The Haunting 'Golden Ratio'

In 2002, I published the book The Golden Ratio, about the irrational number (known in the popular literature as PHI) which is equal to 1.61803...

One of my main goals has been to debunk various myths about this number, and to show that it does not appear in many of the instances in which it had been claimed that PHI plays a central role. In fact, mathematician and author Ian Stewart nicely wrote in his review of the book that I was "careful to separate the myth from the math, explaining the sense and exploding the nonsense."

Needless to say, many "believers" were not convinced. In the years that have passed since the publication of the book, I have been bombarded with e-mails and letters about the Golden Ratio. Many of those letters were fascinating, pointing out actual appearances of the Golden Ratio in a variety of physics phenomena that I had not mentioned in the book, such as the optimal rotations of deformable bodies, the physics of black holes, and symmetries in the quantum world of solid state matter.

Many others, however, only tried (unsuccessfully I might add) to convince me that I had been wrong in dismissing as myths some appearances of the Golden Ratio. In any case, I have happily resigned myself to the idea that the Golden Ratio will continue to follow me wherever I go. Consequently, I was not surprised when during a recent visit to New York I discovered that a restaurant in Brooklyn had a painting depicting the Golden Ratio on its wall (Figure 1 shows me in front of the painting). Only a week later, during a seminar I gave at the Smithsonian in Washington DC, I discovered that a photo exhibit there included an image of the spiral cross-section of a Nautilus pompilius shell. While not precisely exhibiting the Golden Ratio, these shells do form logarithmic spirals (they do not alter their shape as their size increases), and the Golden Ratio can be used to easily generate such logarithmic spirals.

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Figure 1. A painting with the theme of the Golden Ratio in a Brooklyn restaurant.

The bottom line is simple. Exercise caution before accepting any claim about the Golden Ratio as real (most are false), but at the same time, the Golden Ratio does have this uncanny way of popping up where least expected.