← etc / Encyclopedia of Triangle Centers

X₁₉₄₈¶

CROSSDIFFERENCE OF PU(19)

X₁₉₄₈ (CROSSDIFFERENCE OF PU(19)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1948 = CROSSDIFFERENCE OF PU(19)."""

        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,
            mittenpunkt_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01948(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1948 = CROSSDIFFERENCE OF PU(19) on reference triangle ABC."""
            X_1948 = eval_trilinear_point(model, A, B, C, '(((cos(A))**(2) - cos(B)*cos(C))*csc(2*A))', ID="X_1948", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_92 = eval_trilinear_point(model, A, B, C, 'csc(2*A)', ID="X_92", classes=["center", "incident"])
            central_line(model, X_2, X_92, 2, 92, incident=True)
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            X_264 = eval_trilinear_point(model, A, B, C, 'csc(A)*csc(2*A)', ID="X_264", classes=["center", "incident"])
            central_line(model, X_9, X_264, 9, 264, incident=True)
            X_24 = eval_trilinear_point(model, A, B, C, 'sec(A)*cos(2*A)', ID="X_24", classes=["center", "incident"])
            X_547 = eval_trilinear_point(model, A, B, C, '5*cos(B - C) + 2*cos(A)', ID="X_547", classes=["center", "incident"])
            central_line(model, X_24, X_547, 24, 547, incident=True)
            return promote_point_to_top(model, X_1948)


        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_1948 on the given reference triangle."""
            model = create_model('X_1948 = CROSSDIFFERENCE OF PU(19)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01948(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-01948.json"))
            write_center_svg(
                model_acute,
                here / "x-01948.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1948¶

X₁₉₄₈¶