Part 5: Last question on the golden rectangle

Part 5: Last question on the golden rectangle - I got to the end of my search for the truth about the golden ratio. But I had one last question. Is this the "golden rectangle" really more attractive than other rectangles?

The response was not what I thought, not what I wanted hear.

I had always accepted as an aesthetic axiom that rectangle golden section (along with 1 large 1.618) represented the ideal, the same proportion "divine." was there a way to prove it?


in the 1860s, a psychologist named Gustav Fechner conducted experiments to explore this question. He presented subjects with a range of different rectangles, and asked them which was their favorite

the results showed that 76% of all the choices focused on three rectangles with ratios of 1.75: 1, 1.62: 1 and 1.50: 1. the winner was the "Golden Rectangle" (D, above, with a ratio of 1618: 1)..

This seemed to settle the matter for decades Beauty, it seems, could be defined in terms a specific mathematical harmony of proportions.

Unfortunately, the conclusion of Flechner unraveled that future scientists tested the hypothesis rigorously. According to the expert in mathematics Mario Livio,

"[University of Toronto professor Michael] Godkewitsch concluded from a study conducted in 1974 that the preference for the golden rectangle reported in earlier experiments was an artifact . the position of the rectangle in the range of rectangles shown to topics it noted: "the fundamental question of whether there is or not, in the Western world, an aesthetic preference expressed verbally reliable for a particular ratio between the length and width rectangular shapes can probably be answered negatively. "

Thus, it seems, no rectangle is different from other as" gold "or unique beauty. If a gives us a warm feeling, maybe because we're trained to appreciate it.


The more I thought, the more it made sense. If the golden rectangle (1.618: 1) was really the ideal form, why not occur everywhere in our environment carefully designed? Why do we not find in the proportions of the cinema screen (1.37: 1, 1.85: 1, 2.35: 1), photographs (1.50: 1) TV screens (1.33: 1 , 1.78: 1) computer monitors (1.33: 1, 1.60: 1, 1.78: 1), credit cards (1.5858: 1), not to mention iPhones, tablets and paper Office? These rectangles, each so commonplace in our daily lives, vary widely, and none of them quite matches the assumed ideal.

Perhaps there is a deeper truth aesthetic to glean from all this. A masterpiece it is, does not issue fixed mathematical rules. It comes from a blend of all the elements of composition cohering with messy particularity. For a table, a 3x4 rectangle could be the perfect choice; for another, a square can give divine results. The central idea of ​​the image should drive the decision. Just as there is no optimal operation length for a film, no optimal key for a symphony, and no optimal structure for a poem, there is no optimal form for a painting.

I welcomed these revelations as inspiration rather than disillusion. Art can not be reduced to an absolute formula. Gold conditions the situation, not predestined. A great creation pierces our hearts by an unexpected combination of factors. Beauty comes in the night and just flat outside our window, shift and shimmer, floating just beyond the reach of our ropes and stirrups, unwilling to integrate into any box we build for it.

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Book: The Golden Ratio: The Story of PHI, the most amazing number of world by Mario Livio
article: "Golden sales pitch" (selling blue jeans with gold means) by Julie Rehmeyer
site over Math Mario Livio, "the Golden Ratio and aesthetic"
Winding through mathematics by Phil Keenan

more experimental results testing the golden rectangle

graphic Iphone Overthinker

golden mean the complete series on GurneyJourney:

Part 1: Demystifying the average gold (Parthenon)

Part 2: the average gold and Leonardo
Part 3: How the average gold caught on with artists
Part 4: the golden mean and the human body
Part 5: Last question on the golden rectangle