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X₂₀₄₂¶

2nd EULER-VECTEN-GIBERT POINT

X₂₀₄₂ = reflection of X₂₀₄₁ in X₃₈₂

X₂₀₄₂ (2nd EULER-VECTEN-GIBERT POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2042 = 2nd EULER-VECTEN-GIBERT POINT."""

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


        def construct_x_02042(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2042 = 2nd EULER-VECTEN-GIBERT POINT on reference triangle ABC."""
            X_2041 = eval_trilinear_point(model, A, B, C, '(b*c*((b**(2) - c**(2))**(2) - a**(2)*(b**(2) + c**(2)) + 3**(1/2)*a**(2)*(b**(2) + c**(2) - a**(2))))', ID="X_2041", classes=["center"])
            X_382 = eval_trilinear_point(model, A, B, C, 'cos(A) - 4*cos(B)*cos(C)', ID="X_382", classes=["center"])
            X_2042 = reflection_in_point(model, X_2041, X_382, ID="X_2042", classes=["selected", "target"], guide=False)
            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_15 = eval_trilinear_point(model, A, B, C, 'sin(A +  pi  /3)', ID="X_15", classes=["center", "incident"])
            X_486 = eval_trilinear_point(model, A, B, C, 'sec(A +  pi  /4)', ID="X_486", classes=["center", "incident"])
            central_line(model, X_15, X_486, 15, 486, incident=True)
            X_16 = eval_trilinear_point(model, A, B, C, 'sin(A-  pi  /3)', ID="X_16", classes=["center", "incident"])
            X_485 = eval_trilinear_point(model, A, B, C, 'sec(A -  pi  /4)', ID="X_485", classes=["center", "incident"])
            central_line(model, X_16, X_485, 16, 485, incident=True)
            return promote_point_to_top(model, X_2042)


        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_2042 on the given reference triangle."""
            model = create_model('X_2042 = 2nd EULER-VECTEN-GIBERT POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02042(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-02042.json"))
            write_center_svg(
                model_acute,
                here / "x-02042.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2042¶

X₂₀₄₂¶