We explain what the golden ratio is, its history and the golden number. Also, the golden ratio in nature and art.
What is the golden ratio?
It is called the golden ratio, divine proportion, golden section or golden ratio, but also the golden number or the golden rectangle, among other names, a mathematical element whose presence in artistic works architectural and even in objects of nature, supposedly explains its beauty
To understand what the golden ratio is, we must first understand the golden ratio, an irrational algebraic number, represented with the Greek letter phi (ϕ) in honor of the Greek sculptor Phidias (500-431 BC), although sometimes also with tau (Τ) or even with lowercase alpha (α), equivalent to 1.618033988749894… and (1 + √5) / 2.
This number has interesting mathematical properties and was discovered in Antiquity, but not as an arithmetic expression, but rather a geometric one: it is the relationship or proportion between two segments of a line a and b, which comply with the algebraic equation:
(a + b) / a = a / b
This relationship is called the golden ratio
Since then, humans have found this proportion in very different objects in nature, from the leaves of trees to the shells of turtles. It is also observed in various artistic and architectural works. It has even been given a certain mystical importance throughout history.
See also: Aesthetics
History of the golden ratio
According to some interpretations of archaeological discoveries, in the Mesopotamian cultures of 2000 BC. C. There is already evidence of use of the golden ratio, despite the fact that there is no documentation prior to Ancient Greece in which it is discussed.
The first formal studies of the golden ratio belong to the philosopher Euclid (c. 300-265 BC) in his book The elementswhere it is shown that it is an irrational number, and some others are attributed to Plato himself (c. 428-347 BC).
In 1509, the Italian theologian and mathematician Luca Pacioli (c. 1445-1517) suggested the divine connection of such a number in his Of divine proportione (“On divine proportion”). Pacioli claimed that it was defined by three straight segments like the Divine Trinity, which was uncomprehensible in its entirety like God, and presented other characteristics interpretable as a metaphor for the sacred.
No doubt influenced by this idea, the German Renaissance artist Albrecht Dürer (1471-1528) designed the golden spiral in 1525 later called “Dürer's spiral”: the artist described how to draw a golden spiral based on divine proportion with a ruler and compass.
There are other references to the golden ratio in the works of Johannes Kepler (1571-1630) and Martin Ohm (1792-1872), the latter being the one who coined the name “golden section” in 1835. However, there is evidence that the name was in common use already at that time.
Since then it has been represented with the Greek letter tauuntil in 1900 the mathematician Mark Barr replaced it with phias a tribute to the Greek sculptor Phidias.
Golden ratio in nature
Some examples of the golden section being found in nature include:
- The logarithmic spiral inside the shells of marine animals called nautiluses.
- The disposition of the petals of many flowers according to Ludwig's Law.
- The relationship between the veins of the leaves of most trees.
- The number of spirals present in the rind of a pineapple.
- The distance from the navel to the feet of any person, with respect to their total height.
- The arrangement of the artichoke leaves.
Golden ratio in art
According to some scholars, the closer a work is to the golden section, the more beautiful it will be or the closer it will be to definitive beauty. There is no scientific evidence of this, but it is true that the golden ratio can be found in the following artistic, sculptural or architectural works:
- In the relationships between the forms of the Great Pyramid of Giza according to the theses of Herodotus in his History.
- The relationship between the parts, columns and roof of the ancient Greek temple known as the Parthenon in Athens.
- In the formal structures of the sonatas of Wolfgang Amadeus Mozart as well as in Beethoven's Fifth Symphony, and later in works by Schubert and Debussy.
- In the painting atomic leda (1949) by the surrealist painter Salvador Dalí.
- In the time structure of the films Battleship Potemkin (1925) and Ivan the Terrible (1944) by Soviet filmmaker Sergei Eisenstein.
- The Italian pictorial movement of Povera art He based his paintings on the succession of Fibonacci numbers, which embody the golden ratio.
Continue with: Scale
References
- “Golden ratio” on Wikipedia.
- “The Golden Ratio” (video) in Concienciame2.
- “The golden ratio: truths and myths of the “magic” number” in ABC Ciencia (Spain).
- “The divine proportion, the golden ratio, the golden rectangle and the golden number” in Descartes 2D in TIC Resources (Spain).
- “The Golden Ratio” (video) on Khan Academy.
- “Golden ratio (mathematics)” in The Encyclopaedia Britannica.
