The math behind it
The golden ratio is the division ratio of a segment. The ratio correlates the relationship between the whole and larger portion (also called Major) as well as the relationship between the larger portion and smaller portion (Minor). Expressed as a formula:
Whole / Major = Major / Minor ≅ 0,618
Thus, the major portion should occupy 61.8% and the minor portion 38.2%.
It all depends on the right proportions
In the visual arts, the proportional rule of the golden ratio is often incorporated in the composition of the image. Depending on the prevailing conception of art, the golden ratio is considered particularly aesthetic since it can also be found in nature and humans. Since there is little documentation on the golden ratio in earlier paintings, interpretations in image analysis are purely speculative. A good example would be the Mona Lisa by Leonardo da Vinci. When looking at her head, the viewer can notice that the relationship between the chin and the eyebrows (Major) with that of the eyebrows and hairline (Minor) is in accordance with the golden ratio.
The golden ratio is also well known in architecture and can be seen, for instance, in the ancient pyramid of Cheops. This pyramid, built in Egypt in 2470 B.C., has a square layout. By using simple geometry, you can notice the relationship between the distance of the centre line of the side surface and the base edge to the pyramid’s top point (Major) with the distance from the middle point of a base edge to the centre of the base (Minor). The ratio is 0.618 and is thus almost exactly the same as the golden ratio.
In general, the golden ratio is often used for using the correct proportions and is also used in photography. However, the formula is not exactly easy to calculate just off the top of your head. The proportional ratio of 5:3 is sufficient enough to be almost the same as the golden ratio with only a deviation of 1%.
Uses in photography
If an image is divided by its width and height as well as both sides (from left to right and vice versa) and the golden ratio is applied to these lengths, you’ll be left with four intersections. When important parts of the image are located in one of these intersections, the motif appears to be especially harmonious.
Not only the location of these intersections plays an important role in image composition, but also the depiction of surfaces. In photography, for example, the relationship between light and dark surfaces should be taken into consideration. You should also pay attention to what parts appear especially structured, and thus unsettled, and which surfaces appear more smooth and calming.
Tipp: many cameras are capable of displaying orientation lines to help you follow the rule of thirds, but not the golden ratio. As a solution to this problem, you could attach a screen protector to your display and mark the lines of the golden ratio yourself.