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X₃₆₅₂¶

KS(CARNOT TRIANGLE)

Quim Castellsaguer defines the Carnot triangle as the triangle formed by the circumcenters of the triangles BCH, CAH, ABH, where H denotes the orthocenter. The Carnot triangle is also known as the Johnson triangle.

X₃₆₅₂ (KS(CARNOT TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3652 = KS(CARNOT TRIANGLE)."""

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


        def construct_x_03652(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3652 = KS(CARNOT TRIANGLE) on reference triangle ABC."""
            X_3652 = eval_trilinear_point(model, A, B, C, '(a**(6) + a**(4)*(b*c - 3*b**(2) - 3*c**(2)) + a**(3)*b*c*(b + c) + 3*a**(2)*(b**(4) + c**(4)) - a*b*c*(b + c)*(b - c)**(2) - (b**(2) - c**(2))**(2)*(b**(2) + b*c + c**(2)))', ID="X_3652", classes=["selected", "target"])
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center", "incident"])
            central_line(model, X_30, X_40, 30, 40, incident=True)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_79 = eval_trilinear_point(model, A, B, C, '1/(1 + 2*cos(A))', ID="X_79", classes=["center", "incident"])
            central_line(model, X_5, X_79, 5, 79, incident=True)
            X_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center", "incident"])
            X_104 = eval_trilinear_point(model, A, B, C, '1/(-1 + cos(B) + cos(C))', ID="X_104", classes=["center", "incident"])
            central_line(model, X_21, X_104, 21, 104, incident=True)
            return promote_point_to_top(model, X_3652)


        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_3652 on the given reference triangle."""
            model = create_model('X_3652 = KS(CARNOT TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03652(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-03652.json"))
            write_center_svg(
                model_acute,
                here / "x-03652.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3652¶

X₃₆₅₂¶