# Why some shapes are more pleasing to the eye than others

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The Independent Online

The ancient Egyptian pyramids, the Parthenon of 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 half times its width. The proportion is said to pervade art, architecture and nature.

The modernist architect Le Corbusier used the golden ration for conferring harmonius proportions on everything from door handles to high-rise buildings, whereas the surrealist painter Salvadore Dali deliberately incorporated the rule into his painting Sacrament of the Last Supper.

Now a theoretical mathematician has come up with what he believes is a possible reason why the human eye finds shapes in these proportions so particularly appealing. 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 said that the golden ratio – which was first identified mathematically by Euclid in 3rd Century BC – just happens to be the most efficient shape for visual scanning, which could explain why it is behind so many works of art and architectural wonders.

“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,” he said.

Professor Bejan has applied a mathematically-based 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. It may also explain why some faces that approximate more closely than other 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. This was also the proportions of the average face.