What is the Golden Mean?

The Golden Section, or Golden Mean, is one of those concepts that is somewhat shrouded in mystery, yet the ratio it represents is found everywhere in nature, from the breeding patterns of rabbits to the arrangement of seeds in a sunflower head to the proportions of the human hand. It is a proportion that is generally considered to be particularly pleasing to the eye. Mathematically, it when the ratio of the sum of two quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. It repeats itself to infinity. You can keep subdividing the box the same way and end up with the same ratios every time. Put simply, that comes to roughly 1 to 1.6180339887, just shy of a 2/3 ratio.

There’s a lot of information out there about this ratio, how it is applied in architecture, painting, graphic design, music, and the like, applied primarily in the distance from one thing to the next, or the relationship of one element to the whole. (Mathematical info here and here.)

But I want to talk about how I personally use it in my art.

Canvas Size

A quick way to start off with the golden section is to begin with a canvas that uses this ratio. I tend to favor canvases that are generally close to a 2:3 ratio since that is fairly close. I know the 5-inch by 7-inch small canvases I use aren’t that close to this ratio but they work for me since 4 x 6 is too small, and 8x10 is too large. (I’m afraid I’ll get too carried away with the detail at that size.) I’ve used a lot of 3:4 proportioned canvases since they’re pretty easy to find. That’s actually a pretty pleasing proportion as well.

Divide up the canvas along the golden section

Sometimes I use the golden section to compose my artwork by dividing up the canvas to create ratios from parts to the whole. In other words, if I am working with a 22-inch square canvas, I might draw grid lines at something close to 13.596 inches (20·.618), and divide out squares from there. Along those lines I can position elements so that they are harmoniously placed in relationship to each other. An easy way to get close to this is to use the rule of thirds, since phi is actually pretty close to 2/3.

Objects in proportion to each other

Another way to do it is by placing elements so that they are scaled in proportion with each other using the golden mean. So if one element is 5 inches in size, another is roughly 8.09 inches to maintain the 1:1.618 ratio. I can’t say I’ve consciously used this method, though.

There are some really complicated methods for using the golden mean that involve calculating various angles and curves and circles and whatnot and subdividing the canvas in ways more elaborate than the one I demonstrated above. That’s cool and all, but I don’t really have the patience for it.

The only real exception is the “Mystery of the Brevity of Life, Fig. A/B” painting I did a few years back, where a chambered nautilus spiral is depicted, with a series of light and dark lines that get longer by adding the length of the previous line. (1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,etc.) They create a Fibonacci string, which very quickly comes to a ratio close to .618.

Going forward

While Googling for reference images for this post, I found a bunch of really interesting information about “sacred geometry,” and it looks really cool. I want to try my hand at arranging things using interesting shapes that line up with each other in the form of pentagons, etc. which should make for interesting, compelling compositions. I think it should lend itself well to the architecture-influenced abstract realism my work is taking.