident"])
            central_line(model, X_561, X_756, 561, 756, incident=True)
            return promote_point_to_top(model, X_1237)


        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_1237 on the given reference triangle."""
            model = create_model('X_1237 = ISOTOMIC CONJUGATE OF X_1178')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01237(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-01237.json"))
            write_center_svg(
                model_acute,
                here / "x-01237.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1237¶

X₁₂₃₇¶