The Golden Section

There’s a mathematical ratio commonly found in nature —the ratio of 1 to 1.618— that has many names.
Most often it is called the Golden Section, the Gold Ratio or the Golden Mean.
Occasionally it is also called the Golden Number, Divine Proportion or Golden Proportion, Fibonacci Number, and Phi.

The Golden Section is a Law of Proportionality. It is a law that occurs frequently in nature and its use is particularly useful in Art. First developed by Vitruvius, it is most famously known from Leonardo Da Vinci's 1509 drawing 'The Divine Proportion'.

    

Essentially the law states that two unequal parts of a whole must be in relationship to each other to create a satisfactory image to the eye.

Numerically Golden Section is approx. 1.618034 or 38% to 62%. This proportion reoccurs throughout our lives and can be said to create an ideal proportion between two objects or two parts of a whole.

Bonsai and the Golden Section         Bonsai and the Golden Section

Usually you find the golden ratio depicted as a single large rectangle formed by a square and another rectangle. What’s unique about this is that you can repeat the sequence infinitely and perfectly within each section. If you take away the big square on the left, what remains is yet another golden rectangle and so on.

The above images show firstly the Golden rectangle, here each whole rectangle is sub-divided using the Golden Section ration of 38%/62%.
In addition to the golden rectangle, we have the golden spiral. This is where the spiral is marked out traversing successive edges of golden section rectangles. This exact spiral exists in many natural forms such as in seashells and plants.

The naturally occurring Golden Section proportion/ratio reoccurs throughout our lives. For instance the proportion between the forearm and upper arm is 38% to 62% and the same ratio applies between the hand and forearm. Our own faces are comprised of this ratio time and time again; within the relationships between our eyes, ears, mouth and nose, the Golden Section can be found. 

Further (conscious or subconscious) recognition of the Golden Section in inanimate and artistic endeavors therefore feels 'right' to the eye and creates a feeling of satisfaction and harmony within an image.

The Golden Section ratio also shows up in the so-called Fibonacci Series. This is a sequence of numbers where each number is the sum of the two preceding numbers: 1 1 2 3 5 8 13 21 34 55 89 etc.

The ratio of two successive numbers in this sequence is approximately equal to the Golden Section.
0+1=1
1+1=2
1+2=3
2+3=5
3+5=8 ...
This is called the Fibonacci sequence. These numbers are used by nature all the time. for example, the rose has spirals of 3 petals in one direction and 5 petals in the other.

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