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X₃₂₅₉¶

CROSSSUM OF X₁₀₀ AND X₁₀₄

A construction see Aris Pavlakis and Peter Moses, Hyacinthos 28741.

X₃₂₅₉ (CROSSSUM OF X₁₀₀ AND X₁₀₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3259 = CROSSSUM OF X_100 AND X_104."""

        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,
            complement,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            feuerbach_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03259(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3259 = CROSSSUM OF X_100 AND X_104 on reference triangle ABC."""
            X_901 = eval_trilinear_point(model, A, B, C, 'a/((b - c)*(b + c - 2*a))', ID="X_901", classes=["center"])
            X_3259 = complement(model, A, B, C, X_901, ID="X_3259", classes=["selected", "target"])
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_513 = eval_trilinear_point(model, A, B, C, 'b - c', ID="X_513", classes=["center", "incident"])
            central_line(model, X_11, X_513, 11, 513, incident=True)
            X_119 = eval_trilinear_point(model, A, B, C, '(csc(A))*(-1 + cos(B) + cos(C))*(sin(2*B) + sin(2*C) + 2*(-1 + cos(A))*(sin(B) + sin(C)))', ID="X_119", classes=["center", "incident"])
            X_517 = eval_trilinear_point(model, A, B, C, '-1 + cos(B) + cos(C)', ID="X_517", classes=["center", "incident"])
            central_line(model, X_119, X_517, 119, 517, incident=True)
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            X_661 = eval_trilinear_point(model, A, B, C, 'cot(B) - cot(C)', ID="X_661", classes=["center", "incident"])
            central_line(model, X_115, X_661, 115, 661, incident=True)
            return promote_point_to_top(model, X_3259)


        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_3259 on the given reference triangle."""
            model = create_model('X_3259 = CROSSSUM OF X_100 AND X_104')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03259(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-03259.json"))
            write_center_svg(
                model_acute,
                here / "x-03259.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3259¶

X₃₂₅₉¶