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X₁₉₃₈¶

IDEAL POINT OF PU(15)

As the isogonal conjugate of a point on the circumcircle, X₁₉₃₈ lies on the line at infinity.

X₁₉₃₈ (IDEAL POINT OF PU(15)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1938 = IDEAL POINT OF PU(15)."""

        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,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01938(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1938 = IDEAL POINT OF PU(15) on reference triangle ABC."""
            X_1938 = eval_trilinear_point(model, A, B, C, '(cos(A)*cos(B) - (cos(C))**(2))*sin(B) - (cos(A)*cos(C) - (cos(B))**(2))*sin(C)', ID="X_1938", classes=["selected", "target"])
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            central_line(model, X_30, X_511, 30, 511, incident=True)
            X_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
            X_650 = eval_trilinear_point(model, A, B, C, 'cos(B) - cos(C)', ID="X_650", classes=["center", "incident"])
            central_line(model, X_65, X_650, 65, 650, incident=True)
            return promote_point_to_top(model, X_1938)


        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_1938 on the given reference triangle."""
            model = create_model('X_1938 = IDEAL POINT OF PU(15)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01938(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-01938.json"))
            write_center_svg(
                model_acute,
                here / "x-01938.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1938¶

X₁₉₃₈¶