Ancient architects used this ‘divine’ mathematical ratio to inject natural beauty into man-made creations – here’s how it works
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 ratio, otherwise known as of golden ratio, divine proportion or golden ratio. To be precise, it is the number 1.61803399 – represented by the Greek letter phi – which is considered truly unique in its mathematical properties, its prevalence in nature, and its ability to achieve 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 medieval Italian mathematician Leonardo of Pisa and Renaissance astronomer Johannes Kepler, to current scientific personalities such as the physicist of Oxford Roger Penrose, have spent endless hours on this simple report and its properties. But the fascination with the golden ratio is not limited to mathematicians alone. Biologists, artists, musicians, historians, architects, psychologists and even mystics have pondered and debated on the basis of its ubiquity and appeal. In fact, it’s probably fair to say that the golden ratio has inspired thinkers from 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 greater of the two quantities. When the golden ratio is conceptualized in two dimensions, it is usually presented as a regular spiral defined by a series of squares and arcs, each forming “golden rectangles”.
This symbolic potential stems from the way the spiral shape of the average resembles growth patterns seen in nature and its proportions are reminiscent of those of the human body. Thus, these simple spirals and rectangles, which served to suggest the presence of a universal order underlying the world, were thus qualified as “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 to this alluring number are the Parthenon statues in Greece, dating from 490-430 BC. were familiar with the properties of this unique number.
According to some historians, the Egyptians believed 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 pleasing to the eye. They used it in their writing system and in the layout of their temples. The Egyptians knew 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 the Greek mathematician Euclid (c. 325-c. 265 BC) described what he called the “extreme and middle ratio”. However, the unique properties of ratio became popular in the 15th century, when aesthetics were an essential 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 Pythagorean theorem, and the other the division of a straight line into extreme and mean ratios; the first we can compare it to a measure of gold, the second we can 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 result will be more aesthetic. By designing shapes from this relationship, an architect can design a door handle that has a complementary relationship to its door, which in turn has a similar relationship to its surrounding wall, and so on. But more than that, the golden ratio has been used for the facade of grand buildings from the Parthenon to the Great Mosque of Kairouan and up to modern landmarks such as the Sydney Opera House and the National Gallery in London.
The golden ratio in nature
What is perhaps most surprising about the golden ratio is that it can be considered a natural phenomenon in nature. The golden ratio is expressed in the arrangement of the branches along the stems of the plants and the veins of the leaves. It can be seen in the skeletons of animals and humans and in the branching of their veins and nerves. We even see it in the proportions of chemical compounds and the geometry of crystals. Essentially, it is all around and within us and for this reason the German psychologist Adolf Zeising (1810-1876) called it a “universal law”:
in which is contained the fundamental principle of all formative striving for beauty and wholeness in the realms of nature and art, and which pervades, as a primordial spiritual ideal, all structures, forms and proportions, whether cosmic or individual, organic or inorganic, acoustic or optical; which finds its full realization, however, in the human form.
Due to the unique properties of this golden ratio, many consider the ratio to be sacred or divine and a doorway to a deeper understanding of beauty and spirituality in life, unveiling a hidden harmony or connection in much of what we see.
Republished with permission. Read the original on Ancient Origins.