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X₁₈₅₃¶

ZOSMA TRANSFORM OF X₂₀₄

Let A' be the orthocenter of BCX₃, and define B' and C' cyclically; then X₁₈₅₃ is the centroid of A'B'C'.

X₁₈₅₃ (ZOSMA TRANSFORM OF X₂₀₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1853 = ZOSMA TRANSFORM OF X_204."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            orthocenter_of,
            promote_point_to_top,
            reflection_in_point,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01853(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1853 = ZOSMA TRANSFORM OF X_204 on reference triangle ABC."""
            X_154 = eval_trilinear_point(model, A, B, C, '(cos(A) - cos(B)*cos(C))*a**(2)', ID="X_154", classes=["center"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_1853 = reflection_in_point(model, X_154, X_2, ID="X_1853", classes=["selected", "target"], guide=False)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_64 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - cos(B)*cos(C))', ID="X_64", classes=["center", "incident"])
            central_line(model, X_4, X_64, 4, 64, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_66 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(4) + c**(4) - a**(4))', ID="X_66", classes=["center", "incident"])
            central_line(model, X_6, X_66, 6, 66, incident=True)
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", 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_25, X_125, 25, 125, incident=True)
            return promote_point_to_top(model, X_1853)


        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_1853 on the given reference triangle."""
            model = create_model('X_1853 = ZOSMA TRANSFORM OF X_204')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01853(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-01853.json"))
            write_center_svg(
                model_acute,
                here / "x-01853.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1853¶

X₁₈₅₃¶