The number Phi splits the picture division. No, dear nerds, not pi (π) – which we use in numbers, please! already acknowledged accordingly – but onomatopoeic Fffffi (ϕ). In mathematics, it denotes the irrational number 1.61803399 (and so on), which stands for a certain division ratio. In the meantime, you might already have guessed: It’s all about the “golden section”.
The ratio of two distances becomes the harmonious golden section when the long distance is related to the short distance as the total distance is to the long distance. This ratio is also called the “golden number” or simply Greek Phi.
You can rearrange this, solve it and then get the term as the exact solution (1+√5/2)which approximately 1,618 results.
In this section, we present amazing, impressive, informative and funny figures from the fields of IT, science, art, business, politics and of course mathematics every Tuesday.
The golden ratio stands for a ratio that promises a particularly appealing, aesthetic effect. Knowledge of this relationship goes back to Greek antiquity – the first writings on it were made published by the Greek mathematician Euclid. If one examines works of art according to the division ratios used, it is particularly noticeable in the works of great masters that the division often corresponds to that factor Phi (see also the Vitruvian figure in cover photo). There is evidence that this relationship seems particularly pleasant and aesthetic to us. But why is that?
The golden mean is not the golden section
Division ratio 1: Unstable image impression
Division ratio 2: Better, more stable impression
Division ratio 1.618: Maximum stable, harmonious impression
A first attempt at an explanation says that we humans want stability in images. A horizon that divides the image in the middle, 50:50, or a splitting ratio of 1, is at most unstable. Here the viewer cannot tell whether the artist attaches importance to the sky or the sea. The viewer’s eye is not guided, and an indecisive and unbalanced image impression arises. A better division that leads to a more stable result is 2/3 to 1/3, and this ratio is also often suggested to artists, sometimes even incorrectly referred to as the golden ratio. In fact, the divider 2 is only an approximation. The golden ratio is when the ratio is not 2 but 1.618. If you set the horizon according to this measurement, the picture immediately looks much more stable and calm.
A second attempt at explanation relates to nature. It is easy to show that the same division ratio also applies in nature. It is found in pine cones, pineapple, flower petals and romanesco. In the latter, a cousin of the cauliflower, even in the form of a continuous spiral, the Fibonacci spiral. This spiral is reached by dividing further and further according to the “divine proportion”. A kind of strudel is then created, which is actually also found in the same Italian cabbage vegetables. So one can come to the conclusion that we humans simply like what we know from nature. We’re kind of used to it.
No, not a 3D Mandelbrot fractal, but healthy Romanesco cabbage. The Fibonacci spiral comes into play in the structure. The harmonious optics have tangible advantages: the towers hardly get in each other’s way as they grow and thus allow optimal light output.
And knowing about the golden section is of course not only of an academic nature, but is also useful for advertisers in practice. When designing images and logos, image cuts that correspond to the golden ratio or the golden spiral are often chosen in this industry.
Golden section in image processing practice
Now you’re probably already wondering how you can incorporate the golden ratio into your own photographs or illustrations to make your work more pleasing. It’s easy: You can simply use templates, such as those offered by Photoshop for the crop tool. Choose between the “Golden Ratio”, “Golden Spiral” (our Fibonacci Spiral) or the Rule of Thirds. The last-mentioned rule of thirds with a division ratio of 2 is also often encountered in the viewfinder or on the display of your camera.
When applying the golden ratio templates, you will see lines and intersections between those lines in the crop tool. The expert speaks of energetically relevant lines of force and points of force. Then apply the template in such a way that the parts that are important for the image come to rest on those lines or points of force, whereby the focal points of surfaces, eyes, lines of symmetry and edges between objects are generally considered important for the image. In the simple case of a portrait, you could put the dominant eye or the focus of the face on a power point.
It helps to know rules like the golden mean so that you can then consciously break them. Here you can see a completely different image layout that follows the “negative space” principle.
Try it once. You may actually experience a visual “snap” moment as you align your subject with this simple rule. But as always, it goes without saying that rules are made to be broken!
(mawi)
