<-----------------1----------------->
A.......................C........................B
We let the longer side(AB) be 1 unit, and the shorter side(AC) be x units. By this ratio, we get:
1 : x = x : (1-x)
x^2+x-1=0
By solving the equation,we have get
x = [-1+(5)^0.5] / 2
( x = [-1-(5)^0.5] / 2 rejected)
This irregular number is called GOLDEN NUMBER, which is approximately 0.618. Some people may express this as 3 : 5 =0.6 .
x2+x-1=0 can also expressed into x = (x+1) ^ (-1)
By substituting x = (x+1) ^ (-1) continuously, we have
x = [1+(x-1)^(-1)]^(-1) ... x = {1+....[1+(x-1)^(-1)]^(-1)
The number will be closer and closer to the golden number(0.6180339887498948…)
Further More Decimal Places for Golden Section