The golden ratio is, like pi, a special number in nature. It equals 1.6180 and it can be found in many places both in mathematics and the natural world. For example, the lengths of various parts of our bodies are related by the golden ratio, and the ratio of successive numbers in the famous Fibonacci Series approach 1.6180 as well.
While I'm no authority on these matters, I did find this article pretty interesting. Turns out the length-to width ratio of the uterus varies from about 2 at birth to about 1.4 in old age. And during those years when women are most fertile, it hovers right around ... you guessed it, 1.6180. Pretty spiffy.
The fiendishly amusing Vi Hart has a series of three videos explaining about some of the places the Fibonacci series turns up in nature and explains why we might have expected it to be that way. They are totally worth watching!