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X₁₉₈₁¶

VEGA TRANSFORM OF X₆₄₇

lies on the line [\(x:y:z\)] that has x,y,z as coefficients. (The line [\(x:y:z\)] is the trilinear polar of the isogonal conjugate of X.) Thus, the Vega transform of X₆₄₇ lies on the Euler line.

X₁₉₈₁ (VEGA TRANSFORM OF X₆₄₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1981 = VEGA TRANSFORM OF X_647."""

        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_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01981(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1981 = VEGA TRANSFORM OF X_647 on reference triangle ABC."""
            X_1981 = eval_trilinear_point(model, A, B, C, '(sin(2*B)*sin(C - A) - sin(2*C)*sin(A - B))/(sin(2*A)*sin(B - C))', ID="X_1981", 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_651 = eval_trilinear_point(model, A, B, C, '1/(cos(B) - cos(C))', ID="X_651", classes=["center", "incident"])
            X_653 = eval_trilinear_point(model, A, B, C, '1/(sec(B) - sec(C))', ID="X_653", classes=["center", "incident"])
            central_line(model, X_651, X_653, 651, 653, incident=True)
            X_662 = eval_trilinear_point(model, A, B, C, '1/(cot(B) - cot(C))', ID="X_662", classes=["center", "incident"])
            X_811 = eval_trilinear_point(model, A, B, C, '(csc(2*A))/((cos(B))**(2) - (cos(C))**(2))', ID="X_811", classes=["center", "incident"])
            central_line(model, X_662, X_811, 662, 811, incident=True)
            return promote_point_to_top(model, X_1981)


        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_1981 on the given reference triangle."""
            model = create_model('X_1981 = VEGA TRANSFORM OF X_647')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01981(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-01981.json"))
            write_center_svg(
                model_acute,
                here / "x-01981.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1981¶

X₁₉₈₁¶