G.595 construct a cube and comprehend it in a — Code

XIII.15

Construct a cube and comprehend it in a sphere, like the pyramid; and to prove that the square on the diameter of the sphere is triple of the square on the side of the cube.
A B C D E H K N F G L M 
"""Programmatic construction for Book XIII, Proposition 15 (XIII.15).

        Left: Semicircle ADB on diameter AB cut at C with AC = 2 CB, perpendicular CD,
        and chord DB.
        Right: Cube EFGH-KLMN (FN) with side equal to DB, face diagonal EG, and
        space diagonal KG equal to sphere diameter AB.
        """

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0482.g1 using geometor.model."""
            model = Model("XIII.15")

            # Left: Semicircle ADB on diameter AB (centre (94, -110), radius 78)
            A = model.set_point(16.0, -110.0, classes=["given"], ID="A")
            B = model.set_point(172.0, -110.0, classes=["given"], ID="B")
            C = model.set_point(120.0, -110.0, classes=["constructed"], ID="C")
            D = model.set_point(120.0, -36.5, classes=["constructed"], ID="D")
            O = model.set_point(94.0, -110.0, classes=["auxiliary"], ID="O")
            model.construct_circle(O, A)

            # Right: Cube EFGH-KLMN
            E = model.set_point(274.0, -24.0, classes=["given"], ID="E")
            F = model.set_point(274.0, -116.0, classes=["given"], ID="F")
            G = model.set_point(366.0, -116.0, classes=["given"], ID="G")
            H = model.set_point(366.0, -24.0, classes=["given"], ID="H")

            K = model.set_point(250.0, -42.0, classes=["constructed"], ID="K")
            L = model.set_point(250.0, -134.0, classes=["constructed"], ID="L")
            M = model.set_point(342.0, -134.0, classes=["constructed"], ID="M")
            N = model.set_point(342.0, -42.0, classes=["constructed"], ID="N")

            # Polygons, Squares, and Cube
            model.set_polygon([C, D, B])
            model.set_polygon([E, F, G, H])
            model.set_polygon([K, L, M, N])
            model.set_polygon([E, F, L, K])
            model.set_polygon([K, E, G])
            model.set_polygon([E, F, G])
            model.set_polygon([E, F, G, H, K, L, M, N])

            # Segments
            for p1, p2 in [
                (A, B), (A, C), (C, B), (C, D), (D, B),
                (E, F), (F, G), (G, H), (H, E),
                (K, L), (L, M), (M, N), (N, K),
                (E, K), (F, L), (G, M), (H, N),
                (E, G), (K, G), (F, K),
            ]:
                model.set_segment(p1, p2)

            # Section
            model.set_section([A, C, B])

            # Angles
            model.set_wedge(E, K, K, G)
            model.set_wedge(F, E, E, G)

            return model


        if __name__ == "__main__":
            construct_g1()