There is
one thing that ancient Greeks, Renaissance artists, a 17th century
astronomer and 21st century architects all have in common – they all
used the Golden Mean, otherwise
known as the Golden Ratio, Divine Proportion, or Golden Section.
Precisely, this is the number 1.61803399, represented by the Greek letter Phi,
and considered truly unique in its mathematical properties, its prevalence
throughout nature, and its ability to achieve a perfect aesthetic composition.
According
to astrophysicist Mario Livio:
Some of
the greatest mathematical minds of all ages, from Pythagoras and Euclid in
ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and
the Renaissance astronomer Johannes Kepler, to present-day scientific figures
such as Oxford physicist Roger Penrose, have spent endless hours over this
simple ratio and its properties. But the fascination with the Golden Ratio is
not confined just to mathematicians. Biologists, artists, musicians,
historians, architects, psychologists, and even mystics have pondered and
debated the basis of its ubiquity and appeal. In fact, it is probably fair to
say that the Golden Ratio has inspired thinkers of all disciplines like no
other number in the history of mathematics.
In
mathematics and the arts, two quantities are in the golden ratio if their ratio
is the same as the ratio of their sum to the larger of the two quantities. When
the Golden Mean is conceptualised in two dimensions it is typically presented
as a regular spiral that is defined by a series of squares and arcs, each
forming “Golden Rectangles”.
This
symbolic potential arises because of the way the mean’s spiral shape resembles
growth patterns observed in nature and its proportions are reminiscent of those
in human bodies. Thus, these simple spirals and rectangles, which served to
suggest the presence of a universal order underlying the world, were thereby
dubbed “golden” or “divine”.
The
Golden Ratio in History
The
golden ratio has fascinated Western intellectuals of diverse interests for at
least 2,400 years. The earliest known monuments believed to have been built according
to this alluring number are the statues of the Parthenon in Greece, dating back
between 490 and 430 BC. However, there are many who have argued that it
goes back much further than this and that the Egyptians were well versed in the
properties of this unique number.
According
to some historians, the Egyptians thought that the golden ratio was
sacred. Therefore, it was very important in their religion. They
used the golden ratio when building temples and places for the dead. In
addition, the Egyptians found the golden ratio to be pleasing to the eye.
They used it in their system of writing and in the arrangement of their
temples. The Egyptians were aware that they were using the golden ratio,
but they called it the "sacred ratio."
The first
recorded definition of the golden ratio dates back to the period when Greek
mathematician, Euclid (c. 325–c. 265 BC), described what he called the
"extreme and mean ratio". However, the ratio’s unique properties
became popularised in the 15th century when aesthetics were a vital
component of Renaissance art and geometry served both practical and symbolic
purposes. As the famous mathematician, astronomer, and astrologer,
Johannes Kepler (1571 – 1630) wrote:
Geometry
has two great treasures: one is the Theorem of Pythagoras, and the other the
division of a line into extreme and mean ratio; the first we may compare to a
measure of gold, the second we may name a precious jewel.
The
Golden Ratio in Architecture
Many
artists and architects have proportioned their work to approximate the golden
ratio, with the belief that the outcome will be more aesthetically pleasing.
Using any of these ratios, an architect can design a door handle that has
a complementary relationship to its door, which in turn has a similar
relationship to its enclosing wall, and so on. But more than this, the
golden ratio has been used for the façade of great buildings from the Parthenon
to the Great Mosque of Kairouan and all the way through to modern landmarks
such as the Sydney Opera House and the National Gallery in London.
The
Golden Ratio in Nature
Perhaps
what is most surprising about the Golden Ratio is that it can be seen as a
naturally occurring phenomenon in nature. The golden ratio is
expressed in the arrangement of branches along the stems of plants and the
veins in leaves. It can be seen in the skeletons of animals and
humans and the branching of their veins and nerves. It can even be seen
in the proportions of chemical compounds and the geometry of crystals.
Essentially, it is all around us and within us and for this reason, German
psychologist Adolf Zeising (1810 – 1876) labelled it a ‘universal law’:
in which
is contained the ground-principle of all formative striving for beauty and
completeness in the realms of both nature and art, and which permeates, as a
paramount spiritual ideal, all structures, forms and proportions, whether
cosmic or individual, organic or inorganic, acoustic or optical; which finds
its fullest realization, however, in the human form.
As a
result of the unique properties of this golden proportion, many view the ratio
as sacred or divine and as a door to a deeper understanding of beauty and
spirituality in life, unveiling a hidden harmony or connectedness in so much of
what we see.
- See
more at:
http://www.ancient-origins.net/unexplained-phenomena/golden-ratio-sacred-number-links-past-present-001091#sthash.szVdy4Bd.dpuf
