G.10 circle — Code

I.def.15

A circle ( A B ) is a plane figure contained by one arc defined by a center A and a point B establishing its defining radius / A B /, such that all segments / A B /, / A C /, / A D / falling upon the arc from A are equal.

"""Programmatic construction for Book I, Definition 15 (I.def.15 — circle).

        A circle is a plane figure contained by one arc such that all segments falling upon it from its center are equal.
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the foundational figure for I.def.15 (circle ( B C D ) with equal radii)."""
            model = Model("I.def.15")
            A = model.set_point(0, 0, classes=["given"], ID="A")
            B = model.set_point(1, 0, classes=["given"], ID="B")
            model.construct_circle(A, B)
            C = model.set_point(sp.Rational(1, 2), sp.sqrt(3) / 2, ID="C")
            D = model.set_point(-1, 0, ID="D")
            model.set_segment(A, B)
            model.set_segment(A, C)
            model.set_segment(A, D)
            return model


        if __name__ == "__main__":
            construct_g1()