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X₃₀₀₀¶

(ANTIORTHIC AXIS)∩(SODDY LINE)

The antiorthic axis is line X₄₄ X₅₁₃, more simply represented as L(1), meaning the line whose coefficients in trilinear coordinates are \(1 : 1 : 1\), these also being trilinears for X₁. The Soddy line is X₁ X₇, alias L(657). For such identifications as these, use the MathWorld link just before X₃₀₀₀.

X₃₀₀₀ ((ANTIORTHIC AXIS)∩(SODDY LINE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3000 = (ANTIORTHIC AXIS)∩(SODDY LINE)."""

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


        def construct_x_03000(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3000 = (ANTIORTHIC AXIS)∩(SODDY LINE) on reference triangle ABC."""
            X_2310 = eval_trilinear_point(model, A, B, C, '(cos(B) - cos(C))**(2)', ID="X_2310", classes=["center"])
            X_241 = eval_trilinear_point(model, A, B, C, '(cos(B/2))**(4) - ((cos(A/2))**(2))*((cos(B/2))**(2) +(cos(C/2))**(2)) + (cos(C/2))**(4)', ID="X_241", classes=["center"])
            X_3000 = reflection_in_point(model, X_2310, X_241, ID="X_3000", classes=["selected", "target"], guide=False)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            central_line(model, X_1, X_7, 1, 7, incident=True)
            X_44 = eval_trilinear_point(model, A, B, C, 'b + c - 2*a', ID="X_44", classes=["center", "incident"])
            X_513 = eval_trilinear_point(model, A, B, C, 'b - c', ID="X_513", classes=["center", "incident"])
            central_line(model, X_44, X_513, 44, 513, incident=True)
            central_line(model, X_241, X_2310, 241, 2310, incident=True)
            return promote_point_to_top(model, X_3000)


        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_3000 on the given reference triangle."""
            model = create_model('X_3000 = (ANTIORTHIC AXIS)∩(SODDY LINE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03000(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-03000.json"))
            write_center_svg(
                model_acute,
                here / "x-03000.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3000¶

X₃₀₀₀¶