Selected Bibliography Architecture - Form Space and Order | Page 317
G O L D E N SECTIO N
C
b
B
a
A
C
B
A
The geometric construction of the Golden Section, first by extension, and then by division.
A
AB = a
BC = b
Ø = Golden Section
Ø = a = b = 0.618
b
a+b
C
B
Mathematical systems of proportion originate from the Pythagorean
concept of ‘all is number’ and the belief that certain numerical
relationships manifest the harmonic structure of the universe. One
of these relationships that has been in use ever since the days
of antiquity is the proportion known as the Golden Section. The
Greeks recognized the dominating role the Golden Section played
in the proportions of the human body. Believing that both humanity
and the shrines housing their deities should belong to a higher
universal order, they utilized these same proportions in their temple
structures. Renaissance architects also explored the Golden Section
in their work. In more recent times, Le Corbusier based his Modulor
system on the Golden Section. Its use in architecture endures even
today.
The Golden Section can be defined as the ratio between two sections
of a line, or the two dimensions of a plane figure, in which the lesser of
the two is to the greater as the greater is to the sum of both. It can
be expressed algebraically by the equation of two ratios:
a = b
b a+b
A
The Golden Section has some remarkable algebraic and geometric
properties that account for its existence in architecture as well as in
the structures of many living organisms. Any progression based on
the Golden Section is at once additive and geometrical.
B
Another progression that closely approximates the Golden Section
in whole numbers is the Fibonacci Series: 1, 1, 2, 3, 5, 8, 13 . . . . Each
term again is the sum of the two preceding ones, and the ratio
between two consecutive terms tends to approximate the Golden
Section as the series progresses to infinity.
In the numerical progression: 1, Ø 1, Ø 2, Ø 3 . . . Øn, each term is the
sum of the two preceding ones.
C
302 / A R