Put simply the golden ratio is a set of natural geometric relationships that enable artistically pleasing compositions to be easily created using a constant proportion of 1 : 1.618, so for example if a rectangle has a short side that is 1 meter long and a long side that is 1.618 meters long then it can be said to be in the golden proportion.

By further subdividing that rectangle using the 1:1.618 proportions you can create grids that will help to better place the objects in your painting, I’ve illustrated an example below:

A very simple sketch to demonstrate a picture laid out using a basic golden section, notice the extra two diagonal lines drawn to help position the bushes ect - you don’t have to stick to just working with the square grid when composing with the golden ratio.

Fibonacci Spiral

As the Golden Rectangle is subdivided you will notice that squares are formed as well as new rectangles, by continuosly subdividing the sections using the golden ratio you can end up with a sort of ‘spiral’ of squares, which when intersected with arcs form whats known as a Fibonacci Spiral like the one shown below:

So as you can see, the golden ratio can be used to describe organic shapes as well as geometric shapes, apparently nature abounds with examples of organic objects working within the Golden Ratio / Fibonacci sequence. 

It has to be remembered when dealing with the golden ratio however that nature abhors true symmetry - even your face is not symmetrical, so adhering too closely to a grid is never a good idea if you want a natural appearance to your compositions!

Of course mathematicians will concentrate on the pure math involved, but for the purposes of this article that simply isn’t necessary, the golden ratio is a guide not a hard and fast rule and taking it too literally can be just as bad for your painting as ignoring it.

to section about Golden Triangles and Pentagons

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Graham Hanks Portrait painter based in Doncaster Yorkshire producing portraits in oils and pastels