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X₃₅₅₇¶

1st PAPPUS POINT

X₃₅₅₇ was submitted and called the Pappus point by Roland Bacher (March 11, 2009); coordinates and the related point X₃₅₅₈ were found by Peter Moses (March 12, 2009).

X₃₅₅₇ (1st PAPPUS POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3557 = 1st PAPPUS 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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            orthocenter_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03557(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3557 = 1st PAPPUS POINT on reference triangle ABC."""
            X_3557 = eval_trilinear_point(model, A, B, C, 'e*sin(A) + sin(A -  omega  )', ID="X_3557", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_3, X_6, 3, 6, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_3414 = eval_trilinear_point(model, A, B, C, '1/(e*cos(A) + cos(A +  omega  ))', ID="X_3414", classes=["center", "incident"])
            central_line(model, X_4, X_3414, 4, 3414, incident=True)
            X_194 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2)*b**(2) + a**(2)*c**(2) - b**(2)*c**(2))', ID="X_194", classes=["center", "incident"])
            X_3413 = eval_trilinear_point(model, A, B, C, '1/(e*cos(A) - cos(A +  omega  ))', ID="X_3413", classes=["center", "incident"])
            central_line(model, X_194, X_3413, 194, 3413, incident=True)
            return promote_point_to_top(model, X_3557)


        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_3557 on the given reference triangle."""
            model = create_model('X_3557 = 1st PAPPUS POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03557(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-03557.json"))
            write_center_svg(
                model_acute,
                here / "x-03557.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3557¶

X₃₅₅₇¶