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X₁₃₀₅¶

COLLINGS TRANSFORM OF X₄₄₀

X₁₃₀₅ = reflection of X₉₁₇ in X₃

X₁₃₀₅ (COLLINGS TRANSFORM OF X₄₄₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1305 = COLLINGS TRANSFORM OF X_440."""

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


        def construct_x_01305(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1305 = COLLINGS TRANSFORM OF X_440 on reference triangle ABC."""
            X_917 = eval_trilinear_point(model, A, B, C, '(sec(A))/((a - b)*sin(2*B) + (a - c)*sin(2*C))', ID="X_917", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_1305 = reflection_in_point(model, X_917, X_3, ID="X_1305", classes=["selected", "target"], guide=False)
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center", "incident"])
            X_103 = eval_trilinear_point(model, A, B, C, 'a/((a - b)*cot(C) + (a - c)*cot(B))', ID="X_103", classes=["center", "incident"])
            central_line(model, X_20, X_103, 20, 103, incident=True)
            X_106 = eval_trilinear_point(model, A, B, C, 'a/(2*a - b - c)', ID="X_106", classes=["center", "incident"])
            X_347 = eval_trilinear_point(model, A, B, C, '((-1 - cos(A) + cos(B) + cos(C))*(sec(A/2))**(2))', ID="X_347", classes=["center", "incident"])
            central_line(model, X_106, X_347, 106, 347, incident=True)
            X_22 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) - a**(4))', ID="X_22", classes=["center", "incident"])
            X_675 = eval_trilinear_point(model, A, B, C, '(b*c/(b**(3) + c**(3) - a*(b**(2) + c**(2))))', ID="X_675", classes=["center", "incident"])
            central_line(model, X_22, X_675, 22, 675, incident=True)
            return promote_point_to_top(model, X_1305)


        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_1305 on the given reference triangle."""
            model = create_model('X_1305 = COLLINGS TRANSFORM OF X_440')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01305(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-01305.json"))
            write_center_svg(
                model_acute,
                here / "x-01305.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1305¶

X₁₃₀₅¶