← etc / Encyclopedia of Triangle Centers

X₃₁₂₁¶

DANNEELS PERSPECTOR FOR X₃₇

X₃₁₂₁ = crossdifference of every pair of points on the line X₉₉ X₁₀₀

X₃₁₂₁ (DANNEELS PERSPECTOR FOR X₃₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3121 = DANNEELS PERSPECTOR FOR X_37."""

        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,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03121(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3121 = DANNEELS PERSPECTOR FOR X_37 on reference triangle ABC."""
            X_3121 = eval_trilinear_point(model, A, B, C, '(a**(2)*(b + c)*(b - c)**(2))', ID="X_3121", classes=["selected", "target"])
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center", "incident"])
            X_292 = eval_trilinear_point(model, A, B, C, 'a/(a**(2) - b*c)', ID="X_292", classes=["center", "incident"])
            central_line(model, X_100, X_292, 100, 292, incident=True)
            X_244 = eval_trilinear_point(model, A, B, C, '(b - c)**(2)', ID="X_244", classes=["center", "incident"])
            X_665 = eval_trilinear_point(model, A, B, C, 'a*((a - b)**(2)*(a + b - c) - (c - a)**(2)*(c + a - b))', ID="X_665", classes=["center", "incident"])
            central_line(model, X_244, X_665, 244, 665, incident=True)
            X_81 = eval_trilinear_point(model, A, B, C, '1/(b + c)', ID="X_81", classes=["center", "incident"])
            X_893 = eval_trilinear_point(model, A, B, C, 'a/(a**(2) + b*c)', ID="X_893", classes=["center", "incident"])
            central_line(model, X_81, X_893, 81, 893, incident=True)
            return promote_point_to_top(model, X_3121)


        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_3121 on the given reference triangle."""
            model = create_model('X_3121 = DANNEELS PERSPECTOR FOR X_37')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03121(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-03121.json"))
            write_center_svg(
                model_acute,
                here / "x-03121.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3121¶

X₃₁₂₁¶