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X₁₁₁₅¶

EXTERIOR-ANGLE CURVATURE CENTROID

X₁₁₁₅ is the center of mass of a point-mass system obtained by placing at vertex :g:`A <A*>` a mass equal to the magnitude of the exterior angle (that’s π - :g:`A <A*>`) at :g:`A <A*>`, and cyclically for :g:`B <B*>` and :g:`C <C*>`. ( Peter Scales , Hyacinthos #5528, 5/22/02) This description is also found in Honsberger , Episodes in Nineteenth and Twentieth Century Eulidean Geometry , p. 120, where it is mistakenly attributed to the Steiner point, X₉₉.

X₁₁₁₅ (EXTERIOR-ANGLE CURVATURE CENTROID) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1115 = EXTERIOR-ANGLE CURVATURE CENTROID."""

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


        def construct_x_01115(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1115 = EXTERIOR-ANGLE CURVATURE CENTROID on reference triangle ABC."""
            X_360 = eval_trilinear_point(model, A, B, C, 'A/a', ID="X_360", classes=["center"])
            X_1115 = complement(model, A, B, C, X_360, ID="X_1115", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            central_line(model, X_2, X_360, 2, 360, incident=True)
            return promote_point_to_top(model, X_1115)


        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_1115 on the given reference triangle."""
            model = create_model('X_1115 = EXTERIOR-ANGLE CURVATURE CENTROID')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01115(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-01115.json"))
            write_center_svg(
                model_acute,
                here / "x-01115.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1115¶

X₁₁₁₅¶