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# Examples of the Golden Ratio (?)

The Golden Ratio can be found in geometric forms and in nature. But what about art?

We like to see structures. Even more so when surrounded by a certain mystery.
Perhaps the most important example of this phenomenon is the assertion that the Golden Ratio is hidden in the Parthenon. The discovery has been adopted unquestioningly by numerous people. However, it is not based upon fact. The master builders of the Parthenon did not leave any notes. So what happens is: afterwards several measurements are made which show a ratio of approximately 0,6. A ratio determination with greater accuracy is not possible, let alone up to 3 decimals. Furthermore, the claim of the Golden Ratio is underlined by this kind of illustration:

with no accuracy whatsoever.
Many illustrations of works of art can be found on the Internet where attempts are made to point out the proportions of the Golden Ratio with thick lines, in the same way:

Some of these attempts become laughable:

Another widespread misconception concerns the Nautilus shell:

The spiral is not based on Fibonacci numbers but is logarithmic in nature. The principle that growth is proportional with the present measurement causes this kind of growth and can be found in many biological systems. Every new grown part being uniform with the last one is the basis of exponential growth.
The beautiful clip of Cristóbal Vila (see Fibonacci and the Golden Ratio also contains this shell, however it is incorrect (which Vila himself admits).

If a piece of art is not explicitly and precisely based on the Golden Ratio that ratio cannot be found.
An artist who indeed made an effort to make the Golden Ratio an element of his work is Le Corbusier. Between 1940 and 1950 he developed, with his Modular, a measurement system based on the Golden Ratio. Le Corbusier derives the ratios from the human body. He applies the ratios in constructions, however when not convenient for him, he deviates from them.

Another example is Salvador Dali. In his Leda Atomica Dali makes use of the pentagram and the Golden Ratio.

What about music? The presumption that Bartok used Fibonacci numbers is now scientificly rejected. It is tempting to prove things with numbers, but quickly one arrives in the world of cabbalists where all kind of things are tried to be proven with disputable calculation.
For instance the tones of the octave. Many people perceive the numbers 3, 5 and 8 as Fibonacci numbers. For a start: why choose for number 8? Why not 7? After all the 8th tone upon the keynote is the fundamental of the next octave. What about the 5 black keys within the octave? A pure coincidence. And what to do with 3, 5 and 8 when there is no continuation? Again, there is a desire to see something which is not there.

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