The size of your picture and the placement of your center of interest are decisions that shouldn?t be made at random. But how do you know what the best choices are? The answer is simple: Do what has historically proven effective, and that?s where the golden mean and the Rabatman come in. They?ll help you get the most visually pleasing division of space in your painting, and that will set you up for a positive reaction from your viewers before you even begin to show off your other talents.
The Golden Mean
A formula used by the ancient Egyptians and Greeks and still employed today, especially in architecture, the golden mean states that the best division of a line makes the ratio of the shorter part to the longer part equal to the ratio of the longer part to the whole line. The same is true for area.
Mathematically this means that the smaller portion is .618 times the larger, which results in the larger portion being .618 times the entire line or area. This ratio is manifested in the natural growth of seedpods, sunflowers, seashell spirals, pinecones and even cells, and it?s also the constant factor in several geometrical progressions.
What does that mean for you as an artist? First, with the method described here you can use the golden mean to determine the size of your surface so that the relationship of length to width is .618-to-1 (or vice versa). You can also use it to find the possible focal points for the picture, which would divide the space into the same proportions. And, more easily, once you?re familiar with how the golden mean works it can become second nature, and you can approximate the measurements without getting out the ruler and compass.
The only drawback of this method is that the size of the picture created by using the golden mean often doesn?t match the commonly available papers and canvases.
The Shorter Way
There are also a couple of quicker ways to benefit from some of the same principles used for the golden mean. The Rabatman is a method that gives you a division of space much closer to the sizes of paper we?re accustomed to, but it does not involve a repetitive ratio or constant. It?s similar to the golden mean but uses the diagonal of a square as a radius to create a rectangle that turns out a bit shorter. Also, an easy method for locating a center of interest in any picture space is to simply create a diagonal across the picture, then divide it into thirds to find the two points along that diagonal that are comfortable focal points.
Each artistic composition can seem to make its own demands, however, so while these methods give us safe and reliable guidelines, take into account the uniqueness of your picture. Multiple objects, strange shapes and repetitive patterns can force you to break the rules. But always remember that many centuries of art and architecture have taught us a lot about how we see, and a little bit of good engineering can be all you need to take advantage of that.
The Golden Touch
Here?s the precise way to create a pictorial space using the golden mean: Start with a square, then place the center pin of a compass at the midpoint of the bottom edge (B). Swing an arc out from an upper corner and extend the bottom edge of the square out to meet the arc (see segment C), then complete the rectangle with B+C as the base. This method has created an important relationship: the ratio of the height of the rectangle to its width is the same as the ratio of the width to both put together. Mathematically, A is the same proportion (.618) of B+C as B+C is of A+B+C.
The golden mean also can guide you to the best placement of your focal point, which would lie a bit more than a third of the distance away from the two nearest sides (see the example at left), thereby dividing the space into the same proportions. In the diagram above, the ratio of C to B is the same as the ratios already mentioned, so line D is a natural place of focus.
Why does this strategy work? We don?t know for sure, but plenty of experience and research has shown it to be visually satisfying. And once you become familiar with it you won?t have to measure or calculate—just approximate the proportions and you?ll have a picture that falls right into place.