See the relevant Wikipedia article here.
RonL
Let me first give an example of a Golden ration. My body is shaped in the Golden proportion, hence I am perfect.
To divide a line such that the ratio of the whole to the bigger is the bigger to the smaller.
It is often said (but probably false) that the most pleasing figures to gaze upon are those that are shaped in golden (divine) proportion. Which is why I have angelic beautify because I am shaped in divine proportion.
Leonardo was obsessed with the proportions of man, he drew a famous drawing "Virturian Man" which is inscribed in a circle and a square, along with some proportions that naturally arise. Furthermore, Kallikrates and Iktinos shaped the Parthenon in divine proportion.