More Advanced Golden Ratios

With the Golden Ratio you are not just limited to Rectangles and Squares, another (and perhaps more useful) incarnation of the Golden section is the Pentagram shape !

Look at the pentagram inscribed into the pentagon below, the triangles which are formed by these 2 shapes all follow the golden ratio exactly - in other words if the short sides of any triangle measured 1.00 cm, the long sides would measure 1.618 cm! 

In the illustration shown below the shaded triangles all follow the golden ratio - which is why they are known as golden triangles:

Not only that but if you inscribe another pentagram inside the hexagon formed by the centre of first one (drawn here in blue) the proportrions of that shape would all be in a 1:1.618 relationship to the bigger pentagon:

If you dissect a Golden Triangle into successively smaller triangles like we did with the golden Rectangle, you can again create a spiral from the intersections created :

If anything this spiral is actually more organic than the fibonacci spiral and certainly looks more like a true seashell as a result!

One of my favourite compositional ‘grids’ is the Golden Triangle combined with the pentacle / pentagon as shown below:

This simple combination works great for composing figures in a picture and is good with the human face too.

If you redraw the spiral over this combination the spiral should fit exactly with the pentagon too!

Remember that these devices do not need to exactly fit your canvas in order to work, and that you can extend any lines you like to the edges of the canvas to help position items outside the ‘grid’ the example below is the pentagon / triangle combination set into a ‘canvas’ then the lines have been extended to give a larger area grid for a painting.

There are loads more ways in which the golden ratio appears in nature and art, but these simple explanations should be enough to get you started in experimenting with new ways to compose your paintings.

If you want to explore this idea more why not download my ‘golden section viewer’ and experiment with loading your own pics into the software to see how these simple formulas can help recognise compositional patterns in your work.

Enjoy Experimenting!

Download Golden Section Viewer

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