000RM.dvi

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.