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X₃₆₀₉¶

2nd MORLEY-GIBERT PERSPECTOR

X₃₆₀₉ is the perspector of the triangle of the cusps of the Steiner deltoid and the equilateral triangle J defined just before X₃₂₇₂. (Bernard Gibert, November 3, 2010)

X₃₆₀₉ (2nd MORLEY-GIBERT PERSPECTOR) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3609 = 2nd MORLEY-GIBERT PERSPECTOR."""

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


        def construct_x_03609(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3609 = 2nd MORLEY-GIBERT PERSPECTOR on reference triangle ABC."""
            X_3609 = eval_trilinear_point(model, A, B, C, '(cos(A) + 2*cos(B)*cos(C) + 3*sin(A/3+ pi  /6) + 6*sin(B/3)*sin(C/3))', ID="X_3609", classes=["selected", "target"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_3272 = eval_trilinear_point(model, A, B, C, 'cos(B/3 - C/3)', ID="X_3272", classes=["center", "incident"])
            central_line(model, X_5, X_3272, 5, 3272, incident=True)
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center", "incident"])
            X_3334 = eval_trilinear_point(model, A, B, C, 'cos(A) + 2*sin(B/3)*sin(C/3) + sin(A/3 + pi  /6)', ID="X_3334", classes=["center", "incident"])
            central_line(model, X_20, X_3334, 20, 3334, incident=True)
            X_631 = eval_trilinear_point(model, A, B, C, '2*cos(A) + cos(B)*cos(C)', ID="X_631", classes=["center", "incident"])
            X_3335 = eval_trilinear_point(model, A, B, C, '(cos(A) - 2*sin(B/3)*sin(C/3) - sin(A/3 + pi  /6))', ID="X_3335", classes=["center", "incident"])
            central_line(model, X_631, X_3335, 631, 3335, incident=True)
            return promote_point_to_top(model, X_3609)


        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_3609 on the given reference triangle."""
            model = create_model('X_3609 = 2nd MORLEY-GIBERT PERSPECTOR')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03609(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-03609.json"))
            write_center_svg(
                model_acute,
                here / "x-03609.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3609¶

X₃₆₀₉¶