GC-03.04 · Symbolic Model & Source

Companion symbolic Python construction for GC-03.04 · Tran Quang Hung & Elliot McGucken’s 3×3 Grid Circle (GC-03.04).

Programmatic Usage

from geometor.divine.catalog import build_construction

        model, cert = build_construction("GC-03.04")
        assert cert.ratio_expr == sp.GoldenRatio
        

Exact Builder Implementation

def build_tran_mcgucken_3x3_circle() -> ConstructionResult:
            """Tran Quang Hung & Elliot McGucken's 3x3 grid diagonal circle division."""
            m = new_catalog_model("tran-mcgucken-3x3-circle")
            S1 = m.set_point(-3, 3, ID="S1")
            A = m.set_point(3, 3, classes=["given"], ID="A")
            S3 = m.set_point(3, -3, ID="S3")
            S4 = m.set_point(-3, -3, ID="S4")

            C1 = m.set_point(-1, 1, ID="C1")
            C = m.set_point(1, 1, ID="C")
            C3 = m.set_point(1, -1, ID="C3")
            C4 = m.set_point(-1, -1, ID="C4")

            O = m.set_point(0, 0, classes=["given"], ID="O")
            T = m.set_point(1, 3, ID="T")

            m.construct_polygon([S1, A, S3, S4], ID="S1AS3S4")
            m.construct_polygon([C1, C, C3, C4], classes=["auxiliary"], ID="C1CC3C4")

            # Internal 3x3 grid lines
            G1 = m.set_point(-1, 3, guide=True, ID="G1")
            G2 = m.set_point(-1, -3, guide=True, ID="G2")
            G3 = m.set_point(1, -3, guide=True, ID="G3")
            G4 = m.set_point(-3, 1, guide=True, ID="G4")
            G5 = m.set_point(3, 1, guide=True, ID="G5")
            G6 = m.set_point(-3, -1, guide=True, ID="G6")
            G7 = m.set_point(3, -1, guide=True, ID="G7")
            m.construct_segment(G1, G2, classes=["auxiliary"], ID="gV1")
            m.construct_segment(T, G3, classes=["auxiliary"], ID="gV2")
            m.construct_segment(G4, G5, classes=["auxiliary"], ID="gH1")
            m.construct_segment(G6, G7, classes=["auxiliary"], ID="gH2")
            m.construct_segment(O, T, classes=["auxiliary"], ID="OT")

            ln_oa = m.construct_line(O, A, classes=["golden"], ID="OA")
            c_ot = m.construct_circle(O, T, classes=["golden"], ID="cOT")
            m.intersect(c_ot, ln_oa, between=(C, A), classes=["golden"], ID="B")

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

Exact Symbolic Point Coordinates

All points in tran-mcgucken-3x3-circle are certified free of floating-point approximations over \(\mathbb{Q}(\sqrt{2}, \phi)\):

Point	Exact \(x\)	Exact \(y\)
S1	\(-3\)	\(3\)
A	\(3\)	\(3\)
S3	\(3\)	\(-3\)
S4	\(-3\)	\(-3\)
C1	\(-1\)	\(1\)
C	\(1\)	\(1\)
C3	\(1\)	\(-1\)
C4	\(-1\)	\(-1\)
O	\(0\)	\(0\)
T	\(1\)	\(3\)
B	\(\sqrt{5}\)	\(\sqrt{5}\)

Certified Golden Ratio: CB / BA = GoldenRatio.