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X₂₁₄₀¶

EIGENTRANSFORM OF X₁₀₁

X₂₁₄₀ (EIGENTRANSFORM OF X₁₀₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2140 = EIGENTRANSFORM OF X_101."""

        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,
            intersect_lines,
            nine_point_center_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02140(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2140 = EIGENTRANSFORM OF X_101 on reference triangle ABC."""
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center"])
            X_116 = eval_trilinear_point(model, A, B, C, 'b*c*((b - c)**(2)*(b**(2) + b*c + c**(2) - a*b - a*c))', ID="X_116", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_142 = eval_trilinear_point(model, A, B, C, 'b + c - ((b - c)**(2))/a', ID="X_142", classes=["center"])
            central_line(model, X_5, X_116, 5, 116)
            central_line(model, X_3, X_142, 3, 142)
            X_2140 = intersect_lines(model, X_5, X_116, X_3, X_142, ID="X_2140", classes=["selected", "target"])
            X_218 = eval_trilinear_point(model, A, B, C, '((cos(A/2))**(2)*((cos(B/2))**(4) + (cos(C/2))**(4) - (cos(A/2))**(4)))', ID="X_218", classes=["center", "incident"])
            X_226 = eval_trilinear_point(model, A, B, C, '(csc(A))*(cos(B) + cos(C))', ID="X_226", classes=["center", "incident"])
            central_line(model, X_218, X_226, 218, 226, incident=True)
            return promote_point_to_top(model, X_2140)


        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_2140 on the given reference triangle."""
            model = create_model('X_2140 = EIGENTRANSFORM OF X_101')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02140(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-02140.json"))
            write_center_svg(
                model_acute,
                here / "x-02140.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2140¶

X₂₁₄₀¶