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X₁₉₇₂¶

TRILINEAR POLE OF PU(38)

X₁₉₇₂ = reflection of X₆₄₈ in X₂₁₆

X₁₉₇₂ (TRILINEAR POLE OF PU(38)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1972 = TRILINEAR POLE 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,
            point_from_barycentrics,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01972(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1972 = TRILINEAR POLE OF PU(38) on reference triangle ABC."""
            X_648 = eval_trilinear_point(model, A, B, C, '1/(a*(b**(2) - c**(2))*(b**(2) + c**(2) - a**(2)))', ID="X_648", classes=["center"])
            X_216 = eval_trilinear_point(model, A, B, C, 'sin(2*A)*cos(B - C)', ID="X_216", classes=["center"])
            X_1972 = reflection_in_point(model, X_648, X_216, ID="X_1972", classes=["selected", "target"], guide=False)
            X_95 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)*sec(B - C)', ID="X_95", classes=["center", "incident"])
            central_line(model, X_95, X_216, 95, 216, incident=True)
            X_287 = eval_trilinear_point(model, A, B, C, 'cot(A)*sec(A +  omega  )', ID="X_287", classes=["center", "incident"])
            X_401 = eval_trilinear_point(model, A, B, C, '(sin(2*B)*sin(2*C) - (sin(2*A))**(2))*(csc(A))', ID="X_401", classes=["center", "incident"])
            central_line(model, X_287, X_401, 287, 401, incident=True)
            X_925 = eval_trilinear_point(model, A, B, C, '(sin(A))/(sec(2*B) - sec(2*C))', ID="X_925", classes=["center", "incident"])
            X_1298 = point_from_barycentrics(model, A, B, C, 0.54395477, 1.0720972, -0.61605193, ID="X_1298", classes=["center", "incident"])
            central_line(model, X_925, X_1298, 925, 1298, incident=True)
            return promote_point_to_top(model, X_1972)


        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_1972 on the given reference triangle."""
            model = create_model('X_1972 = TRILINEAR POLE OF PU(38)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01972(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-01972.json"))
            write_center_svg(
                model_acute,
                here / "x-01972.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1972¶

X₁₉₇₂¶