← etc / Encyclopedia of Triangle Centers

X₃₁₃¶

ISOTOMIC CONJUGATE OF X₅₈

X₃₁₃ (ISOTOMIC CONJUGATE OF X₅₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_313 = ISOTOMIC CONJUGATE OF X_58."""

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


        def construct_x_00313(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_313 = ISOTOMIC CONJUGATE OF X_58 on reference triangle ABC."""
            X_313 = eval_trilinear_point(model, A, B, C, '(b + c)*b**(3)*c**(3)', ID="X_313", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            central_line(model, X_10, X_75, 10, 75, incident=True)
            X_71 = eval_trilinear_point(model, A, B, C, '(b + c)*cos(A)', ID="X_71", classes=["center", "incident"])
            X_190 = eval_trilinear_point(model, A, B, C, 'b*c/(b - c)', ID="X_190", classes=["center", "incident"])
            central_line(model, X_71, X_190, 71, 190, incident=True)
            X_42 = eval_trilinear_point(model, A, B, C, 'a*(b + c)', ID="X_42", classes=["center", "incident"])
            X_308 = eval_trilinear_point(model, A, B, C, 'b**(3)*c**(3)/(b**(2) + c**(2))', ID="X_308", classes=["center", "incident"])
            central_line(model, X_42, X_308, 42, 308, incident=True)
            return promote_point_to_top(model, X_313)


        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_313 on the given reference triangle."""
            model = create_model('X_313 = ISOTOMIC CONJUGATE OF X_58')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00313(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-00313.json"))
            write_center_svg(
                model_acute,
                here / "x-00313.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X313¶

X₃₁₃¶