From Leonardo da Vinci to Le Corbusier, the golden ratio is believed to have guided artists and architects over the centuries.
Leonardo is thought to have used the golden ratio, a geometric proportion regarded as the key to creating aesthetically pleasing art, when painting the Mona Lisa. The Dutch painter Mondrian used it in his abstract compositions, as did Salvador Dali in his masterpiece The Sacrament of the Last Supper.
Now a US academic believes he has discovered the reason why it pleases the eye. According to Adrian Bejan, professor of mechanical engineering at Duke University, in Durham, North Carolina, the human eye is capable of interpreting an image featuring the golden ratio faster than any other.
Bejan argues that an animal's world – whether you are a human being in an art gallery or an antelope on the savannah – is orientated on the horizontal. For the antelope scanning the horizon, danger primarily comes from the sides or from behind, not from below or above, so the scope of its vision evolved accordingly. As vision developed, he argues, animals got "smarter" and safer by seeing better and moving faster as a result.
"It is well known that the eyes take in information more efficiently when they scan side to side, as opposed to up and down. When you look at what so many people have been drawing and building, you see these proportions everywhere."
Many artists since the Renaissance have proportioned their work in accordance with the golden ratio or "divine proportion", particularly in the form of the golden rectangle, which has informed Leonardo's work. It describes a rectangle with a length roughly one and a half times its width.
Works most usually associated with it are the Mona Lisa and the Parthenon in Athens, although Swiss architect Le Corbusier relied on it for his Modulor system for the scale of architectural proportion and Dali explicitly used it in The Sacrament of the Last Supper. The Parthenon's facade is said to be circumscribed by golden rectangles, though some scholars argue that this is a coincidence.
According to Bejan, these arguments are academic. Whether intentional or not, the ratio represents the best proportions to transfer to the brain. "This is the best flowing configuration for images from plane to brain and it manifests itself frequently in human-made shapes that give the impression they were 'designed' according to the golden ratio," said Bejan.
"We really want to get on, we don't want to get headaches while we are scanning and recording and understanding things," he said. "Shapes that resemble the golden ratio facilitate the scanning of images and their transmission through vision organs to the brain. Animals are wired to feel better and better when they are helped and so they feel pleasure when they find food or shelter or a mate. When we see the proportions in the golden ratio, we are helped. We feel pleasure and we call it beauty."
Bejan, an award-winning engineer who developed a new law of physics governing the design of matter as it moves through air and water in 1996, believes this "constructal law" governs systems that evolve in time, from cars in traffic to blood in the circulation, to how vision develops.
Vision and cognition evolved together, he said. "Cognition is the name of the constructal evolution of the brain's architecture, every minute and every moment," Bejan said. "This is the phenomenon of thinking, knowing, and then thinking again more efficiently. Getting smarter is the constructal law in action."
Earlier this year, in a paper published in the Journal of Experimental Biology, Bejan demonstrated how this law was behind his theory of how elite athletes had got taller, bigger and thus faster in the past 100 years. His latest application of constructal law to explain the golden ratio is published online in the International Journal of Design & Nature and Ecodynamics.