G.79 Pythagorean theorem — Code

I.47

In a right-angled triangle, the square on the hypotenuse equals the sum of the squares on the two legs (Pythagorean Theorem).

"""Programmatic construction for Book I, Proposition 47 (I.47).

        In right-angled triangles the square on the side subtending the right angle is
        equal to the squares on the sides containing the right angle.
        """

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the windmill figure for Book I, Proposition 47 using geometor.model."""
            model = Model("I.47")

            # 1. Right-angled triangle ABC with right angle BAC
            A = model.set_point(118, -133, classes=["given"], ID="A")
            B = model.set_point(91, -186, classes=["given"], ID="B")
            C = model.set_point(222, -186, classes=["given"], ID="C")

            model.set_segment(A, B)
            model.set_segment(B, C)
            model.set_segment(A, C)
            model.set_polygon([A, B, C])

            # 2. Square BDEC described on BC [I. 46]
            D = model.set_point(91, -319, ID="D")
            E = model.set_point(222, -319, ID="E")
            model.set_segment(B, D)
            model.set_segment(D, E)
            model.set_segment(C, E)
            model.set_polygon([B, D, E, C])

            # 3. Square BAGF (GB) described on BA [I. 46]
            F = model.set_point(38, -159, ID="F")
            G = model.set_point(65, -106, ID="G")
            model.set_segment(B, F)
            model.set_segment(F, G)
            model.set_segment(G, A)
            model.set_polygon([B, A, G, F])

            # 4. Square ACKH (HC) described on AC [I. 46]
            H = model.set_point(171, -29, ID="H")
            K = model.set_point(275, -82, ID="K")
            model.set_segment(A, H)
            model.set_segment(H, K)
            model.set_segment(C, K)
            model.set_polygon([A, C, K, H])

            # 5. Parallel AL through A to BD or CE, meeting BC at M and DE at L [I. 31]
            M = model.set_point(118, -186, ID="M")
            L = model.set_point(118, -319, ID="L")
            model.construct_line(A, L)
            model.set_segment(A, L)
            model.set_segment(A, M)
            model.set_segment(M, L)
            model.set_segment(B, M)
            model.set_segment(M, C)
            model.set_segment(D, L)
            model.set_segment(L, E)

            # Split rectangles BL (BDLM) and CL (CELM)
            model.set_polygon([B, D, L, M])
            model.set_polygon([C, E, L, M])

            # Collinear extensions CA-AG and BA-AH [I. 14]
            model.construct_line(C, A)
            model.construct_line(B, A)
            model.set_segment(G, C)
            model.set_segment(B, H)

            # 6. Auxiliary transversals AD, FC, AE, BK and triangles ABD, FBC, ACE, KCB
            model.set_segment(A, D)
            model.set_segment(F, C)
            model.set_segment(A, E)
            model.set_segment(B, K)
            model.set_polygon([A, B, D])
            model.set_polygon([F, B, C])
            model.set_polygon([A, C, E])
            model.set_polygon([K, C, B])

            # 7. Referenced angles (wedges)
            model.set_wedge(A, B, B, C)  # < B A C )
            model.set_wedge(A, B, B, G)  # < B A G )
            model.set_wedge(B, D, D, C)  # < D B C )
            model.set_wedge(B, F, F, A)  # < F B A )
            model.set_wedge(B, A, A, C)  # < A B C )
            model.set_wedge(B, D, D, A)  # < D B A ) / < A B D )
            model.set_wedge(B, F, F, C)  # < F B C )

            return model


        if __name__ == "__main__":
            construct_g1()