G.13 equilateral, isosceles, and scalene triangles — Code

I.def.20

Of trilateral figures, an equilateral triangle < A B C > has three equal sides, an isosceles triangle < D E F > has two equal sides, and a scalene triangle < G H K > has three unequal sides.

"""Programmatic construction for Book I, Definition 20 (I.def.20 — equilateral, isosceles, and scalene triangles).
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct equilateral < A B C >, isosceles < D E F >, and scalene < G H K > triangles."""
            model = Model("I.def.20")
            A = model.set_point(0, 0, ID="A")
            B = model.set_point(1, 0, ID="B")
            C = model.set_point(sp.Rational(1, 2), sp.sqrt(3) / 2, ID="C")
            model.set_polygon([A, B, C])

            D = model.set_point(sp.Rational(3, 2), 0, ID="D")
            E = model.set_point(sp.Rational(9, 4), 0, ID="E")
            F = model.set_point(sp.Rational(15, 8), 1, ID="F")
            model.set_polygon([D, E, F])

            G = model.set_point(sp.Rational(11, 4), 0, ID="G")
            H = model.set_point(4, 0, ID="H")
            K = model.set_point(sp.Rational(25, 8), sp.Rational(7, 8), ID="K")
            model.set_polygon([G, H, K])
            return model


        if __name__ == "__main__":
            construct_g1()