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X₆₄₄¶

TRILINEAR MULTIPLIER FOR YFF PARABOLA

X₆₄₄ satisfies the equation X*(incircle) = Yff parabola, where * denotes trilinear multiplication, defined by

X₆₄₄ (TRILINEAR MULTIPLIER FOR YFF PARABOLA) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_644 = TRILINEAR MULTIPLIER FOR YFF PARABOLA."""

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


        def construct_x_00644(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_644 = TRILINEAR MULTIPLIER FOR YFF PARABOLA on reference triangle ABC."""
            X_644 = eval_trilinear_point(model, A, B, C, '((b + c - a)/(b - c))', ID="X_644", classes=["selected", "target"])
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center", "incident"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            central_line(model, X_100, X_101, 100, 101, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_220 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)**(2)', ID="X_220", classes=["center", "incident"])
            central_line(model, X_8, X_220, 8, 220, incident=True)
            X_145 = eval_trilinear_point(model, A, B, C, 'b*c*(3*a - b - c)', ID="X_145", classes=["center", "incident"])
            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"])
            central_line(model, X_145, X_218, 145, 218, incident=True)
            return promote_point_to_top(model, X_644)


        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_644 on the given reference triangle."""
            model = create_model('X_644 = TRILINEAR MULTIPLIER FOR YFF PARABOLA')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00644(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-00644.json"))
            write_center_svg(
                model_acute,
                here / "x-00644.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X644¶

X₆₄₄¶