In the quest for beauty, one of the most immutable traditions – and controversial fascinations – in Western architecture (and furniture and art and music and mathematics) is the golden section, a proportioning system first described by ancient Greek mathematicians such as Euclid and Pythagoras, but also observable in nature.

And even if the equation to derive the ratio – (a+b)/a = a/b = 1.618 – is, well, Greek to most of us, the manifestations – what it looks like – shouldn’t be. It shows up constantly: It’s the aesthetically pleasing shape of a standard credit card (the ultimate golden rectangle, as it were); Aston Martin uses it to proportion its expensive (yet undeniably sexy) sports cars. It was used by painters such as Da Vinci, Dali and Mondrian to compose their masterpieces, and it’s often ascribed to the front facade of the Parthenon (although some academics say there is no proof that it was done so consciously).

As further evidence of its ubiquity, in 2010, Singaporean industrial designer Olivia Lee released a sketchpad with grid lines based on the proportion. She then used the pad to sketch out famous buildings and products that were influenced by the ratio, including a Chanel clutch, a Philippe Starck lemon juicer, the famous Verner Panton chair and a building by architect Rem Koolhaas (Beijing’s CCTV headquarters, which looks a bit like a jagged bagel).

This last example is part of the reason the ratio is particularly special: It’s among the few aesthetic traditions that has lasted more-or-less continuously throughout the history of Western architecture. While no one seems too keen on building pyramids or Baroque cathedrals any more, a structure that has windows or rooms sized according to the golden ratio is not uncommon. And it happens as much in large public buildings – famed American architect Steven Holl is a proponent, having recently finished an addition to the Glasgow School of Art in Scotland based around the golden section – as in homes.

There is scientific evidence to suggest that the appeal of the proportion is, in fact, natural. In 2009, Adrian Bejan, a professor of mechanical engineering at Duke University, in North Carolina, completed a study on the proportion. He found that things shaped according to the golden ratio – be it a paragraph of text or a painted canvas – were the easiest for a human’s eyes and brain to perceive and understand. Because the shape helps with quick cognition, and because humans appreciate being helped, it makes us feel good, so “we feel pleasure and we call it beauty,” Bejan told The Guardian in 2009.

But he also notes: “I understand the golden section as a tool. Someone with no talent will never produce something good by using it. To make poetry, you have to know more than grammar, but you have to know grammar nonetheless.”

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