The twelfth century was a golden age for photography. Let’s step back from that statement a little, because obviously photography didn't exist way back then. What did exist though was mathematics and in particular an Italian gentleman by the name of Leonardo Bonacci, also known as Fibonacci. So what does this chap have to do with modern photography. Well, it's all about composition. Some of the fundamental rules of photographic composition come directly from Fibonacci’s studies of mathematics. He discovered what is known as the Golden Ratio or Divine Proportion. Oddly, the source of his discovery was the breeding habits of rabbits, but that is perhaps for another time. What he noticed overall is that the ratio he had discovered with the rabbits seem to apply to many aspects in nature. That ratio is 1.61803 to 1.

### What Does the Golden Ratio Mean to Us Photographers?

Well, as we said above, the Golden Ratio is also known as the Divine Proportion. This is because it occurs virtually everywhere in nature. When we are shooting, our eyes are naturally accustomed to seeing this proportion wherever we look. If in our compositions we break this natural ratio, the image will look uncomfortable, jarring our eyes. Although not strictly a Fibonacci rule, the rule of thirds is one of the most fundamental composition techniques in photography. It works because it is very close to the Divine Proportion and our eyes accept it as natural. However, if you want to take your compositions to the next level you can apply Mr. Fibonacci’s rules to two more advanced techniques, the Golden Rectangle and the Golden Spiral.

### The Golden Rectangle

Think of this as almost a center weighted rule of thirds. Whereas in the rule of thirds, each third is equidistant from the other, in the Golden Rectangle we use the Fibonacci Ratio to determine the distance between them. To explain a bit better if we split our image into three vertical lines, the distance of the first line from the left compared to the second line will be at a ratio of 1.618 to 1. In other words as you can see in the example, the outer boxes of the thirds are larger than the inner boxes. When we compose our shots, by placing our subject matter on the lines of these thirds we are using the Golden Rectangle. An even better composition would be to use the intersection of the thirds and moving beyond that you can use a counterpoint composition where you position subjects on diametrically opposite thirds.

Although this might sound a little complicated, next time you are our shooting, visualize the image on the regular thirds, then just move those thirds a little more to the center of the image.

### The Golden Spiral

This is a little more complicated compositional rule but an extremely powerful one. It uses a series of boxes increasing in size by the Golden Ratio. The centre-point of the composition starts on the corner of the smallest rectangle. Then a spiral is imagined, moving out from the smallest box and intersecting through each of the larger boxes until it finishes on the corner of the largest box. This image demonstrates the route of the spiral.

By placing subjects along the route of the spiral and where the spiral intersects one of the Golden Rectangles we can create a visually pleasing image that allows our eye to follow a natural route through the image. This is quite tricky to visualise through the viewfinder but if you try to find a primary subject, then imaging a spiral emanating from it. By placing compositional elements on that imaginary spiral, you will start to understand the power of the Golden Spiral.

It might seem odd at first that a twelfth century mathematician should be so important to photographic composition, but remember, most photographic composition has been around for centuries, practiced by artists long before the discovery of silver halide. We have just adapted their techniques to a more contemporary medium.

So the next time your are visualising a great shot in front of you, take your mind back 800 or so years and remember, Fibonacci Rules, OK?