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X₁₄₉₂¶

COLUMBUS POINT

X₁₄₉₂ (COLUMBUS POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1492 = COLUMBUS 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,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01492(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1492 = COLUMBUS POINT on reference triangle ABC."""
            X_1491 = eval_trilinear_point(model, A, B, C, 'b**(3) - c**(3)', ID="X_1491", classes=["center"])
            X_1492 = isogonal_conjugate(model, A, B, C, X_1491, ID="X_1492", classes=["selected", "target"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            X_660 = eval_trilinear_point(model, A, B, C, '1/((a**(2) - b*c)*(b - c))', ID="X_660", classes=["center", "incident"])
            central_line(model, X_101, X_660, 101, 660, incident=True)
            X_190 = eval_trilinear_point(model, A, B, C, 'b*c/(b - c)', ID="X_190", classes=["center", "incident"])
            X_692 = eval_trilinear_point(model, A, B, C, 'a**(2)/(b - c)', ID="X_692", classes=["center", "incident"])
            central_line(model, X_190, X_692, 190, 692, incident=True)
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            X_789 = eval_trilinear_point(model, A, B, C, 'a **(- 2)/(b**(3) - c**(3))', ID="X_789", classes=["center", "incident"])
            central_line(model, X_110, X_789, 110, 789, incident=True)
            return promote_point_to_top(model, X_1492)


        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_1492 on the given reference triangle."""
            model = create_model('X_1492 = COLUMBUS POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01492(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-01492.json"))
            write_center_svg(
                model_acute,
                here / "x-01492.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1492¶

X₁₄₉₂¶