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X₃₆₅¶

SQUARE ROOT POINT

For a construction of X₃₆₅, see the note at X₂, which provides for a construction barycentric square roots which one can easily extend to a construction for trilinear square roots.

X₃₆₅ (SQUARE ROOT POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_365 = SQUARE ROOT POINT."""

        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,
            incenter_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00365(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_365 = SQUARE ROOT POINT on reference triangle ABC."""
            X_365 = eval_trilinear_point(model, A, B, C, 'a**(1/2)', ID="X_365", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_364 = eval_trilinear_point(model, A, B, C, 'b**(1/2) + c**(1/2) - a**(1/2)', ID="X_364", classes=["center", "incident"])
            central_line(model, X_1, X_364, 1, 364, incident=True)
            X_43 = eval_trilinear_point(model, A, B, C, 'a*b + a*c - b*c', ID="X_43", classes=["center", "incident"])
            X_2068 = eval_trilinear_point(model, A, B, C, '(a + b**(1/2)*c**(1/2))', ID="X_2068", classes=["center", "incident"])
            central_line(model, X_43, X_2068, 43, 2068, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_2118 = eval_trilinear_point(model, A, B, C, '(a*(a + b + c)*(b*c)**(1/2) + (b*c + c*a + a*b)*(a - (a*b)**(1/2) - (a*c)**(1/2)))', ID="X_2118", classes=["center", "incident"])
            central_line(model, X_6, X_2118, 6, 2118, incident=True)
            return promote_point_to_top(model, X_365)


        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_365 on the given reference triangle."""
            model = create_model('X_365 = SQUARE ROOT POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00365(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-00365.json"))
            write_center_svg(
                model_acute,
                here / "x-00365.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X365¶

X₃₆₅¶