000RM.dvi

11.3 Hofstetter’s 5-step division of a segment in the golden section 325

11.3 Hofstetter’s 5-step division of a segment in the golden

section

K. Hofstetter has also found the following parsimonious division of a
given segment in the golden section.^3

A B

C

D

E

F

G

H

G′

C 1

C 2

C 3

C 4

Construction 11.2.Given a segmentAB, construct

1.C 1 =A(B),

2.C 2 =B(A), intersectingC 1 atCandD,

3.C 3 =C(A), intersectingC 1 again atE,

4.the segmentCDto intersectC 3 atF,

5.C 4 =E(F)to intersectABatG.

The pointGdivides the segmentABin the golden section.

(^3) K. Hofstetter, A 5-step division of a segment in the golden section,Forum Geom., 3 (2003) 205–206.
After the publication of this paper, it was found that the same construction has been given previously by
E. Lemoine,G ́eom ́etrographie ou art des Constructions g ́eom ́etriques, C. Naud, Paris, 1902, p.51, and
J. Reusch, Planimetrische Konstruktionen in geometrographischer Ausfuhrung, (Teubner 1904), pg 37.