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X₁₂₆₆¶

ISOTOMIC CONJUGATE OF X₁₁₂₀

X₁₂₆₆ is the isotomic conjugate of X₁₁₂₀.

X₁₂₆₆ (ISOTOMIC CONJUGATE OF X₁₁₂₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1266 = ISOTOMIC CONJUGATE OF X_1120."""

        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,
            gergonne_point_of,
            isotomic_conjugate,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01266(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1266 = ISOTOMIC CONJUGATE OF X_1120 on reference triangle ABC."""
            X_1120 = eval_trilinear_point(model, A, B, C, '(b*c/(b**(2) + c**(2) + b*a + c*a - 4*b*c))', ID="X_1120", classes=["center"])
            X_1266 = isotomic_conjugate(model, A, B, C, X_1120, ID="X_1266", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            central_line(model, X_10, X_75, 10, 75, incident=True)
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_145 = eval_trilinear_point(model, A, B, C, 'b*c*(3*a - b - c)', ID="X_145", classes=["center", "incident"])
            central_line(model, X_7, X_145, 7, 145, incident=True)
            X_142 = eval_trilinear_point(model, A, B, C, 'b + c - ((b - c)**(2))/a', ID="X_142", classes=["center", "incident"])
            X_192 = eval_trilinear_point(model, A, B, C, 'b*c*(c*a + a*b - b*c)', ID="X_192", classes=["center", "incident"])
            central_line(model, X_142, X_192, 142, 192, incident=True)
            return promote_point_to_top(model, X_1266)


        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_1266 on the given reference triangle."""
            model = create_model('X_1266 = ISOTOMIC CONJUGATE OF X_1120')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01266(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-01266.json"))
            write_center_svg(
                model_acute,
                here / "x-01266.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1266¶

X₁₂₆₆¶