GC-06.03 · Symbolic Model & Source¶
Companion symbolic Python construction for GC-06.03 · Bùi Quang Tuân’s Four Congruent Golden Circles (GC-06.03).
Programmatic Usage¶
from geometor.divine.catalog import build_construction
model, cert = build_construction("GC-06.03")
assert cert.ratio_expr == sp.GoldenRatio
Exact Builder Implementation¶
def build_bui_four_golden_circles() -> ConstructionResult:
"""Bùi Quang Tuân's four congruent circles generating a vertical golden chain."""
m = new_catalog_model("bui-four-golden-circles")
s3 = sp.sqrt(3)
s15 = sp.sqrt(15)
A = m.set_point(-sp.Rational(1, 2), 0, classes=["given"], ID="A")
B = m.set_point(sp.Rational(1, 2), 0, classes=["given"], ID="B")
c_a = m.construct_circle(A, B, classes=["primary"], ID="cA")
c_b = m.construct_circle(B, A, classes=["primary"], ID="cB")
E = m.intersect(c_a, c_b, side_of=(A, B, 1), classes=["golden"], ID="E")
N = m.intersect(c_a, c_b, side_of=(A, B, -1), classes=["golden"], ID="N")
ln_axis = m.construct_line(N, E, classes=["golden"], ID="NE")
_ = ln_axis
# Congruent unit circles centered at D=(0, sqrt(15)/2) and C=(0, -sqrt(15)/2) tangent to cA, cB
D = m.set_point(0, s15 / 2, classes=["golden"], ID="D")
C = m.set_point(0, -s15 / 2, classes=["golden"], ID="C")
T1 = m.set_point(-sp.Rational(1, 4), s15 / 4, guide=True, ID="T1")
T2 = m.set_point(-sp.Rational(1, 4), -s15 / 4, guide=True, ID="T2")
m.construct_circle(D, T1, classes=["golden"], ID="cD")
m.construct_circle(C, T2, classes=["compass"], ID="cC")
_ = s3
return make_result(m, ("E", "N"), ("E", "D"), ("N", "E", "D"))
Exact Symbolic Point Coordinates¶
All points in bui-four-golden-circles are certified free of floating-point approximations over \(\mathbb{Q}(\sqrt{3}, \phi)\):
Point |
Exact \(x\) |
Exact \(y\) |
|---|---|---|
|
\(- \frac{1}{2}\) |
\(0\) |
|
\(\frac{1}{2}\) |
\(0\) |
|
\(0\) |
\(\frac{\sqrt{3}}{2}\) |
|
\(0\) |
\(- \frac{\sqrt{3}}{2}\) |
|
\(0\) |
\(\frac{\sqrt{15}}{2}\) |
|
\(0\) |
\(- \frac{\sqrt{15}}{2}\) |
Certified Golden Ratio: EN / ED = GoldenRatio.