The golden section (or golden ratio) has fascinated Western intellectuals of diverse interests for over two thousand years. Basically, two quantities are ‘golden’ if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. If you can get your head around this, you may start to notice how this ratio appears frequently in mathematics, architecture and the arts — especially in the form of the ‘golden rectangle’, in which the ratio of the longer side to the shorter is, in the above sense, ‘golden’. Through the ages, the golden ratio has been regarded as having unique and interesting properties, both because it is intrinsically aesthetically pleasing and because it may have a deeper meaning. Some of the greatest mathematical minds in history, from Pythagoras and Euclid in ancient Greece, to the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, have spent endless hours musing over the golden ratio and its properties. Even today, the golden ratio is used in the analysis of financial markets, in strategies such as Fibonacci retracement. But the fascination with the golden ratio is not confined just to mathematicians: biologists, artists, musicians, historians, architects, psychologists, and even mystics have for centuries pondered and debated the basis of its ubiquity and appeal. This inevitably invites the question – what is it about the golden ratio that has so intrigued thinkers of all disciplines?
Ghost Cities 