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X₃₅₉¶

HOFSTADTER ONE POINT

The Hofstadter ellipse E(1/2), given by \(x^{2}\) + \(y^{2}\) + \(z^{2}\) - 2yz - 2xz - 2xy = 0, has center X₃₇ and passes through X_i for these i: 244, 678, 2310, 2632, 2638, 2643, 3248, 4094, 4117, 10501, 23063, 24012.

X₃₅₉ (HOFSTADTER ONE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_359 = HOFSTADTER ONE POINT."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00359(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_359 = HOFSTADTER ONE POINT on reference triangle ABC."""
            X_359 = eval_trilinear_point(model, A, B, C, 'a/A', ID="X_359", classes=["selected", "target"])
            return promote_point_to_top(model, X_359)


        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_359 on the given reference triangle."""
            model = create_model('X_359 = HOFSTADTER ONE POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00359(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-00359.json"))
            write_center_svg(
                model_acute,
                here / "x-00359.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X359¶

X₃₅₉¶