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X₃₆₂₈¶

H⁻¹(X₅; M, 2)

For another construction see Antreas Hatzipolakis and Peter Moses, Euclid 2576.

X₃₆₂₈ (H⁻¹(X₅; M, 2)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3628 = H⁻¹(X_5; M, 2)."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            midpoint,
            nine_point_center_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03628(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3628 = H⁻¹(X_5; M, 2) on reference triangle ABC."""
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center"])
            X_140 = eval_trilinear_point(model, A, B, C, '2*cos(A) + cos(B - C)', ID="X_140", classes=["center"])
            X_3628 = midpoint(model, X_5, X_140, ID="X_3628", classes=["selected", "target"], guide=False)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_156 = eval_barycentric_point(model, A, B, C, 'a**(2)*(a**(8) - 3*a**(6)*(b**(2) + c**(2)) + a**(4)*(3*b**(4) + 2*b**(2)*c**(2) + 3*c**(4)) - a**(2)*(b**(6) + c**(6)) + b**(2)*c**(2)*(b**(2) - c**(2))**(2))', ID="X_156", classes=["center", "incident"])
            X_182 = eval_trilinear_point(model, A, B, C, 'cos(A-  omega  )', ID="X_182", classes=["center", "incident"])
            central_line(model, X_156, X_182, 156, 182, incident=True)
            X_17 = eval_trilinear_point(model, A, B, C, 'csc(A +  pi  /6)', ID="X_17", classes=["center", "incident"])
            X_395 = eval_trilinear_point(model, A, B, C, 'cos(B - C) + 2*cos(A +  pi  /3)', ID="X_395", classes=["center", "incident"])
            central_line(model, X_17, X_395, 17, 395, incident=True)
            return promote_point_to_top(model, X_3628)


        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_3628 on the given reference triangle."""
            model = create_model('X_3628 = H⁻¹(X_5; M, 2)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03628(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-03628.json"))
            write_center_svg(
                model_acute,
                here / "x-03628.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3628¶

X₃₆₂₈¶