THE UNIQUE PROPERTIES



The question must arise as to why the golden proportion is special - and more importantly, is there any difference between the Golden Proportion and another pleasing proportion? A brief study of figures below will answer this question.

Lines Divided in any proportion   Divided in Golden Proportion
 
The smaller AB  

2

 
---------------------

=

------

= 0.4
The larger BC  

5

 
 
The smaller AB  

0.618

 
--------------------

=

---------

= 0.618
The larger BC  

1

 
The larger BC  

5

 
------------------- =

----

= 0.71
The whole AC  

7

 
 
The larger BC  

1

 
--------------------

=

-------

= 0.618
The whole AC  

1.618

 
The two equations give different answers.   The two equations give identical answers.

Thus the proportion of the smaller to the greater is the same as the proportion of the greater to the whole. The division of the line by point C thus represents a point of equilibrium between these two proportions. If you move the point a fraction one way or the other, then you have two proportions which are neither the same nor are they in equilibrium. The only time that these two proportions are the same is when they are Golden.
This point of division is a mathematical confirmation of how the eye senses the balance of this magical proportion that appears so frequently in nature and art.