Here’s something interesting:
Most people surely don’t realize that a rectangle with sides of 8 inches and 12.944271912 has been mathematically more pleasing to the eye than, say, a rectangle with sides of 5 inches and 10 inches? While it may sound farfetched to believe that aesthetics are so intimately related so such a thing as the size of a rectangle, rest assured that, for some strange reason, it happens to be unavoidably true.
A Mathematical Definition
While scientists have been unable to determine exactly what it is that makes a rectangle of this size more palatable than other sizes from a neurological perspective, they have at least been able to explain it mathematically.
Mathematicians call this phenomenon the Golden Ratio (often denoted in mathematics by the Greek symbol “phi” – j), and, as such, the rectangle previously described would be considered a Golden Rectangle. The Golden Ratio is slightly easier to understand if one considers a line divided into two segments; a long segment (A) and a short segment (B).
This remarkable ratio occurs when the ratio of A to B is equal to the ratio of the entire line (A+B) to the longer segment (A). Perhaps this seems complicated, but only until one actually takes the time to draw these line segments and get a visual perspective of this.
In other words, the rectangle described above is a golden rectangle because the ratio of the length of the short side to the length of the long side is exactly equal to the ratio between both of them put together to the length of the long side. In exact terms, this “golden” ratio between the sides of the rectangle is 1.618033989. Exactly.
The Golden Ratio in History
So, providing any of the preceding was understood (though rest assured, the mathematics do not have to be completely understood in order to understand or appreciate the principle itself), why is the Golden Ratio important to humanity? Well, for one thing, it has great historical value.
The ancient Greeks understood the unexplainable beauty in this ratio and used Golden Rectangles quite frequently in their famous architecture. The Parthenon in Greece particularly consists of several such ratios in many aspects of its design, as are the Great Pyramids in Egypt (referring to their height to base ratio). This focus on the aesthetics of mathematics spread throughout the world, and today the Golden Ratio can be seen in architecture in many countries across the globe. In addition, anyone who has overtaken a photography class has most likely heard of the 'rule of thirds,' which is referring specifically to the use of the ratio in taking photographs that are pleasing to the eye. This rule is based on the golden ratio.
Musicians might recognize that the golden ratio can be applied to the distance between the tonic note, the fifth and the major and minor sixth, among many other elements of theory. Those who place priorities on physical appearance might be interested in the theory that the Golden Ratio has been theorized to be directly related to human perceptions of beauty, though this has yet to be fully proven.
Indeed, there really seems to be no limit to places in the world that one can potentially observe the Golden Ratio in use. But this raises an important question:
Were all these uses of this ratio purposeful? Did the architects, engineers and artists understand the principle of the golden ratio and then design their works based on this knowledge, or was the purpose of their work simply to be as aesthetically pleasing as possible, and thus end up with the golden ratio as a result?
These questions are often disputed and rarely answered, but fortunately, they are not the point. The point is simply to recognize the existence of this phenomenon, and to begin to contemplate why it might be that the human brain has any preference at all in terms of ratio.
References:
“The Golden Ratio.” Wolfram Mathworld.
“The Golden Section Ratio: Phi.”
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