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X₃₇₁¶

KENMOTU POINT (CONGRUENT SQUARES POINT)

There exist three congruent squares U, V, W positioned in ABC as follows: U has opposing vertices on segments AB and AC; V has opposing vertices on segments BC and BA; W has opposing vertices on segments CA and CB, and there is a single point common to U, V, W. The common point, X₃₇₁, may have first been published in Kenmotu’s Collection of Sangaku Problems in 1840, indicating that its first appearance may have been anonymously inscribed on a wooden board hung up in a Japanese shrine or temple. (The Kenmotu configuration uses only half-squares; i.e., isosceles right triangles). Trilinears were found by John Rigby.

X₃₇₁ (KENMOTU POINT (CONGRUENT SQUARES POINT)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_371 = KENMOTU POINT."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00371(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_371 = KENMOTU POINT on reference triangle ABC."""
            X_371 = eval_trilinear_point(model, A, B, C, 'cos(A -  pi  /4)', ID="X_371", classes=["selected", "target"])
            return promote_point_to_top(model, X_371)


        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_371 on the given reference triangle."""
            model = create_model('X_371 = KENMOTU POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00371(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-00371.json"))
            write_center_svg(
                model_acute,
                here / "x-00371.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X371¶

X₃₇₁¶