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X₁₃₅₄¶

BRISSE TRANSFORM OF X₇₄

The following ten points lie on a circle: X_i for i = 11, 36, 65, 80, 108, 759, 1354, 1845, 2588, 2589. (Chris Van Tienhoven, Hyacinthos, January 4, 2011)

X₁₃₅₄ (BRISSE TRANSFORM OF X₇₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1354 = BRISSE TRANSFORM OF X_74."""

        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,
            gergonne_point_of,
            intersect_lines,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01354(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1354 = BRISSE TRANSFORM OF X_74 on reference triangle ABC."""
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center"])
            X_759 = eval_trilinear_point(model, A, B, C, '(1/(a**(0)*(b**(3) + c**(3)) - a**(2)*(b**(1) + c**(1))))', ID="X_759", classes=["center"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center"])
            X_1367 = point_from_barycentrics(model, A, B, C, 0.34721271, 0.6328996, 0.019887687, ID="X_1367", classes=["center"])
            central_line(model, X_56, X_759, 56, 759)
            central_line(model, X_7, X_1367, 7, 1367)
            X_1354 = intersect_lines(model, X_56, X_759, X_7, X_1367, ID="X_1354", classes=["selected", "target"])
            X_942 = eval_trilinear_point(model, A, B, C, '2*a*b*c + (b + c)*(a - b + c)*(a + b -c)', ID="X_942", classes=["center", "incident"])
            X_1364 = eval_trilinear_point(model, A, B, C, 'csc(A)*tan(A/2) / (sec(B) - sec(C))', ID="X_1364", classes=["center", "incident"])
            central_line(model, X_942, X_1364, 942, 1364, incident=True)
            return promote_point_to_top(model, X_1354)


        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_1354 on the given reference triangle."""
            model = create_model('X_1354 = BRISSE TRANSFORM OF X_74')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01354(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-01354.json"))
            write_center_svg(
                model_acute,
                here / "x-01354.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1354¶

X₁₃₅₄¶