GC-07.04 · Symbolic Model & Source

Companion symbolic Python construction for GC-07.04 · Tran Quang Hung’s 60° Isosceles Trapezoid Diagonal Division (GC-07.04).

Programmatic Usage

from geometor.divine.catalog import build_construction

        model, cert = build_construction("GC-07.04")
        assert cert.ratio_expr == sp.GoldenRatio
        

Exact Builder Implementation

def build_tran_isosceles_trapezoid_60() -> ConstructionResult:
            """Tran Quang Hung's 60-degree half-hexagon trapezoid & reflected compass arc."""
            m = new_catalog_model("tran-isosceles-trapezoid-60")
            s3 = sp.sqrt(3)

            D = m.set_point(-2, 0, classes=["given"], ID="D")
            C = m.set_point(2, 0, classes=["given"], ID="C")
            B = m.set_point(1, s3, ID="B")
            A = m.set_point(-1, s3, ID="A")
            K = m.set_point(3, -s3, ID="K")

            m.construct_polygon([A, B, C, D], ID="ABCD")
            m.construct_line(B, K, classes=["auxiliary"], ID="BK")
            ln_ac = m.construct_line(A, C, classes=["golden"], ID="AC")

            c_kb = m.construct_circle(K, B, classes=["golden"], ID="cKB")
            m.intersect(c_kb, ln_ac, between=(A, C), classes=["golden"], ID="M")

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

Exact Symbolic Point Coordinates

All points in tran-isosceles-trapezoid-60 are certified free of floating-point approximations over \(\mathbb{Q}(\sqrt{3}, \phi)\):

Point	Exact \(x\)	Exact \(y\)
D	\(-2\)	\(0\)
C	\(2\)	\(0\)
B	\(1\)	\(\sqrt{3}\)
A	\(-1\)	\(\sqrt{3}\)
K	\(3\)	\(- \sqrt{3}\)
M	\(\frac{7}{2} - \frac{3 \sqrt{5}}{2}\)	\(\frac{- \sqrt{3} + \sqrt{15}}{2}\)

Certified Golden Ratio: CM / MA = GoldenRatio.