The appeal of the divine proportion to the human eye and brain has been scientifically tested. Dozens of psychological tests, beginning with those of Gustav Fechner in the 19th century, have shown that, when subjects are presented with a range of rectangles, they invariably pick out as most pleasing ones whose sides are in the golden ratio.
But the most surprising thing is that a number deemed aesthetically pleasing by human beings also crops up in nature and science. Take the arrangement of leaves on the stem of a plant. As each new leaf grows, it does so at an angle offset from that of the leaf below. The most com mon angle between successive leaves is 137.5 – the golden angle. Why? Because 137.5 = 360 – 360/G, where G is the golden ratio. Why does the golden ratio play a role in the arrangement of leaves? It’s all down to the “irrationality” of the number. Irrational numbers are ones that cannot be expressed as the ratio of two whole numbers – for instance, 5/2.
The golden rule. It links art, music and even architecture. Marcus Chown on an enigmatic number