In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller. The golden ratio is approximately 1.6180339887. The golden ratio can be expressed as a mathematical constant, usually denoted by the Greek letter 
At least since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. Mathematicians have studied the golden ratio because of its unique and interesting properties.
It is sometimes stated that nautilus shells get wider in the pattern of a golden spiral, and hence are related to both φ and the Fibonacci series. In truth, nautilus shells exhibit logarithmic spiral growth, but at a rate distinctly different from that of the golden spiral. The reason for this growth pattern is that it allows the organism to grow at a constant rate without having to change shape.Saw this at the underwater world, and thought it was very pretty. This fossil reminded me of the greek exhibit we saw back then at the national museum, think it's the lighting. Anyway, everything above is from wikipedia.
