GC-03.06 · Symbolic Model & Source

Companion symbolic Python construction for GC-03.06 · Ercole Suppa’s Square Midpoint Inradii Ratio (2015) (GC-03.06).

Programmatic Usage

from geometor.divine.catalog import build_construction

        model, cert = build_construction("GC-03.06")
        assert cert.ratio_expr == sp.GoldenRatio
        

Exact Builder Implementation

def build_suppa_square_inradii() -> ConstructionResult:
            """Ercole Suppa's square midpoint inradii ratio (2015)."""
            m = new_catalog_model("suppa-square-inradii")
            D = m.set_point(0, 0, classes=["given"], ID="D")
            C = m.set_point(2, 0, classes=["given"], ID="C")
            B = m.set_point(2, 2, ID="B")
            A = m.set_point(0, 2, ID="A")
            M = m.set_point(0, 1, ID="M")

            m.construct_polygon([A, B, C, D], ID="ABCD")
            ln_cm = m.construct_line(C, M, ID="CM")
            m.construct_segment(B, M, ID="BM")

            # Incenter E of isosceles BCM (inradius R = 1/phi, tangent to BC at H=(2,1))
            ex = (5 - sp.sqrt(5)) / 2
            E = m.set_point(ex, 1, classes=["golden"], ID="E")
            H = m.set_point(2, 1, ID="H")
            m.construct_circle(E, H, classes=["golden"], ID="cEH")

            # Incenter F of right CDM (inradius r = 1/phi^2, tangent to CD at P=((3-sqrt(5))/2, 0))
            fx = (3 - sp.sqrt(5)) / 2
            F = m.set_point(fx, fx, classes=["golden"], ID="F")
            P = m.set_point(fx, 0, ID="P")
            m.construct_circle(F, P, classes=["compass"], ID="cFP")

            ln_ef = m.construct_line(E, F, classes=["golden"], ID="EF")
            m.intersect(ln_ef, ln_cm, classes=["golden"], ID="K")

            return make_result(m, ("E", "K"), ("K", "F"), ("E", "K", "F"))
        

Exact Symbolic Point Coordinates

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

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

Certified Golden Ratio: EK / KF = GoldenRatio.