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X₃₅₆₉¶

BELTRAMI-PARRY POINT

X₃₅₆₉ = perspector of hyperbola {{A, B, C,X₆,X₂₃₂}}

X₃₅₆₉ (BELTRAMI-PARRY POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3569 = BELTRAMI-PARRY POINT."""

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


        def construct_x_03569(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3569 = BELTRAMI-PARRY POINT on reference triangle ABC."""
            X_2966 = eval_trilinear_point(model, A, B, C, '(sec(A +  omega  ))/(b**(2) - c**(2))', ID="X_2966", classes=["center"])
            X_3569 = isogonal_conjugate(model, A, B, C, X_2966, ID="X_3569", classes=["selected", "target"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            X_111 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(2) - b**(2) - c**(2))', ID="X_111", classes=["center", "incident"])
            central_line(model, X_74, X_111, 74, 111, incident=True)
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            X_112 = eval_trilinear_point(model, A, B, C, 'a/(sin(2*B) - sin(2*C))', ID="X_112", classes=["center", "incident"])
            central_line(model, X_110, X_112, 110, 112, incident=True)
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            X_125 = eval_trilinear_point(model, A, B, C, 'cos(A)*(sin(B - C))**(2)', ID="X_125", classes=["center", "incident"])
            central_line(model, X_115, X_125, 115, 125, incident=True)
            return promote_point_to_top(model, X_3569)


        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_3569 on the given reference triangle."""
            model = create_model('X_3569 = BELTRAMI-PARRY POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03569(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-03569.json"))
            write_center_svg(
                model_acute,
                here / "x-03569.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3569¶

X₃₅₆₉¶