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X₄₁₂¶

EULER X₂₉-2nd-SUBSTITUTION POINT

X₄₁₂ = orthocentroida1-circle-inverse of X₅₂₂₄₈

X₄₁₂ (EULER X₂₉-2nd-SUBSTITUTION POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_412 = EULER X_29-2nd-SUBSTITUTION 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,
            centroid_of,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00412(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_412 = EULER X_29-2nd-SUBSTITUTION POINT on reference triangle ABC."""
            X_412 = eval_barycentric_point(model, A, B, C, '(a**(2) + b**(2) - c**(2)) * (a**(2) - b**(2) + c**(2)) * (a**(6) + a**(5)*b - 2*a**(4)*b**(2) - 2*a**(3)*b**(3) + a**(2)*b**(4) + a*b**(5) + a**(5)*c - a**(4)*b*c - a*b**(4)*c + b**(5)*c - 2*a**(4)*c**(2) + 2*a**(2)*b**(2)*c**(2) - 2*a**(3)*c**(3) - 2*b**(3)*c**(3) + a**(2)*c**(4) - a*b*c**(4) + a*c**(5) + b*c**(5))', ID="X_412", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center", "incident"])
            X_92 = eval_trilinear_point(model, A, B, C, 'csc(2*A)', ID="X_92", classes=["center", "incident"])
            central_line(model, X_40, X_92, 40, 92, incident=True)
            X_46 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A)', ID="X_46", classes=["center", "incident"])
            X_158 = eval_trilinear_point(model, A, B, C, '(sec(A))**(2)', ID="X_158", classes=["center", "incident"])
            central_line(model, X_46, X_158, 46, 158, incident=True)
            return promote_point_to_top(model, X_412)


        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_412 on the given reference triangle."""
            model = create_model('X_412 = EULER X_29-2nd-SUBSTITUTION POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00412(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-00412.json"))
            write_center_svg(
                model_acute,
                here / "x-00412.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X412¶

X₄₁₂¶