## Golden Ratio

Another visual concept formulated in antiquity and still used today comes to us from ancient Greek art. It's known as the Golden Ratio  (also referred to as the Golden Mean or Golden Section). We'll talk a bit about the math behind it in a moment, but at its essence this is - like the rule of thirds -  simply a way of dividing the image frame into rectangular segments. These 'golden rectangles' have proportions that the ancient Greeks thought to be especially harmonious and pleasing to the eye. Placing compositional elements of importance either inside of or at the intersection of these rectangles can give them greater prominence and create a well-balanced image, such as the one you see below. This image has a pleasing balance between the main subject and the environment. The composition was created in aacordance with the Golden Ratio, which I'll explain on this page.

The mathematics behind the golden ratio are less obvious than those for the rule of thirds, so this ratio is a little less widely known among artists than say, mathematicians or engineers. But it pays to be at least familiar with the underlying concept.

The golden ratio is roughly equivalent to 1:1.6, or more practically, 3/8:5/8. In the figure below you have two line segments, a and b. Line segment a is 1.6x longer than segment b. And the combined segment, a+b is also 1.6x longer than segment a. So the proportions of line segments a and b express the golden ratio. Visual depiction of the elements of the Golden Ratio (courtesy Wikimedia).

golden rectangle (shown below) is one whose short side (a) and long side (a+b) are in this 1:1.6 proportion. With any golden rectangle you can further divide it with a line that divides the long side by this same 1:1.6 ratio. This is exactly what has been done in the illustration below, to create line segment b. You can continue this pattern of division to create smaller and smaller rectangles, one inside the other.

So how exactly does this work compositionally? Let's take a closer look at the photograph we started with at the top of the page. Because a 1:1.6 ratio is not very easy to visualize, we can think of it instead as 3/8:5/8, which means we are looking to divide the frame along one side by 3/8 (a bit less than the halfway point). In the first  image below that is exactly what we've done, adding a vertical gridline roughly 3/8 in from the left edge.  A vertical line placed approximately 3/8 of the way from the left edge marks the creation of our first golden rectangle. A horizontal line placed approximately 3/8 of the way from the top edge creates another golden rectangle.

With our first golden rectangle created, we can repeat this process to create a second, smaller golden rectangle inside of that one, as you can see in the second image above. The more dramatically lit portion of the model's body lies within our first rectangle. And her face lies largely in the second rectangle. It is by including compositionally important elements inside these rectangles that we can draw attention to them. As with the Rule of Thirds, this approach creates an asymmetrical composition that serves to direct the viewer's gaze. You can continue dividing the frame into smaller and smaller rectangles by adding vertical and horizontal lines in succession that create the 3/8:5/8 golden ratio. In this image the smallest rectangle (in blue) lays directly over the portion of the model's face closest to the camera.