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X₃₃₁¶

ISOTOMIC CONJUGATE OF X₂₁₉

X₃₃₁ (ISOTOMIC CONJUGATE OF X₂₁₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_331 = ISOTOMIC CONJUGATE OF X_219."""

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


        def construct_x_00331(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_331 = ISOTOMIC CONJUGATE OF X_219 on reference triangle ABC."""
            X_219 = eval_trilinear_point(model, A, B, C, 'cos(A)*cot(A/2)', ID="X_219", classes=["center"])
            X_331 = isotomic_conjugate(model, A, B, C, X_219, ID="X_331", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_150 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(4) + c**(4) - a**(4) + a*(b*c**(2) +c*b**(2) - b**(3) - c**(3)) - b*c*(a**(2) + b**(2) + c**(2)) + (b + c)*a**(3)))', ID="X_150", classes=["center", "incident"])
            central_line(model, X_4, X_150, 4, 150, 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_92 = eval_trilinear_point(model, A, B, C, 'csc(2*A)', ID="X_92", classes=["center", "incident"])
            central_line(model, X_85, X_92, 85, 92, incident=True)
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_286 = eval_trilinear_point(model, A, B, C, '(csc(2*A))/(sin(B) + sin(C))', ID="X_286", classes=["center", "incident"])
            central_line(model, X_7, X_286, 7, 286, incident=True)
            return promote_point_to_top(model, X_331)


        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_331 on the given reference triangle."""
            model = create_model('X_331 = ISOTOMIC CONJUGATE OF X_219')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00331(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-00331.json"))
            write_center_svg(
                model_acute,
                here / "x-00331.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X331¶

X₃₃₁¶