What united ancient Greeks, Renaissance artists, 17th century astronomers, and 21st century architects was that they all used the golden ratio, otherwise known as the golden ratio.
This Phi number - 1.61803399 - has truly unique mathematical properties, manifests itself everywhere in nature, thanks to its use, artists can create works that are ideal in composition.
According to astrophysicist Mario Livi, some of the greatest mathematicians of all eras: Pythagoras and Euclid in Ancient Greece, the Italian mathematician Leonardo of Pisa in the Middle Ages and the astronomer Johannes Kepler in the Renaissance, and the modern scientist, physicist Roger Penrose of Oxford, spent infinitely long pondering over this special number and studying its properties. Not only mathematicians were fond of the golden ratio.
Biologists, artists, musicians, historians, architects, psychologists and even mystics discuss the reason for its ubiquity and appeal. It's safe to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.
In mathematics and art, the golden proportion is manifested when the ratio of the sum of two quantities to the larger of them is equal to the ratio of the greater to the lesser. When the Golden Ratio is conceptualized in two dimensions, it is usually represented as a spiral, which is defined by a series of squares and arcs that form “golden rectangles”.
The spiral shape expresses the growth dynamics of plants and other natural objects, the golden proportion is also manifested in the structure of the human body. Thus, this particular relationship of simple spirals and rectangles testifies to the presence of a universal order underlying the world, which is why it has been called golden or divine.
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The golden ratio in history
The Golden Ratio has fascinated Western intellectuals for at least 2,400 years. The earliest known monuments - the statues and the temple of the Parthenon in Greece (490-430 BC) were built in accordance with the golden ratio.
However, many argue that it was known much earlier and that the Egyptians were well versed in the properties of this unique number.
According to some historians, the Egyptians considered the Golden Ratio sacred. They used the golden ratio to create temples and burial sites. In addition, the Egyptians found that everything that corresponds to the golden ratio is pleasing to the eye. They used it in their writing and design systems.
The Greek mathematician Euclid (c. 365 - 300 BC), described what he called "a unique average proportion." However, the golden ratio did not become popular until the 15th century, when aesthetics became a vital component of life during the Renaissance, and art and geometry served both practical and symbolic purposes.
The famous mathematician, astronomer, astrologer Johannes Kepler (1571 - 1630) wrote: “There are two treasures in geometry: the Pythagorean theorem and the mean ratio; the first we can compare with the measure of gold, the second can be called a precious stone."
Golden ratio in architecture
Many artists and architects have created their creations according to the golden ratio in the hope of getting the best results in terms of aesthetics. Using any of the golden ratios, the architect can create a doorknob that matches the door, which in turn has a similar relationship to the walls and the room as a whole, and so on.
But most of all, the golden ratio is manifested in the facade of buildings-masterpieces of architecture: from the Parthenon to the Great Mosque of Kairouan, from the Sydney Opera House to the National Gallery in London.
The golden ratio in nature
The most amazing thing about the golden ratio is that it can be seen as a natural phenomenon in nature. The golden ratio is expressed in the arrangement of branches along the tree trunks, veins in the leaves. It can be seen in the structure of the skeletons of animals and people, in the branching of their veins and nerves.
It can even be seen in the proportions of chemical compounds and crystal geometry. In fact, it is around and within us, and for this reason the German psychologist Adolph Zeising (1810 - 1876) called it “a universal law, which contains the basic principle of the formation of everything, the pursuit of beauty and completeness in nature and art, which permeates as the primary spiritual ideal, all structures, forms and proportions, whether cosmic or individual, organic or inorganic, acoustic or optical; which is fully realized in the human body."
Due to the unique properties of the golden ratio, many consider it sacred or divine, allowing one to gain a deeper understanding of beauty and spirituality in life, to see the hidden harmony and coherence in everything that surrounds us.