1.618 - spirals of reflection

The shape above is a rectangle of special proportions. When a square with the same width as the rectangle is placed inside it, the rectangle which remains to the right, standing up, is of the same proportions as the overall rectangle. Another square can be placed inside that one and so on, spiralling rapidly downwards in size. The rectangle is known as a 'golden rectangle' and the ratio of length to width is a special number which is often abreviated to 1.618.

1.6180339887..
The golden ratio crops up in more places in art, music and so on than any other number except pi. Debussy used it in his music and Le Corbusier in architecture. Leonardo da Vinci used it for the Mona Lisa's face, the Greeks in building the Parthenon and ancient Egyptians in the construction of the Great Pyramid of Khufu. In 2003AD, Andy Roberts used it for his ultraversity website.