The beauty of the golden ratio, surely, lies in the discovery of harmony in imbalance — that is, it’s not a symmetrical division, but a bit more interesting and lively. In architecture, the piers and windows of Durham Cathedral seem to apply it as assiduously as in the Parthenon in Athens. But why such mystique?
The attitude of the ancient Greek thinker Pythagoras to number (that it is the key to the secret harmony of the universe) survived in the middle ages in Muslim and Christian architecture. In the Renaissance, Leonardo da Vinci took it to new extremes, analysing the perfect proportions of a horse and a human and finding number at the heart of nature. In 1504 he was designing fortifications for an Italian town. While researching this, I puzzled over diagrams of pyramids that keep interrupting plans for towers — until I understood that Leonardo believed so passionately in the power of proportion that he thought it could make a castle invulnerable. He illustrated his friend Fra Luca Pacioli’s book The Divine Proportion, which praises the golden ratio, and so helped to create one of the most persistent cults in maths and art.
Whether or not the golden ratio really has any special significance in human psychology, it has been given that status by artists like Leonardo and the great 15th-century painter Piero della Francesca, whose geometrically pleasing art is rooted in mathematics. The persistent pursuit of this proportion right down to Le Corbusier proves that mathematics and art come from the same beautiful place in our minds.
So how do you find this special proportion? Divide a straight line in two so that the ratio of the whole length to the larger part is the same as the ratio of the larger part to the smaller part. The result (roughly 1.62 to 1) is the golden ratio. — © Guardian Newspapers Limited, 2009
( Note: Jonathan Jones’s book about Leonardo da Vinci will be published by Simon and Schuster in April 2010.)