The Golden Ratio: in harmony with the Universe
January 27th,2009
The Golden Ratio has been (and is) interpreted in different ways, depending on the period, country, religion etc.:
The Golden Section as “Universal Harmonic Ratio“
- 5th century b.C.
The mathematical concept of proportion, meant to relation of parts, has been introduced first by Pitagora (Pythagoras of Samos, a great mathematician, mystic and scientist), who combines balance with mathematic.
Pythagoras and his followers (the Pythagoreans), re-created the composing principles of musical harmony to obtain a kind of “universal harmony”, in order to obtain a stable equilibrium. - 18th - 20th century A.D.
The concept of “the Golden Section as Universal Harmonic Ratio” has been used, in classical music, by great composers as Bach (fugues), Mozart (piano sonatas), Beethoven (Symphony No. 5 in C minor, Op. 67), Schubert (Piano Sonata D 959), Debussy (La Mer) and Strawinski (Le Sacre du Printemps - Symphony in Three Movements). These pieces carry the music back to its pythagoric orgin: by mathematical nature, in which the Golden Ratio is the core of the opus.
The Golden Section as “Pleasant-looking Ratio“
- 3rd century b.C.
In the Euclid’s Elements (a mathematical and geometric treatise) the shape of the triangle is one of the most important, in particular the sublime triangle.
The sublime triangle is a isosceles triangle. It can be formed by the conjunction of two diagonals starting from the vertex of a pentagon. The side of the regular pentagon is the Golden Section of the sublime triangle (its base). Triangle inscribed into a regular pentagon form into a star. The golden star. - 16th century A.D.
In 1509 has been published the De divina proporzione ( The divine proportion - a treatise on mathematical and artistic proportion, especially the mathematics of the golden ratio and its application in architecture) written by Luca Pacioli, an italian mathematician and franciscan friar and illustrated by Leonardo da Vinci. The adjective “divina” (divine) used in the title of the treatise referes to two deity’s characteristics: the golden section is UNIQUE and TRIPLE as the Trinity ( indefinable, irrational and invariable ). Luca Pacioli has been probably the first who used the term Sectio Aurea (Golden Section). - 18th century A.D.
The concept of formal beauty has been increased by Kant (German philosopher), who introduced the category of sublime in the aesthetics experience. His main claim is that the mathematic judgments are synthetic a priori.
Synthetic because the result expand the knowledge; a priori because the geometric and mathematic judgments are valid also without experience. According to Kant, the Sublime is endless (synthetic demonstration of Space as geometrical space and synthetic demonstration of Time as arithmetic series).
The Golden Section as “Holy Ratio“
- 9th century b.C. - 3rd century A.D.
The Golden Ratio has been highly used in holy symbolism, as in the Pentaculum Salomonis, in the Sigillum Pythagorae (symbol of health), in the Templar Cross and, in Germany, in the Druidenfuss (druid’s foot). Some of these symbols were considered diabolic; others, as the golden star, symbol of union between God and the human being.
The Golden Section as “Mathematical Ratio“
- 12th century A.D.
In the Liber Abaci (Book of Abacus) of Fibonacci, Italian mathematician, he introduces a problem involving the growth of a hypothetical population of rabbits. The solution is a sequence of numbers known as Fibonacci numbers. This sequence can be found in natural phenomenon: ray of light’s optics, male bee’s genealogical tree, fire genealogy and so on.
In the Fibonacci sequence, each number is the sum of the previous two. The higher up in the sequence, numbers divided by each other will approach the Golden Ratio: 1.618 (phi).
IN SUMMARY: The Golden Section can be found in lots of fields and it is conceived in different ways. By the way, it is symbol of harmony and perpetual perfection.
There is someting more! Have a look on the <art>IMHO</art> main menu on top. The philosophy button is showing part of the Luca Pacioli’s De divina proporzione. I’ve a copy of the real manuscript. It’s really amazing! I will try to share part of it with you, later.
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Thank you
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