The ancient Egyptian Pyramids, the Parthenon in Athens, Mona Lisa's face and the head of George Clooney all have one thing in common. Their attractiveness is said to be based on the "golden ratio", which is supposed to be the most aesthetically pleasing shape to the human eye.
The golden ratio, also known as the divine proportion, produces a shape similar to a widescreen television or a cinema screen and describes a rectangle with a length roughly one-and-a-half times its width. The proportion is said to pervade art, architecture and nature in both its horizontal or vertical format.
The modernist architect Le Corbusier used the golden ratio for conferring harmonius proportions on everything from door handles to high-rise buildings, whereas the surrealist painter Salvadore Dalí deliberately incorporated the rule into his painting Sacrament of the Last Supper.
Now a theoretical mathematician has come up with a possible reason why the human eye finds shapes in this proportion so appealing, saying it comes down to how easy it is for the eye and the brain to scan such an image for important details, based on our evolutionary history.
Professor Adrian Bejan of Duke University in North Carolina has claimed that the golden ratio is the most efficient shape for visual scanning. "When you look at what so many people have been drawing and building, you see these proportions everywhere. It is well known that the eyes take in information more efficiently when they scan side-to-side, as opposed to up and down," Professor Bejan said.
"Scanning left to right is five times faster than scanning up and down and that is largely due to the left or right eye taking over when the opposite eye gives up. When you scan vertically, it's like having just one eye. The eyes are also arranged on a horizontal axis, which happens to fit in with the landscape."
Professor Bejan has applied a mathematical law he devised in 1996 to describe how designs in nature, from the flow of water in river deltas to the branching airways in a set of lungs, are geared towards ever-increasing efficiency of movement, such as the faster flow of water, air, blood or even individuals in a crowd.
Vision is also subject to increased efficiency based on the faster flow of information from the eye to the brain. And the visual scene that is easiest to scan is one where the horizontal axis is wider than the vertical, Professor Bejan said. This is true for a gazelle scanning the African horizon for predators, or early human hunter-gatherers searching their territory for food.
"Animal vision should be configured in a way that seeing and scanning should be the fastest and the easiest. And when the proportions allow this to be done, it should be a source of pleasure because of its past evolutionary associations with finding food or a mate," Professor Bejan said. According to the theoretical study published in The International Journal of Design and Nature and Ecodynamics, the most efficient proportions for the human eyes to scan is a rectangular shape where the horizontal is about one-and-a-half times the vertical, which Professor Bejan said approximates to the golden ratio.
"[It] is a consequence of the fact that our perceived world is roughly a horizontal tableau. Our supply of images reflects the orientation of the landscape. Danger comes to the animal from the sides and from behind, not from above, and not from below," Professor Bejan said.
Perceiving the world through a rectangular box has led to this particular shape becoming aesthetically pleasing and being subconsciously incorporated into works of art whether the rectangle is horizontally or vertically positioned. It may also explain why some faces are viewed as being the most attractive.
A recent study by scientists at the University of Toronto found that female faces were judged the most attractive if the vertical distance between the eyes and the mouth was approximately 36 per cent of the face's length, and the horizontal distance between the eyes was approximately 46 per cent of the facial width. These were also the proportions of the average face.
* The golden ratio was first described about 300BC by Euclid of Alexandria, who came to it by describing how to divide a straight line in a certain proportion. The ratio came out approximately as the number 1.618, known by the Greek letter "phi".
* Since then, successive generations of mathematicians have pondered over its properties and significance. Others have pointed out that the golden ratio - in terms of a rectangle with certain proportions - can also be seen in many works of art and architecture.
* The Parthenon in Athens is described as a prime example of the golden ratio, yet there is no evidence that the Greek architect Phidias knew of its existence.
* The same goes for Leonardo da Vinci, despite his Mona Lisa apparently using a golden-ratio rectangle in the face of La Gioconda. Leonardo was a close friend of Luca Pacioli, who published a three-volume treatise on the ratio in 1509.
* Le Corbusier, the modernist artist and architect, is known to have been fascinated with the golden ratio and incorporated it into his designs.
* Salvadore Dalí also consciously used it in his painting The Sacrament of the Last Supper, where a huge dodecahedron based on the golden ratio engulfs the sacred table.
* The golden ratio is also seen in nature and perhaps the most intriguing place is in the human face. George Clooney, left, is said to epitomise the golden ratio - and most women (and a lot of men) agree.
Visual alchemy The golden ratio