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X₁₂₂₆¶

ISOTOMIC CONJUGATE OF X₁₁₆₇

X₁₂₂₆ is the isotomic conjugate of X₁₁₆₇.

X₁₂₂₆ (ISOTOMIC CONJUGATE OF X₁₁₆₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1226 = ISOTOMIC CONJUGATE OF X_1167."""

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


        def construct_x_01226(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1226 = ISOTOMIC CONJUGATE OF X_1167 on reference triangle ABC."""
            X_1167 = point_from_barycentrics(model, A, B, C, 0.35929716, 0.32223282, 0.31847002, ID="X_1167", classes=["center"])
            X_1226 = isotomic_conjugate(model, A, B, C, X_1167, ID="X_1226", 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_85 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)/(b + c - a)', ID="X_85", classes=["center", "incident"])
            X_264 = eval_trilinear_point(model, A, B, C, 'csc(A)*csc(2*A)', ID="X_264", classes=["center", "incident"])
            central_line(model, X_85, X_264, 85, 264, incident=True)
            X_311 = eval_trilinear_point(model, A, B, C, '(csc(A))**(2)*cos(B - C)', ID="X_311", classes=["center", "incident"])
            X_349 = eval_trilinear_point(model, A, B, C, '(cos(B) + cos(C))*(csc(A))**(3)', ID="X_349", classes=["center", "incident"])
            central_line(model, X_311, X_349, 311, 349, incident=True)
            return promote_point_to_top(model, X_1226)


        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_1226 on the given reference triangle."""
            model = create_model('X_1226 = ISOTOMIC CONJUGATE OF X_1167')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01226(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-01226.json"))
            write_center_svg(
                model_acute,
                here / "x-01226.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1226¶

X₁₂₂₆¶