G.525 solid angle contained — Code

XI.20

If a solid angle be contained by three plane angles, any two, taken together in any manner, are greater than the remaining one.

"""Programmatic construction for Book XI, Proposition 20 (XI.20).

        If a solid angle be contained by three plane angles, any two, taken together in
        any manner, are greater than the remaining one.
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure for Book XI, Proposition 20 using geometor.model."""
            model = Model("XI.20")

            # 1. Let the solid angle at A be contained by the three plane angles
            #    BAC, CAD, DAB.
            A = model.set_point(0, 0, classes=["given"], ID="A")
            D = model.set_point(sp.Rational(15, 60), sp.Rational(59, 60), classes=["given"], label="D")
            B = model.set_point(sp.Rational(-141, 60), sp.Rational(-47, 60), classes=["given"], label="B")
            C = model.set_point(sp.Rational(77, 60), sp.Rational(-47, 60), classes=["given"], label="C")

            # 2. In the plane through BA, AC construct angle BAE equal to angle DAB,
            #    make AE equal to AD, and draw BEC across through E cutting AB, AC at B, C.
            E = model.set_point(sp.Rational(38, 60), sp.Rational(-47, 60), label="E")

            # 3. Join DB, DC.
            model.set_segment(A, B)
            model.set_segment(A, C)
            model.set_segment(A, D)
            model.set_segment(A, E)
            model.set_segment(B, C)
            model.set_segment(B, E)
            model.set_segment(E, C)
            model.set_segment(B, D)
            model.set_segment(D, C)
            model.set_section([B, E, C])

            # Triangles and planes
            model.set_polygon([B, A, C])
            model.set_polygon([B, A, E])
            model.set_polygon([E, A, C])
            model.set_polygon([D, A, B])
            model.set_polygon([D, A, C])
            model.set_polygon([B, D, C])

            return model


        if __name__ == "__main__":
            construct_g1()