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X₁₉₇₁¶

CROSSDIFFERENCE OF PU(38)

X₁₉₇₁ (CROSSDIFFERENCE OF PU(38)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1971 = CROSSDIFFERENCE OF PU(38)."""

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


        def construct_x_01971(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1971 = CROSSDIFFERENCE OF PU(38) on reference triangle ABC."""
            X_1971 = eval_trilinear_point(model, A, B, C, 'a*((sin(2*A))**(2) - sin(2*B)*sin(2*C))', ID="X_1971", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            central_line(model, X_6, X_25, 6, 25, incident=True)
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            X_230 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2)*(2*a**(2) - b**(2) - c**(2)) + (b**(2) - c**(2))**(2))', ID="X_230", classes=["center", "incident"])
            central_line(model, X_98, X_230, 98, 230, incident=True)
            X_237 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A +  omega  )', ID="X_237", classes=["center", "incident"])
            X_248 = eval_trilinear_point(model, A, B, C, 'sin(2*A)*sec(A +  omega  )', ID="X_248", classes=["center", "incident"])
            central_line(model, X_237, X_248, 237, 248, incident=True)
            return promote_point_to_top(model, X_1971)


        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_1971 on the given reference triangle."""
            model = create_model('X_1971 = CROSSDIFFERENCE OF PU(38)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01971(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-01971.json"))
            write_center_svg(
                model_acute,
                here / "x-01971.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1971¶

X₁₉₇₁¶