G.545 there equal plane — Code

XI.35

If there be two equal plane angles, and on their vertices there be set up elevated segments containing equal angles with the original segments respectively, if on the elevated segments points be taken at random and perpendiculars be drawn from them to the planes in which the original angles are, and if from the points so arising in the planes segments be joined to the vertices of the original angles, they will contain, with the elevated segments, equal angles.

"""Programmatic construction for Book XI, Proposition 35 (XI.35).

        Two equal plane rectilineal angles BAC and EDF with elevated straight lines
        AG and DM containing equal angles with the original straight lines respectively,
        and perpendiculars GL, HK and MN dropped to the planes BAC and EDF.
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the two elevated angle figures for XI.35 using geometor.model."""
            model = Model("XI.35")

            # Left figure
            A = model.set_point(sp.Rational(46, 100), sp.Rational(78, 100), classes=["given"], label="A")
            H = model.set_point(sp.Rational(126, 100), sp.Rational(146, 100), label="H")
            G = model.set_point(sp.Rational(146, 100), sp.Rational(163, 100), classes=["given"], label="G")
            K = model.set_point(sp.Rational(122, 100), sp.Rational(74, 100), label="K")
            L = model.set_point(sp.Rational(141, 100), sp.Rational(73, 100), label="L")
            B = model.set_point(sp.Rational(112, 100), sp.Rational(95, 100), classes=["given"], label="B")
            C = model.set_point(sp.Rational(104, 100), sp.Rational(34, 100), classes=["given"], label="C")

            # Right figure
            D = model.set_point(sp.Rational(248, 100), sp.Rational(62, 100), classes=["given"], label="D")
            M = model.set_point(sp.Rational(308, 100), sp.Rational(152, 100), classes=["given"], label="M")
            E = model.set_point(sp.Rational(298, 100), sp.Rational(104, 100), classes=["given"], label="E")
            N = model.set_point(sp.Rational(332, 100), sp.Rational(80, 100), label="N")
            F = model.set_point(sp.Rational(318, 100), sp.Rational(46, 100), classes=["given"], label="F")

            # Left segments and triangles
            for p1, p2 in [
                (A, H), (H, G), (A, G),
                (G, L), (H, K),
                (A, K), (K, L), (A, L),
                (A, B), (A, C), (B, C),
                (K, B), (K, C), (H, B), (H, C),
            ]:
                model.set_segment(p1, p2)

            for pts in [
                [A, B, C], [G, A, L], [H, A, K], [H, A, C], [H, A, B],
                [B, C, K], [K, A, C], [H, C, K], [H, B, K],
            ]:
                model.set_polygon(pts)

            # Right segments and triangles
            for p1, p2 in [
                (D, M), (M, N), (D, N),
                (D, E), (D, F), (E, F),
                (N, E), (N, F), (M, E), (M, F),
            ]:
                model.set_segment(p1, p2)

            for pts in [
                [D, E, F], [M, D, N], [M, D, F], [M, D, E],
                [E, F, N], [N, D, F], [M, F, N],
            ]:
                model.set_polygon(pts)

            return model


        if __name__ == "__main__":
            construct_g1()