The golden section is based on the Fibonacci sequence of numbers and is visually pleasing found in much art since the time of Leonardo.
The canvas can be said to be divided into three sections vertically and horizontally in which the dividing line separates the image into a and b in the image below, such that the ratio of a to b is the same as that of a+b to a
a/b = a+b/a
image sourced on line Dec 2014 from: http://en.wikipedia.org/wiki/Golden_ratio
In mathematics this ratio is expressed as phi and its value is 1.6180339887…….. a is this amount greater than the line b, and a+b is similarly greater than a by the same amount. The value is a little less than one-third of the distance across or down the canvas.
Kepler proved that the golden ratio is related to Fibonacci numbers (which are a sequence of numbers in which the one is produced by the addition of the two previous numbers starting at one plus one…1+1=2, 1+2=3, 3+2=5, 5+3=8
image off the Fibonacci numbers as incorporated in the golden sections of a rectangle sourced on line Dec 2014 from:http://math2033.uark.edu/wiki/index.php/Golden_ratio
If one Fibonacci number is divided by the previous number the product is 1.6180339887…….. (the same as the golden section ratio)
Shapes based on the golden section and the Fibonacci numbers are common in nature:
and often used in art to produce aesthetically pleasing compositions.
Leonardo Da Vinci The Vitruvian man uses the golden section between umbilicus and top of the head.
Da Vinci’s the Last Supper showing the many golden sections into which its areas can be divided:
sourced on line Dec 2014 from: http://www.goldennumber.net/art-composition-design/
The golden section used by Georges Seurat:
sourced on line Dec 2014 from:http://www.goldennumber.net/art-composition-design/
An image painted in early 19th century believed to incorporate many aspects of the golden section theory.
Ham Hall by Thomas Peploe Wood sourced on line (Dec 2014) from:http://www.bbc.co.uk/arts/yourpaintings/artists/thomas-peploe-wood/paintings/slideshow#/3
and of the geometrical compositon of the Mona Lisa:
I think the use of the golden section can be read, perhaps wrongly, into many pieces of art and am unsure if all of these images considered the geometry to such an extent when they were conceived, although I trust Da Vinci was exceptionally interested in geometry and the hidden meanings of the magical proportions.
Landscape paintings and the golden section
Pieter Breughel the Elder Hunters in the snow
the middle tree and middle man on the left appear to be at a vertical golden section and the line separating the two lakes on a horizontal golden section
playing with creativity 