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X₃₈₀₄¶

X₆₄₇com[INVERSE(nT(a², a² + c²))]

X₃₈₀₄ (X₆₄₇com[INVERSE(nT(a², a² + c²))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3804 = X_647com[INVERSE(nT(a², a² + c²))]."""

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


        def construct_x_03804(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3804 = X_647com[INVERSE(nT(a², a² + c²))] on reference triangle ABC."""
            X_3804 = eval_barycentric_point(model, A, B, C, '(a**(2)*(b**(2) - c**(2))*(3*a**(2) + b**(2) + c**(2)))', ID="X_3804", classes=["selected", "target"])
            X_187 = eval_trilinear_point(model, A, B, C, 'a*(2*a**(2) - b**(2) - c**(2))', ID="X_187", classes=["center", "incident"])
            X_237 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A +  omega  )', ID="X_237", classes=["center", "incident"])
            central_line(model, X_187, X_237, 187, 237, incident=True)
            X_1499 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))*(b**(2) + c**(2) - 5*a**(2))', ID="X_1499", classes=["center", "incident"])
            X_3265 = eval_trilinear_point(model, A, B, C, '((csc(A))**(2))*(cos(A))*(sin(2*B) - sin(2*C))', ID="X_3265", classes=["center", "incident"])
            central_line(model, X_1499, X_3265, 1499, 3265, incident=True)
            X_2525 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(4) - c**(4))*(b**(2) + c**(2) - a**(2)))', ID="X_2525", classes=["center", "incident"])
            X_3566 = eval_trilinear_point(model, A, B, C, '(b*c*(3*a**(2) - b**(2) - c**(2))*(b**(2) - c**(2)))', ID="X_3566", classes=["center", "incident"])
            central_line(model, X_2525, X_3566, 2525, 3566, incident=True)
            return promote_point_to_top(model, X_3804)


        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_3804 on the given reference triangle."""
            model = create_model('X_3804 = X_647com[INVERSE(nT(a², a² + c²))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03804(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-03804.json"))
            write_center_svg(
                model_acute,
                here / "x-03804.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3804¶

X₃₈₀₄¶