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Secret of the golden ratio revealed

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December 22, 2009

Leonardo da Vinci used the golden ratio in the Mona Lisa

Leonardo da Vinci used the golden ratio in the Mona Lisa

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The golden ratio describes a rectangle with a length roughly one and a half times its width. Also known as the golden section, golden mean and divine proportion, among other names, it has intrigued mathematicians and artists alike for centuries. The Egyptians supposedly used it to guide the construction the Pyramids, the architecture of ancient Athens is thought to have been based on it, and many artists have fashioned their works around it. This includes Leonardo da Vinci, who used it in the Mona Lisa and the Vitruvian Man. Now a Duke University scientist believes he has figured out the secret behind the golden ratio’s popularity – and it’s all down to evolution.

Adrian Bejan, professor of mechanical engineering at Duke's Pratt School of Engineering says the reason the golden ratio is thought to be the most aesthetically pleasing geometric proportion is because the eye is able to scan an image the fastest when it is shaped as a golden-ratio rectangle.

"When you look at what so many people have been drawing and building, you see these proportions everywhere," Bejan said. "It is well known that the eyes take in information more efficiently when they scan side-to-side, as opposed to up and down."

In 1996 Bejan developed his Constructal Law, which basically says that every finite-size (flow) system is destined to remain imperfect and the best that can be done is to optimally distribute the imperfections of the system. It is this optimal distribution of imperfection that generates the geometry or shape of the system. The theory says that flowing systems – from airways in the lungs to the formation of river deltas – evolve in time so that they flow more easily. Bejan believes that this same theory can be applied to the natural design that connects vision and cognition and thus explains the popularity of the golden ratio.

Bejan argues that the world – whether it is a human looking at a painting or a gazelle on the open plain scanning the horizon – is basically oriented on the horizontal. For the gazelle, danger primarily comes from the sides or from behind, not from above or below, so their scope of vision evolved to go side-to-side. As vision developed, he argues, the animals got "smarter" by seeing better and moving faster and more safely.

"As animals developed organs for vision, they minimized the danger from ahead and the sides," Bejan said. "This has made the overall flow of animals on earth safer and more efficient. The flow of animal mass develops for itself flow channels that are efficient and conducive to survival – straighter, with fewer obstacles and predators."

For Bejan, vision and cognition evolved together and are one and the same design as locomotion. The increased efficiency of information flowing from the world through the eyes to the brain corresponds with the transmission of this information through the branching architecture of nerves and the brain.

"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."

In numerous papers and books over past decade, Bejan has demonstrated that the constructal law predicts a wide range of flow system designs seen in nature, from biology and geophysics to social dynamics and technology evolution. Its latest application to explain the mystery of the golden ratio appears in the International Journal of Design & Nature and Ecodynamics.

About the Author
Darren Quick Darren's love of technology started in primary school with a Nintendo Game & Watch Donkey Kong (still functioning) and a Commodore VIC 20 computer (not still functioning). In high school he upgraded to a 286 PC, and he's been following Moore's law ever since. This love of technology continued through a number of university courses and crappy jobs until 2008, when his interests found a home at Gizmag.   All articles by Darren Quick
9 Comments

Don't tell this to the Chinese who have read vertically for millenia... ;)

matthew.rings
23rd December, 2009 @ 03:28 pm PST

Seriously, for a website/magazine that owes it's very existence to showing the world the amazing DESIGNS that people have come up with, you constantly tout random mindless evolution as the provider of every brilliant natural design out there, this is so logically inconsistent it boggles the mind.

glen.grady
23rd December, 2009 @ 04:49 pm PST

So if the tall tale of evolution is to be believed those with the best eyesight are the more highly evolved (according to "The secret of the golden ratio")...then eagles and flies are more highly evolved than humans and can appreciate beauty more....yeah right.... evolution makes so much sense....

Lora
24th December, 2009 @ 08:34 pm PST

Someone seems to be confusing ratios with orientations. I don't see the link here at all. It starts out talking about the golden ratio, but concludes with a rationalization for horizontal/landscape orientation. And since when has the golden ration be used or seen exclusively in one orientation?

soupisgoodfood
27th December, 2009 @ 08:31 am PST

Sounds like pseudo-science to me. Bejan forgot to mention that as animals developed olfactory cells, they minimized danger from upwind, thus making the flow of animals in that direction much safer. And thus the danger from predators was minimized by 50%. Especially if the predators were particularly stinky. Kind of like this article.

tjshire
29th December, 2009 @ 05:57 am PST

Lora, all living things that are alive today are, by definition, equally evolved. Please try to understand evolution before you discount it entitrely.

Facebook User
29th December, 2009 @ 03:11 pm PST

Felix: What a load of garbage you just spouted.

It is claimed by evolutionists, that all living things came from one single organism somewhere in the depths of time and that random, undirected mutations resulted in all the different species we have now. Putting aside the fact that this is also a load of garbage for a minute - If we assume that it is true (for the sake of argument) and then take your comment that all creatures are equally evolved, then logically we'd all be the same creature at the same "evolutionary" level, not different species/creatures. Therefore, the fact that different species exist at all, totally disproves your statement, so it just goes to show, that you don't even understand how evolution supposedly works anyway.

glen.grady
30th December, 2009 @ 04:06 pm PST

Aren't most "golden ratio" rectangles found in art, especially in the Mona Lisa, oriented vertically? The most widely used examples in architecture, like the Parthenon, or the Cathedral de Notre Dame have about one horizontal rectangle in their form for every 30 or so vertical ones, if I correctly recall my art appreciation class lectures. How does the use of these shapes in classical art have anything to do with scanning a horizontal horizon?

Eddie Sarphie
3rd January, 2010 @ 04:42 pm PST

What I have a difficult time with is why the computer industry has thrown out the Golden Ratio i.e approx 3 x 4 (portrait orientation) ratio which most printed materials (letters, magazines, newspapers, books) have used for years and going to HD which is 9 x 15 ratio?

If the Golden Ratio was good enough for deVinci, who today says they know better?

I've yet to see a printer printing in HD ratio when paper is based on 3 x 4

Azell
17th September, 2012 @ 06:05 pm PDT
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