For more than 2,000 years, philosophers, mathematicians and artists have marveled at the unique properties of the “golden rectangle”: subtract a square from a golden rectangle, and what remains is another golden rectangle, and so on and so on — an infinite spiral. These so-called magical proportions (about 5 by 8) are common in the shapes of books, television sets and credit cards, and they provide the underlying structure for some of the most beloved designs in history: the facades of the Parthenon and Notre Dame, the face of the “Mona Lisa,” the Stradivarius violin and the original iPod.

Experiments going back to the 19th century repeatedly show that people invariably prefer images in these proportions, but no one has known why.

Then, in 2009, a Duke University professor demonstrated that our eyes can scan an image fastest when its shape is a golden rectangle. For instance, it’s the ideal layout of a paragraph of text, the one most conducive to reading and retention. This simple shape speeds up our ability to perceive the world, and without realizing it, we employ it wherever we can.

Lance Hosey, author of The Shape of Green: Aesthetics, Ecology, and Design, exploring the beauty of the golden ratio and fractals in The New York Times.