GC-01.06 · Symbolic Model & Source¶
Companion symbolic Python construction for GC-01.06 · Hofstetter’s Fixed-Aperture Rusty-Compass Division (GC-01.06).
Programmatic Usage¶
from geometor.divine.catalog import build_construction
model, cert = build_construction("GC-01.06")
assert cert.ratio_expr == sp.GoldenRatio
Exact Builder Implementation¶
def build_hofstetter_rusty_compass() -> ConstructionResult:
"""Kurt Hofstetter's 2005 fixed-opening rusty-compass golden division."""
m = new_catalog_model("hofstetter-rusty-compass")
A = m.set_point(0, 0, classes=["given"], ID="A")
B = m.set_point(1, 0, classes=["given"], ID="B")
ln_ab = m.construct_line(A, B, ID="AB")
c_ab = m.construct_circle(A, B, classes=["compass"], ID="cAB")
c_ba = m.construct_circle(B, A, classes=["compass"], ID="cBA")
C = m.intersect(c_ab, c_ba, side_of=(A, B, 1), ID="C")
D = m.intersect(c_ab, c_ba, side_of=(A, B, -1), ID="D")
ln_cd = m.construct_line(C, D, classes=["auxiliary"], ID="CD")
M = m.intersect(ln_ab, ln_cd, ID="M")
# Rusty compass opening fixed at |AB| = 1 placed at midpoint M
R1 = m.set_point(sp.Rational(3, 2), 0, guide=True, ID="R1")
c_m = m.construct_circle(M, R1, classes=["compass"], ID="cM")
F = m.intersect(c_m, c_ba, side_of=(A, B, 1), ID="F")
ln_df = m.construct_line(D, F, classes=["golden"], ID="DF")
m.intersect(ln_df, ln_ab, classes=["golden"], ID="G")
return make_result(m, ("A", "G"), ("G", "B"), ("A", "G", "B"))
Exact Symbolic Point Coordinates¶
All points in hofstetter-rusty-compass are certified free of floating-point approximations over \(\mathbb{Q}(\sqrt{3}, \phi)\):
Point |
Exact \(x\) |
Exact \(y\) |
|---|---|---|
|
\(0\) |
\(0\) |
|
\(1\) |
\(0\) |
|
\(\frac{1}{2}\) |
\(\frac{\sqrt{3}}{2}\) |
|
\(\frac{1}{2}\) |
\(- \frac{\sqrt{3}}{2}\) |
|
\(\frac{1}{2}\) |
\(0\) |
|
\(\frac{3}{4}\) |
\(\frac{\sqrt{15}}{4}\) |
|
\(- \frac{1}{2} + \frac{\sqrt{5}}{2}\) |
\(0\) |
Certified Golden Ratio: AG / GB = GoldenRatio.