324 Constructions with the golden section
1.C 1 =A(B),
2.C 2 =B(A), intersectingC 1 atCandD,
3.CDto intersectABat (their common midpoint)M,
4.C 3 =A(M)to intersectC 2 atE,
5.C 4 =E(A)to intersectC 3 atFandF′,Fcloser toMthenG′,
6.EFand extend to intersectABatG.
The pointGdivides the segmentABin the golden section.
A
B
C
D
M
E
F
F′
G
C 1 C 2
C 3
C 4
Proof.By [1],FdividesF′Bin the golden section. SinceEFis parallel
toF′A,GdividesABin the golden section as well.
Remark.If the linesEF′andABintersect atG′, thenAdividesG′Bin
the golden section.