What is this ratio?
Dan Brown in his book De Vince Code explained how the golden ration interferes with artists work, Living creatures and Plants.
Some scientists linked it to more than 2400 years ago.
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.
Ancient Greeks studied it for its frequent appearance in Geometry. They attributed the discovery to Pythagoras.
Beginning in the Renaissance, a body of literature on the aesthetics of the golden ratio was developed.
As a result, architects, artists, book designers, and others have been encouraged to use the golden ratio in the dimensional relationships of their works.
A geometrical analysis of the Great Mosque of Kairouan, Tunisia, reveals a consistent application of the golden ratio throughout the design, according to Boussora and Mazouz.
It is found in the overall proportion of the plan and in the dimensioning of the prayer space, the court, and the minaret. Boussora and Mazouz also examined earlier archaeological theories about the mosque, and demonstrate the geometric constructions based on the golden ratio by applying these constructions to the plan of the mosque to test their hypothesis.
Speaking about Islamic Architect, it is worth mentioning that the Quran emphasized in so many verses that God created everything in proportion, Gave wealth and power in proportion, caused rain in proportion.
Miracle of Kaaba - English Version from Erdem Cetinkaya on Vimeo.
Some Islamic scholars are trying to prove that Mecca and Kaaba are good examples of the golden proportion.
This is why scientists refer to is as the Divine Ratio.
Both Egyptian pyramids and those mathematical regular square pyramids that resemble them can be analyzed with respect to the golden ratio and other ratios.
One Egyptian pyramid is remarkably close to a "golden pyramid" – the Great Pyramid of Giza (also known as the Pyramid of Cheops or Khufu).
The golden ratio is also apparent in the organization of the sections in the music of Debussy's Reflets dans l'eau (Reflections in Water), from Images (1st series, 1905), in which "the sequence of keys is marked out by the intervals 34, 21, 13 and 8, and the main climax sits at the phi position.
Its slope of 51° 52' is extremely close to the "golden" pyramid inclination of 51° 50' and the π-based pyramid inclination of 51° 51'; other pyramids at Giza (Chephren, 52° 20', and Mycerinus, 50° 47' are also quite close.
The height of the great pyramid is equal = 146.515 meters, and its base equals 230.363 meters.
The Pharaohs used a simple math to find that half of the base is 115.182 m and the "slant height" is 186.369 meters.
Dividing the "slant height" 186.369m by "half base" 115.182m gives 1.6180, which is practically equal to the golden ration!
The Pharaohs bring this ratio by discovering that the earth/moon relationship is the only one in the solar system that contains this unique golden section ratio that "squares the circle.
If the base of the great pyramid is equated with the diameter of the earth, then the radius of the moon can be generated by subtracting the radius of the earth from the height of the pyramid.
The height of the great pyramid times 2p exactly equals the perimeter of the pyramid.
This proportion results from elegant design of the pyramid with the height equal two diameters of a circle and the base equal to the circumference of the circle.
The number Pi is the mathematical constant 3.1415, with the ratio of the diameter to the distance around the circle, called the circumference.
In the pyramid it is the ratio of the height to twice the length of the base.
Whether the relationship to the golden ratio in these pyramids is by design or by accident remains controversial. Several other Egyptian pyramids are very close to the rational 3:4:5 shape.
Trezise finds the intrinsic evidence "remarkable," but cautions that no written or reported evidence suggests that Debussy consciously sought such proportions.
Also, many works of Chopin, mainly Etudes (studies) and Nocturnes, are formally based on the golden ratio. This results in the biggest climax of both musical expression and technical difficulty after about 2/3 of the piece.
Pearl Drums positions the air vents on its Masters Premium models based on the golden ratio. The company claims that this arrangement improves bass response and has applied for a patent on this innovation.
Long before the advent of digital recordings, the Babylonians and Hindus, and then Pythagoras and his followers translated music into number and geometric proportions (Durant 1939).
For example, by dividing a vibrating string into various ratios they discovered that several very pleasing musical intervals could be produced.
Hence, the ratio 1:2 was found to yield an octave, 2:3 a fifth, and 3:4 a fourth, 4:5 a major third, and 5:6 a minor third (McClain 1978).
The harmonic system utilized in the nineteenth century by various composers was based on these same ratios. Indeed, Bartok utilized these ratios in his musical compositions.
These same musical ratios, the Pythagorians discovered, also were found to have the capability of reproducing themselves. That is, the ratio can reproduce itself within itself and form a unique geometrical configuration which Pythagoras and the ancient Greeks referred as the the "golden ratio" or "golden rectangle." The gold rectangle was postulated to have divine inspirational origins. Indeed, music itself was thought by early man to be magical, whereas musicians were believed by the ancient Greeks to be "prophets favored by the Gods" (Worner, 1973).
The Golden Ratio has fascinated layman and mathematician for centuries.
It seems like magic that it turns up in such different arenas as pine cones, earth-moon and planet relationships, the Cheops Pyramid in Egypt, the Mona Lisa and even our DNA.
Indeed its widespread appearance shows that there is a unifying mathematical principle that is more subtle than science has thus far been able to define.
It remains a mathematical mystery or should we say .......
God's Mystery...
Sami Cherkaoui
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