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X₃₃₃₄¶

PERSPECTOR OF TRIANGLES T1T2T3 AND J1J2J3

The equilateral triangles T₁T₂T₃ and J₁J₂J₃ are defined just before X₃₂₇₂. The points X₃₃₃₄ and X₃₃₃₅, contributed April 16, 2008 by Peter Moses, complete a list (just before X₃₂₇₂ of perspectors associated with equilateral triangles.

X₃₃₃₄ (PERSPECTOR OF TRIANGLES T1T2T3 AND J1J2J3) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3334 = PERSPECTOR OF TRIANGLES T1T2T3 AND J1J2J3."""

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


        def construct_x_03334(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3334 = PERSPECTOR OF TRIANGLES T1T2T3 AND J1J2J3 on reference triangle ABC."""
            X_3334 = eval_trilinear_point(model, A, B, C, 'cos(A) + 2*sin(B/3)*sin(C/3) + sin(A/3 + pi  /6)', ID="X_3334", classes=["selected", "target"])
            X_16 = eval_trilinear_point(model, A, B, C, 'sin(A-  pi  /3)', ID="X_16", classes=["center", "incident"])
            X_358 = eval_trilinear_point(model, A, B, C, 'cos(A/3)', ID="X_358", classes=["center", "incident"])
            central_line(model, X_16, X_358, 16, 358, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_3272 = eval_trilinear_point(model, A, B, C, 'cos(B/3 - C/3)', ID="X_3272", classes=["center", "incident"])
            central_line(model, X_3, X_3272, 3, 3272, incident=True)
            return promote_point_to_top(model, X_3334)


        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_3334 on the given reference triangle."""
            model = create_model('X_3334 = PERSPECTOR OF TRIANGLES T1T2T3 AND J1J2J3')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03334(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-03334.json"))
            write_center_svg(
                model_acute,
                here / "x-03334.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3334¶

X₃₃₃₄¶