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X₂₆₂₃¶

BARYCENTRIC PRODUCT OF PU(73)

X₂₆₂₃ = crossdifference of every pair of points on line X₅ X₅₁

X₂₆₂₃ (BARYCENTRIC PRODUCT OF PU(73)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2623 = BARYCENTRIC PRODUCT OF PU(73)."""

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


        def construct_x_02623(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2623 = BARYCENTRIC PRODUCT OF PU(73) on reference triangle ABC."""
            X_2623 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(B - C)', ID="X_2623", classes=["selected", "target"])
            X_50 = eval_trilinear_point(model, A, B, C, 'sin(3*A)', ID="X_50", classes=["center", "incident"])
            X_647 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))*(b**(2) + c**(2) - a**(2))', ID="X_647", classes=["center", "incident"])
            central_line(model, X_50, X_647, 50, 647, incident=True)
            X_323 = eval_trilinear_point(model, A, B, C, 'sin(3*A)*(csc(A))**(2)', ID="X_323", classes=["center", "incident"])
            X_401 = eval_trilinear_point(model, A, B, C, '(sin(2*B)*sin(2*C) - (sin(2*A))**(2))*(csc(A))', ID="X_401", classes=["center", "incident"])
            central_line(model, X_323, X_401, 323, 401, incident=True)
            return promote_point_to_top(model, X_2623)


        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_2623 on the given reference triangle."""
            model = create_model('X_2623 = BARYCENTRIC PRODUCT OF PU(73)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02623(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-02623.json"))
            write_center_svg(
                model_acute,
                here / "x-02623.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2623¶

X₂₆₂₃¶