Golden ratio dating - The Golden Ratio of Attraction - The Good Men Project


Let’s examine the golden section ratio, to understand how it works, by comparing two ratios as described by a famous Greek mathematician, Euclid of Alexandria, about 2,300 years ago.

Here is the connection the other way round, where we can discover the Fibonacci numbers arising from the number Φ . The graph on the right shows a line whose gradient is Φ , that is the line y = Φ x = 1·6180339.. x
Since Φ is not the ratio of any two integers, the graph will never go through any points of the form (i,j) where i and j are whole numbers - apart from one trivial exception - can you spot it?
So we can ask What are the nearest integer-coordinate points to the Φ line? Let's start at the origin and work up the line.
The first is (0,0) of course, so these are the two integer coordinates of the only whole-number point exactly on the line! In fact ANY line y = k x will go through the origin, so that is why we will ignore this point as a "trivial exception" (as mathematicians like to put it).
The next point close to the line looks like (0,1) although (1,2) is nearer still. The next nearest seems even closer: (2,3) and (3,5) is even closer again. So far our sequence of "integer coordinate points close to the Phi line" is as follows: (0,1), (1,2), (2,3), (3,5)
What is the next closest point? and the next? Surprised? The coordinates are successive Fibonacci numbers ! Let's call these the Fibonacci points . Notice that the ratio y/x for each Fibonacci point (x,y) gets closer and closer to Phi = 1·618... but the interesting point that we see on this graph is that the Fibonacci points are the closest points to the Φ line.
1·61803 39887 49894 84820 45868 34365 63811 77203 09179 80576 .. More ..

In popular text on the golden ratio , one often finds the claim that the navel in the Vitruvian Man divides his hight in the golden ratio. This may be approximately true, but claiming it to be intentional from daVinci's hand is to the best of my knowledge unsubstantiated, and it seems unlikely for several reasons. All the other proportions are rational (where as the golden ratio is irrational), and no texts dated before the 19th century discuss the golden ratio as an aestethical proportion.


Golden ratio dating

Golden ratio dating