GC-03.03 · Symbolic Model & Source

Companion symbolic Python construction for GC-03.03 · Nguyen Thanh Dung’s 2×2 Grid Compass Arc (GC-03.03).

Programmatic Usage

from geometor.divine.catalog import build_construction

        model, cert = build_construction("GC-03.03")
        assert cert.ratio_expr == sp.GoldenRatio
        

Exact Builder Implementation

def build_nguyen_2x2_square() -> ConstructionResult:
            """Nguyen Thanh Dung's 2x2 square grid compass arc construction."""
            m = new_catalog_model("nguyen-2x2-square")
            P1 = m.set_point(-1, 1, ID="P1")
            P2 = m.set_point(1, 1, ID="P2")
            P3 = m.set_point(1, -1, ID="P3")
            P4 = m.set_point(-1, -1, ID="P4")

            A = m.set_point(-1, 0, classes=["given"], ID="A")
            O = m.set_point(0, 0, ID="O")
            B = m.set_point(1, 0, classes=["given"], ID="B")
            D = m.set_point(0, 1, ID="D")
            E = m.set_point(0, -1, ID="E")
            C = m.set_point(2, 0, ID="C")

            m.construct_polygon([P1, P2, P3, P4], ID="P1P2P3P4")
            ln_ab = m.construct_line(A, B, classes=["golden"], ID="AB")
            m.construct_segment(D, E, classes=["auxiliary"], ID="DE")
            m.construct_segment(C, D, classes=["auxiliary"], ID="CD")
            _ = O

            c_cd = m.construct_circle(C, D, classes=["golden"], ID="cCD")
            m.intersect(c_cd, ln_ab, between=(A, B), classes=["golden"], ID="M")

            return make_result(m, ("M", "B"), ("A", "M"), ("A", "M", "B"))
        

Exact Symbolic Point Coordinates

All points in nguyen-2x2-square are certified free of floating-point approximations over \(\mathbb{Q}(\phi)\):

Point	Exact \(x\)	Exact \(y\)
P1	\(-1\)	\(1\)
P2	\(1\)	\(1\)
P3	\(1\)	\(-1\)
P4	\(-1\)	\(-1\)
A	\(-1\)	\(0\)
O	\(0\)	\(0\)
B	\(1\)	\(0\)
D	\(0\)	\(1\)
E	\(0\)	\(-1\)
C	\(2\)	\(0\)
M	\(2 - \sqrt{5}\)	\(0\)

Certified Golden Ratio: MB / AM = GoldenRatio.