# Golden ratio

What is golden ratio and how is it solved?

In short, 'golden ratio' refers to when a line is divided into two parts, resulting in the whole length divided by the long part is also equal to the long part divided by the short part.Take 100 for example-nice round number to work with.We will experiment with different proportions until we find two values that yield an equal result. So:100 divided into two random parts, let's say 52 and 48. We will perform two sums to see if they yield equal answers:First our two chosen portions:52 / 48 = 1.083Secondly our total divided by our biggest portion:100/ 52 = 1.923Our answers here are not equal, and so we have not found the golden ratio.Let's try again, this time using a larger 'long' portion.Chosen Values:62 and 38.62/48 = 1.291100/62 = 1.612Close!As I am so close, I will now work with decimal values until I get it right.61.8/38.2 = 1.617100/ 61.8 = 1.618They are near enough the same- the golden ratio for 100 then, is two portions of 61.8 and 38.2.Hope this has helped- in my experience, it is trial and error.
Kirsty C.
28 March 2017
Say a line is being divided in the golden ratio. I'll try to draw the situation using charactors. _____________________________|    a        |                 b                  |(a+b)/b  = b/a       say b/a =x which is the golden ratio.Hence, ab + b/b = a/b                1/x + 1 = x               (x+1)x  = x               x+1 = x^2             x^2 - x -1 = 0            Calculate the roots of the X and see the amazing results.
shafraz
07 April 2017