In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger one equals the ratio of the larger one to the smaller. The golden ratio is an irrational mathematical constant, approximately 1.6180339887.
What has mathematics got to do with beauty? Actually, a lot. Physical attraction depends on ratio.
Our attraction to another person's body increases if that body is symmetrical and in proportion. Likewise, if a face is in proportion, we are more likely to notice it and find it beautiful. Scientists believe that we perceive proportional bodies to be more healthy.
Leonardo da Vinci's drawings of the human body emphasised its proportion. The ratio of the following distances is the Golden Ratio:
(foot to navel) : (navel to head)
Similarly, buildings are more attractive if the proportions used follow the Golden Ratio.
A good Golden Ratio Face Analyzer is located at this page: http://cuip.uchicago.edu/~dlnarain/golden/activity8.htm