The Golden Ratio: Design's Biggest Myth (features Keith Devlin)

In the world of art, architecture, and design, the golden ratio has earned a tremendous reputation. Greats like Le Corbusier and Salvador Dalí have used the number in their work. The Parthenon, the Pyramids at Giza, the paintings of Michelangelo, the Mona Lisa, even the Apple logo are all said to incorporate it.

It's bullshit. The golden ratio's aesthetic bona fides are an urban legend, a myth, a design unicorn. Many designers don't use it, and if they do, they vastly discount its importance. There's also no science to really back it up. Those who believe the golden ratio is the hidden math behind beauty are falling for a 150-year-old scam.

First described in Euclid's Elements 2,300 years ago, the established definition is this: two objects are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The value this works out to is usually written as 1.6180.

The most famous application of the golden ratio is the so-called golden rectangle, which can be split into a perfect square, and a smaller rectangle that has the same aspect ratio as the rectangle it was cut away from. You can apply this theory to a larger number of objects by similarly splitting them down. In plain English: if you have two objects (or a single object that can be split into two objects, like the golden rectangle), and if, after you do the math above, you get the number 1.6180, it's usually accepted that those two objects fall within the golden ratio. Except there's a problem. When you do the math, the golden ratio doesn't come out to 1.6180. It comes out to 1.6180339887... And the decimal points go on forever.

"Strictly speaking, it's impossible for anything in the real-world to fall into the golden ratio, because it's an irrational number," says Keith Devlin, a professor of mathematics at Stanford University. You can get close with more standard aspect ratios. The iPad's 3:2 display, or the 16:9 display on your HDTV all "float around it," Devlin says. But the golden ratio is like pi. Just as it's impossible to find a perfect circle in the real world, the golden ratio cannot strictly be applied to any real world object. It's always going to be a little off.

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