G.539 parallelepipedal solids base — Code

XI.29

Parallelepipedal solids which are on the same base and of the same height, and in which the extremities of the sides which stand up are on the same segments, are equal.

"""Programmatic construction for Book XI, Proposition 29 (XI.29).

        Parallelepipedal solids CM and CN on the same base AB (ACBL) and of the same height,
        with the extremities of their standing sides on the same straight lines FN and DK.
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the two parallelepipeds CM and CN for Book XI, Proposition 29."""
            model = Model("XI.29")

            # Top back collinear line DK
            D = model.set_point(sp.Rational(24, 100), sp.Rational(185, 100), classes=["given"], label="D")
            E = model.set_point(sp.Rational(88, 100), sp.Rational(185, 100), classes=["given"], label="E")
            H = model.set_point(sp.Rational(168, 100), sp.Rational(185, 100), classes=["given"], label="H")
            K = model.set_point(sp.Rational(232, 100), sp.Rational(185, 100), classes=["given"], label="K")

            # Top front collinear line FN
            F = model.set_point(sp.Rational(34, 100), sp.Rational(161, 100), classes=["given"], label="F")
            G = model.set_point(sp.Rational(98, 100), sp.Rational(161, 100), classes=["given"], label="G")
            M = model.set_point(sp.Rational(178, 100), sp.Rational(161, 100), classes=["given"], label="M")
            N = model.set_point(sp.Rational(242, 100), sp.Rational(161, 100), classes=["given"], label="N")

            # Base parallelogram ACBL
            C = model.set_point(sp.Rational(80, 100), sp.Rational(74, 100), classes=["given"], label="C")
            B = model.set_point(sp.Rational(224, 100), sp.Rational(74, 100), classes=["given"], label="B")
            A = model.set_point(sp.Rational(74, 100), sp.Rational(40, 100), classes=["given"], label="A")
            L = model.set_point(sp.Rational(218, 100), sp.Rational(40, 100), classes=["given"], label="L")

            # Collinear sub-segments on DK and FN
            for p, q in [
                (D, K), (D, H), (E, K), (E, H), (D, E), (H, K),
                (F, N), (F, M), (G, N), (G, M), (F, G), (M, N),
            ]:
                model.set_segment(p, q)

            # Standing edges and base/top transverse edges
            for p, q in [
                (C, B), (A, L), (A, C), (B, L),
                (D, F), (E, G), (H, M), (K, N),
                (A, G), (A, F), (L, M), (L, N),
                (C, D), (C, E), (B, H), (B, K),
            ]:
                model.set_segment(p, q)

            # Triangles and parallelograms
            model.set_polygon([D, C, E])
            model.set_polygon([H, B, K])
            model.set_polygon([A, F, G])
            model.set_polygon([M, L, N])

            model.set_polygon([A, C, B, L])
            model.set_polygon([C, D, H, B])
            model.set_polygon([C, E, K, B])
            model.set_polygon([D, E, G, F])
            model.set_polygon([H, K, N, M])
            model.set_polygon([C, D, F, A])
            model.set_polygon([B, H, M, L])
            model.set_polygon([C, E, G, A])
            model.set_polygon([B, K, N, L])
            model.set_polygon([G, E, H, M])

            return model


        if __name__ == "__main__":
            construct_g1()