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X₄₀₉¶

EULER X₂₁-1st-SUBSTITUTION POINT

X₄₀₉ (EULER X₂₁-1st-SUBSTITUTION POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_409 = EULER X_21-1st-SUBSTITUTION 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_barycentric_point,
            eval_trilinear_point,
            incenter_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00409(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_409 = EULER X_21-1st-SUBSTITUTION POINT on reference triangle ABC."""
            X_409 = eval_barycentric_point(model, A, B, C, 'a*(a + b) * (a + c) * (a**(4) - a**(3)*b + a*b**(3) - b**(4) - a**(3)*c + a**(2)*b*c + a*b**(2)*c + b**(3)*c + a*b*c**(2) + 4*b**(2)*c**(2) + a*c**(3) + b*c**(3) - c**(4))', ID="X_409", 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_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
            X_1098 = eval_trilinear_point(model, A, B, C, '(1/(cos(B) + cos(C))**(2))', ID="X_1098", classes=["center", "incident"])
            central_line(model, X_65, X_1098, 65, 1098, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_1247 = point_from_barycentrics(model, A, B, C, 0.47979502, 0.29838347, 0.22182151, ID="X_1247", classes=["center", "incident"])
            central_line(model, X_1, X_1247, 1, 1247, incident=True)
            return promote_point_to_top(model, X_409)


        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_409 on the given reference triangle."""
            model = create_model('X_409 = EULER X_21-1st-SUBSTITUTION POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00409(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-00409.json"))
            write_center_svg(
                model_acute,
                here / "x-00409.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X409¶

X₄₀₉¶