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X₃₅₆₄¶

1st MOSES INFINITY POINT

X₃₅₆₄ = crossdifference of every pair of points on line X₆ X₉₂₄

X₃₅₆₄ (1st MOSES INFINITY POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3564 = 1st MOSES INFINITY 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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            isogonal_conjugate,
            nine_point_center_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03564(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3564 = 1st MOSES INFINITY POINT on reference triangle ABC."""
            X_3563 = eval_trilinear_point(model, A, B, C, '(sec(A))/(b**(2)*(cos(C))**(2) + c**(2)*(cos(B))**(2) - b*c*cos(A))', ID="X_3563", classes=["center"])
            X_3564 = isogonal_conjugate(model, A, B, C, X_3563, ID="X_3564", classes=["selected", "target"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_5, X_6, 5, 6, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            central_line(model, X_3, X_69, 3, 69, incident=True)
            X_26 = eval_trilinear_point(model, A, B, C, 'a*(b**(2)*cos(2*B) + c**(2)*cos(2*C) - a**(2)*cos(2*A))', ID="X_26", classes=["center", "incident"])
            X_159 = eval_trilinear_point(model, A, B, C, '(a*((a**(2) + b**(2) + c**(2))*sin(2*A) + (c**(2) - b**(2) - a**(2))*sin(2*B) + (b**(2) - c**(2) - a**(2))*sin(2*C)))', ID="X_159", classes=["center", "incident"])
            central_line(model, X_26, X_159, 26, 159, incident=True)
            return promote_point_to_top(model, X_3564)


        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_3564 on the given reference triangle."""
            model = create_model('X_3564 = 1st MOSES INFINITY POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03564(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-03564.json"))
            write_center_svg(
                model_acute,
                here / "x-03564.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3564¶

X₃₅₆₄¶