ABSTRACT
All this work on proportioning and measures is the outcome of a passion, disinterested
and detached, an exercise, a game, a preoccupation and an occupation, a need and a
duty, a ceaseless facing up to life, a seeking after proof, a right to march forward, a duty
15.1 THE REDISCOVERY OF THE GOLDEN SECTION
As we saw in Chapter 8, the golden section, or division in extreme and mean ratio,
figures largely in the Elements of Euclid, but despite the many modern attempts to show
that it was also the basis of proportions of the Parthenon and other Greek temples,2 there
is no positive evidence for this. Later, the golden section was an object of interest to
Medieval Arabic mathematicians. Influenced by them, Leonardo of Pisa, called Fibonacci
(c. 1170-1240), investigated the geometry of the regular pentagon, icosahedron and
dodecahedron, all of which involve the golden section,3 but he is associated in particular
with the number series that bears his name, and which converges towards ! as limit. The mathematical revival during the Renaissance brought renewed interest in the golden
section, seen in the mathematical works of, among others, Piero della Francesca, Luca
Pacioli and Johannes Kepler. However, there is no firm evidence that Piero applied the
golden section in his paintings, and although Leonardo da Vinci was the illustrator of
Pacioli’s De divina proportione (1498-1509), there too the golden section is approached
from a strictly mathematical viewpoint. P.H.Scholfield even concludes that it is
not very clear how far it is correct to speak of the rediscovery of the principle of
the golden section in the nineteenth century…A fairly good case could be made
out for the view that the nineteenth century actually discovered the golden
section as an instrument of architectural proportion, however close other periods
The earliest use of the name ‘golden section’ or ‘goldene Schnitt’ appears to have been in
1835, in Ohm’s treatise Die reine Elementar-Mathematik,5 and it was first put forward
unambiguously as the underlying secret of all natural and artistic form by Adolf Zeising
in his New Theory of the Proportions of the Human Body (1854). Even so, as late as 1914
Sir Theodore Cook was writing of the ! progression as ‘a new mathematical conception’.6 Only eight years later we find him attacking the rapid growth of the cult of
the golden section, being promoted at that time by writers like Jay Hambidge, as ‘a new
disease in architecture’.7 It is significant that this resurgence of the golden section in art,
and in the relatively new sciences of biology, psychology and aesthetics, occurred at a
time when pure mathematics and ‘hard’ sciences like physics and astronomy were
becoming increasingly abstract and remote from normal human experience. Nature’s laws
ceased to be seen as evidence of a universal concinnitas, so that, as Wittkower says, ‘Beauty and
proportion were no longer regarded as being universal, but were turned into psychological
phenomena originating and existing in the mind of the artist.’8 A way out of this total sub-
jectivism seemed to be offered by the discovery of logarithmic spirals based on the gold-
en section, and of the Fibonacci series, in the organic growth of plants and animals, and
also by the scientific investigation of the psychology of perception and aesthetic choice.
