GC-06.02 · Symbolic Model & Source

Companion symbolic Python construction for GC-06.02 · Elliot McGucken & Thanos Kalogerakis’s Equal Tangent Circles (GC-06.02).

Programmatic Usage

from geometor.divine.catalog import build_construction

        model, cert = build_construction("GC-06.02")
        assert cert.ratio_expr == sp.GoldenRatio
        

Exact Builder Implementation

def build_mcgucken_kalogerakis_equal_circles() -> ConstructionResult:
            """Elliot McGucken & Thanos Kalogerakis's two externally tangent equal circles."""
            m = new_catalog_model("mcgucken-kalogerakis-equal-circles")
            B = m.set_point(0, 0, classes=["given"], ID="B")
            C = m.set_point(1, 0, classes=["given"], ID="C")
            D = m.set_point(2, 0, ID="D")
            F = m.set_point(0, 1, ID="F")
            A = m.set_point(0, -1, ID="A")

            m.construct_circle(B, C, classes=["primary"], ID="cB")
            c_d = m.construct_circle(D, C, classes=["primary"], ID="cD")
            m.construct_segment(A, F, classes=["auxiliary"], ID="AF")
            m.construct_line(B, D, classes=["auxiliary"], ID="BD")

            ln_fd = m.construct_line(F, D, classes=["golden"], ID="FD")
            m.intersect(c_d, ln_fd, between=(F, D), classes=["golden"], ID="H")
            m.intersect(c_d, ln_fd, beyond=(F, D), classes=["golden"], ID="I")

            return make_result(m, ("H", "I"), ("F", "H"), ("F", "H", "I"))
        

Exact Symbolic Point Coordinates

All points in mcgucken-kalogerakis-equal-circles are certified free of floating-point approximations over \(\mathbb{Q}(\phi)\):

Point	Exact \(x\)	Exact \(y\)
B	\(0\)	\(0\)
C	\(1\)	\(0\)
D	\(2\)	\(0\)
F	\(0\)	\(1\)
A	\(0\)	\(-1\)
H	\(2 - \frac{2 \sqrt{5}}{5}\)	\(\frac{\sqrt{5}}{5}\)
I	\(\frac{2 \sqrt{5}}{5} + 2\)	\(- \frac{\sqrt{5}}{5}\)

Certified Golden Ratio: HI / FH = GoldenRatio.