i am very interested in Golden Ratio and its value. the Golden Ratio itself is not hard thing to visualize and understand in 5 minutes. But i am trying to reach the historical, logical reasons of origin of this ratio.
my first question is: why is the value of the ratio $\frac{a+b}{a}=\frac{a}{b}=1.618$ ? it is the positive root of $a^2-a-1=0$. can someone pls give me more clues,facts and properties of this phenomenon?