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X₂₀₈₆¶

PK-TRANSFORM OF X₉₉

X₂₀₈₆ = crossdifference of every pair of points on line X₉₉ X₅₁₂

X₂₀₈₆ (PK-TRANSFORM OF X₉₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2086 = PK-TRANSFORM OF X_99."""

        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,
            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_02086(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2086 = PK-TRANSFORM OF X_99 on reference triangle ABC."""
            X_2086 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) - c**(2))**(2)*(a**(4) - b**(2)*c**(2)))', ID="X_2086", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_2, X_6, 2, 6, incident=True)
            X_351 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) - c**(2))*(b**(2) + c**(2) - 2*a**(2)))', ID="X_351", classes=["center", "incident"])
            X_865 = eval_trilinear_point(model, A, B, C, '(sin(2*B)*(csc(C))**(2)*sin(C - A)*csc(A - B) - sin(2*C)*(csc(B))**(2)*sin(B - A)*csc(A - C))', ID="X_865", classes=["center", "incident"])
            central_line(model, X_351, X_865, 351, 865, incident=True)
            X_671 = eval_trilinear_point(model, A, B, C, '1/(a*(2*a**(2) - b**(2) - c**(2)))', ID="X_671", classes=["center", "incident"])
            X_729 = eval_trilinear_point(model, A, B, C, '1/(a**(-3)*(b**(0) + c**(0)) - a **(-1)*(b**(-2) + c **(-2)))', ID="X_729", classes=["center", "incident"])
            central_line(model, X_671, X_729, 671, 729, incident=True)
            return promote_point_to_top(model, X_2086)


        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_2086 on the given reference triangle."""
            model = create_model('X_2086 = PK-TRANSFORM OF X_99')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02086(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-02086.json"))
            write_center_svg(
                model_acute,
                here / "x-02086.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2086¶

X₂₀₈₆¶