Divine Harmony

The ratio of the golden proportion is cropping up in the strangest of places.

One of the surviving biographies of Pythagoras relates the story of one of his followers who falls sick and stops at an inn. The innkeeper lavishes care on the man, but despite all the money he spends, is unable to save him. The dying man draws a pentagram at the gates of the inn. Years later a Pythagorean happening to pass by sees the pentagram and repays the innkeeper. For Pythagoreans, the pentagram, a five-pointed star, was a divine symbol identifying them as disciples of Pythagoras. It incorporated the golden ratio, a ratio best described by a rectangle of sides a and a+b where a/b = (a+b)/a. This ratio is roughly 1.618 and is believed to give rise to the rectangle that is most pleasing to human eyes. It has been argued that buildings such as the Parthenon and Taj Mahal make use of the golden ratio. So much so that artists and architects ranging from Leonardo da Vinci to Le Corbusier have used the ratio extensively.

Now Adrian Bejan, professor of mechanical engineering at Duke University, in Durham, North Carolina, has claimed that human eyes interpret an image featuring the golden ratio faster than any other: “It is well known that the eyes take in information more efficiently when they scan side to side, as opposed to up and down. When you look at what so many people have been drawing and building, you see these proportions everywhere.”

But just because our brains are designed to find this ratio pleasing does not mean that it does not reflect a fundamental symmetry of the universe. Scientists studying quantum effects have recently announced the result of their work on the magnetic material cobalt niobate. They found that under the effects of a magnetic field, the chain of atoms act like a very miniature guitar string. Dr Radu Coldea from Oxford University explains: “…we found a series of resonant notes: The first two notes show a perfect relationship with each other. Their frequencies are in the ratio of 1.618…, which is the golden ratio.” Pythagoras would not have been surprised.

golden proportionPythogoras