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X₄₅₀¶

X₃-HIRST INVERSE OF X₄

X₄₅₀ (X₃-HIRST INVERSE OF X₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_450 = X_3-HIRST INVERSE OF X_4."""

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


        def construct_x_00450(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_450 = X_3-HIRST INVERSE OF X_4 on reference triangle ABC."""
            X_450 = eval_trilinear_point(model, A, B, C, '(sec(A))*((cos(A))**(4) - (cos(B)*cos(C))**(2))', ID="X_450", classes=["selected", "target"])
            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"])
            central_line(model, X_2, X_3, 2, 3)
            X_107 = eval_trilinear_point(model, A, B, C, '1/(cos(A)*(sin(2*B) - sin(2*C)))', ID="X_107", classes=["center", "incident"])
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            central_line(model, X_107, X_511, 107, 511, incident=True)
            X_155 = eval_trilinear_point(model, A, B, C, '(cos(A))*((cos(B))**(2) + (cos(C))**(2) - (cos(A))**(2))', ID="X_155", classes=["center", "incident"])
            X_1075 = eval_trilinear_point(model, A, B, C, '(sec(A))*((sec(B))**(2) + (sec(C))**(2) - (sec(A))**(2))', ID="X_1075", classes=["center", "incident"])
            central_line(model, X_155, X_1075, 155, 1075, incident=True)
            return promote_point_to_top(model, X_450)


        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_450 on the given reference triangle."""
            model = create_model('X_450 = X_3-HIRST INVERSE OF X_4')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00450(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-00450.json"))
            write_center_svg(
                model_acute,
                here / "x-00450.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X450¶

X₄₅₀¶