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X₁₈₈₅¶

ZOSMA TRANSFORM OF X₇₇₄

X₁₈₈₅ (ZOSMA TRANSFORM OF X₇₇₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1885 = ZOSMA TRANSFORM OF X_774."""

        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,
            crosspoint,
            eval_trilinear_point,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01885(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1885 = ZOSMA TRANSFORM OF X_774 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_1105 = eval_trilinear_point(model, A, B, C, '((sec(A))/((cos(B))**(2) + (cos(C))**(2)))', ID="X_1105", classes=["center"])
            X_1885 = crosspoint(model, A, B, C, X_4, X_1105, ID="X_1885", classes=["selected", "target"])
            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_389 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(2*A)*cos(B - C)', ID="X_389", classes=["center", "incident"])
            X_974 = eval_trilinear_point(model, A, B, C, '(s*a**(10) - a**(8)*(3*b**(4) - 2*b**(2)*c**(2) + 3*c**(4)) + a**(6)*s*(2*b**(4) - 3*b**(2)*c**(2) + 2*c**(4)) + a**(4)*(b**(2) - c**(2))**(2)*(2*b**(4) - 7*b**(2)*c**(2) + 2*c**(4)) - 3*a**(2)*s*(b**(2) - c**(2))**(2)*(b**(4) - 3*b**(2)*c**(2) + c**(4)) + (b**(2) - c**(2))**(4)*(b**(4) + b**(2)*c**(2) + c**(4)))*cos(A)', ID="X_974", classes=["center", "incident"])
            central_line(model, X_389, X_974, 389, 974, incident=True)
            X_497 = eval_trilinear_point(model, A, B, C, '1 - cos(B)*cos(C)', ID="X_497", classes=["center", "incident"])
            X_1398 = eval_trilinear_point(model, A, B, C, '(sec(A)*(sin(A/2))**(4))', ID="X_1398", classes=["center", "incident"])
            central_line(model, X_497, X_1398, 497, 1398, incident=True)
            return promote_point_to_top(model, X_1885)


        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_1885 on the given reference triangle."""
            model = create_model('X_1885 = ZOSMA TRANSFORM OF X_774')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01885(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-01885.json"))
            write_center_svg(
                model_acute,
                here / "x-01885.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1885¶

X₁₈₈₅¶