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X₄₄₇¶

X₂-HIRST INVERSE OF X₂₇

X₄₄₇ (X₂-HIRST INVERSE OF X₂₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_447 = X_2-HIRST INVERSE OF X_27."""

        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,
            centroid_of,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            intersect_lines,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00447(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_447 = X_2-HIRST INVERSE OF X_27 on reference triangle ABC."""
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_340 = eval_trilinear_point(model, A, B, C, 'sec(A)*sin(3*A)*(csc(A))**(3)', ID="X_340", classes=["center"])
            X_540 = point_from_barycentrics(model, A, B, C, -0.66946852, -0.070060659, 0.73952918, ID="X_540", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            central_line(model, X_340, X_540, 340, 540)
            X_447 = intersect_lines(model, X_2, X_3, X_340, X_540, ID="X_447", classes=["selected", "target"])
            X_350 = eval_trilinear_point(model, A, B, C, '(a**(2) - b*c)*b**(2)*c**(2)', ID="X_350", classes=["center", "incident"])
            X_811 = eval_trilinear_point(model, A, B, C, '(csc(2*A))/((cos(B))**(2) - (cos(C))**(2))', ID="X_811", classes=["center", "incident"])
            central_line(model, X_350, X_811, 350, 811, incident=True)
            return promote_point_to_top(model, X_447)


        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_447 on the given reference triangle."""
            model = create_model('X_447 = X_2-HIRST INVERSE OF X_27')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00447(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-00447.json"))
            write_center_svg(
                model_acute,
                here / "x-00447.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X447¶

X₄₄₇¶