"The discovery and subsequent fascination with the golden ratio arose
with the ancient Greeks. Since Western civilization is mostly a product of the
Enlightenment, which was a product of the Renaissance, which was a product of
ancient Greece and Rome, it is highly probable that the fascination with the
golden ratio is an exclusively Western phenomenon.
Livio notes that "one clear source
of the mystical attitude toward whole numbers was the manifestation of such
numbers in human and animal bodies and in the cosmos, as perceived by the early
cultures" (22). Indeed, the number two, for example, is found in many places on the
human body: two eyes, two ears, two arms, two legs, et cetera. There are
four seasons, three tenses of time (past, present, and future), seven days of
the week, the list goes on. Early societies were filled with whole numbers, and
it is precisely for this reason that the golden ratio, which is derived from
whole numbers, shocked people with its irrationality, as discussed earlier. Clearly the world has yet to recover.
History also shows that early cultures
were fascinated with numerology. The Jews, Muslims, and Greeks all hd systems
in which numbers could be translated to words by assigning numerical
combinations to letters. This is still done today on the back of children's
cereal boxes occasionally. Also, the number 666 has captivated Christians as
the "number of the Beast." "Amusingly, in 1994, a relation was
'discovered' (and appeared in the Journal of Recreational Mathematics)
even between the 'number of the Beast' and the Golden Ratio" (Livio
"Story," 23): the sine of 666
degrees plus the cosine of six cubed (six times six times six) is a good
approximation of negative phi. Is this an eerie connection, or just a
coincidence resulting from residual fascination in numerology?
Plato himself was fascinated with numbers
and geometry. In his Laws, he argues that the optimal number of citizens
in a state is 5,040, because it has some rather peculiar arithmetical
properties (like that it has 59 divisors, including all the whole numbers from
1 to 12, that its twelfth part can be evenly divided by 12, etc.). In Timaeus,
Plato attempts to explain matter using what are now known as the Platonic solids:
"the only existing solids in which all the faces are identical and
equilateral, and each of the solids can be circumscribed by a sphere" (Livio
"Story," 67). The golden ratio
can be observed in the dimensions and symmetry of some Platonic solids. Since
it is nearly impossible for any American college student to graduate without
reading some of Plato's works, and because of Plato's revered status as one of
history's greatest philosophers, the concept of the golden ratio as an ideal
still continues.
In
our earlier discussion of the history of phi,
we mentioned Luca Pacioli, who really brought about a revival of the ideal of
the golden ratio and its subsequent rechristening as the Divine Proportion. I created several compositions in which I used golden ratio. All the figures has been drawn by the golden ratio rule.
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