Composition:  The Golden Ratio.  By Don Finkeldei:  The golden ratio has been used by architects, mathematicians, sculptors and painters for thousands of years.   The Ratio is  1.618 but how do I use it in art today without being a mathematician?  Here’s how.

Leonardo da Vinci used it.  Even the Great Pyramid of Giza built around 2560 BC is close to the golden ratio of 1.618.  That’s the ratio of the base to the height of the pyramid.  Euclid formulated the math in 365 BC.  It goes like this:
The golden ratio of 1.618 will be achieved If the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one.

That is easily said but hard to understand.  Here are some visuals.   One depicting the golden ratio for a line, the other is the golden ratio for a rectangle.  If you don’t want to go through the reasoning, skip to the bottom of this article for the artists 60/40 rule.  It’s close enough for artists.

The golden Ratio for a line:

The Golden Ratio for a rectangle:

For both the line and the rectangle:

In the rectangle above the darker gray area is a square while the lighter gray area is a non-square rectangle.  The width of each rectangle added together divided by the common height equals 1.618 AND the width of the square plus the width of the non-square = 1.618.

Here’s a different rectangle where the widths of each gray areas are the same as above but the height of each is ½ the height of the above rectangle.

In the above case the width of the darker rectangle divided by the width of the lighter rectangle is still 1.618 BUT the width of each rectangle added together divided by the common height is not 1.618.  The ratio is twice as big as 1.618.  It is 3.236.  Therefore, it doesn’t match the criteria for the age old “Golden Ratio”.

What does all this mean and why even inject this principle into landscape painting anyway?

In a landscape painting, almost every mass/object relationship will not match the golden ratio anyway.  You’ll agree that almost nothing fits the golden ratio rule, so why even inject this principle into landscape painting anyway?  Even most canvas sizes don’t match the golden rule.

THE ARTIST’S 60/40 GUIDELINE

One interesting thing that we haven’t discussed that always matches one part of the golden rule is the ratio of the areas of each rectangle.  In both rectangular cases above the larger darker gray area divided by the smaller lighter gray area is the golden ratio of 1.618.  I've simplified it by making it easier and  ratios close to the golden ratio but not exactly the ratio.  it's 60% to 40%.
This is the principle landscape artists should keep in mind.

1. When placing a horizon separating terra firma from sky, make it 60% sky and 40% terra firma, or, 40% sky and 60% terra firma.  That’s not quite 1.618 (it’s 1.6) but close enough to match the area criteria of the golden rule.

2. When dividing shadow vs. sunlit areas of a scene, make 60% in shadow and 40% in sunlight – or vice versa.
3. If you are deciding how much of a canyon wall to place in shadow vs. sunlight, use the 60/40 rule.

4. To place a focal point area in the canvas, make it 40% either from the right or left edge and 40% from top or bottom.  Or, within a value plane, do the same from the edges of the value plane to the focal point.

5. When sketching in a horizontal line of trees, put either 40% or 60% trees and the rest gaps of unequal measures.  Or, the other way around.

6. Vary the height of trees on a horizontal line by the same 60/40 or 40/60 ratio.

Of course, you’ve always heard that it’s not good composition to divide a canvas in half or place the focal point in the center of the canvas.  Now you know why.    But here’s a good application of the golden ratio for artists to keep in mind.  Of course, these are generalities but if you keep the 40/60 ratio in mind when making decisions about shadow/light, focal point or line height/width you’ll not make the mistake of making things too repetitive and perfectly balanced.  Variety and unequal measures make a painting interesting.