# How to design with the Fibonacci Sequence

A Fibonacci sequence is a sequence in which each number is the sum of the previous two numbers. The string usually starts with 0 and 1, although some authors skip the initial words and start the string with 1 and 1 or 1 and 2. Starting with 0 and 1, the next few values in the string are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. Its name comes from the Italian mathematician Leonardo of Pisa, later known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book Liber Abaci.

The Fibonacci sequence is strongly related to the golden ratio, and Binet’s formula expresses the nth number in the Fibonacci sequence in terms of n and the golden ratio and suggests that the ratio of two consecutive numbers in the Fibonacci sequence tends toward the golden ratio as n increases. The Fibonacci sequence is also closely related to the Lucas numbers, which follow the same recursive relation and form a complementary pair of Lucas sequences with the Fibonacci sequence.

Proportional systems have been used for centuries. The golden ratio was first mentioned around 500 BC by Phidias, Plato, and then Euclid. By this, we can assume that the ratio has been discovered several times throughout history – hence its many names, such as the golden mean, the golden ratio, the divine ratio, or the Greek symbol φ. The golden ratio is a mathematical proportion between elements of different sizes that are considered the most aesthetically pleasing to the human eye. The golden ratio is 1:1,618 and is often illustrated with shell-shaped spirals.

The golden spiral can be found in nature, including in plants and weather patterns such as hurricanes. In addition, the golden ratio has been used to analyze quantities found in architecture, painting, and music. Examples of buildings and works of art that preserve the golden ratio include the pyramids at Giza, the Parthenon in Athens, and Leonardo da Vinci’s Mona Lisa.

I am interested in User Experience, which is the entire experience a user has when using a product. One of the main features of effective design is a clear user interface. All elements must be well balanced and placed in harmony so that users can easily perceive information on the screen and effortlessly interact with the product. To create an effective design composition, professionals use various techniques and methods from the art sciences as well as basic mathematical theories. One of the common tools that help in creating design compositions, is the aforementioned golden ratio.

First of all, it can be used at the wireframing stage. In this way, you can plan the layout structure by placing and adjusting the UI components according to the golden ratio. However, it should be noted that there is no objective way to apply the golden ratio to the design. Some designers choose to apply it according to their needs. It is, among other things, the golden ratio that is taken into account for typography. The mathematical proportions of typography are extremely important to how readers perceive both the site and the content.

Composition is a key design element. All elements must work together to maximize a pleasing experience. Moreover, each separate element, even as small as an icon, must be harmoniously created. The golden ratio has a positive effect on visual perception. Understanding the theory of golden ratio is essential to be able to work with proportions. Many designers use this tool when creating various graphics, especially for small but significant design elements such as logos. Composition is also important when creating attractive images, and a quick and easy way to crop graphics and create compositions is to apply a golden spiral to their center point. We can find the golden ratio in the layout of popular websites as well, and it works especially well for content-heavy websites such as blogs.

Some designers are fascinated by the golden ratio and use it to create and edit all kinds of interface elements. Others believe that the golden ratio is no more important than any other method used to determine size and proportion. Regardless, the golden ratio is a helpful reference for visual designers who want to improve their skills with a concrete, mathematical approach. Here, someone might ask why this is so important?  Why is it so important to make sure that the first impression of a product is pleasant? Because when users first try a product, they scan the user interface and then decide whether they like something or not. This process happens within seconds of looking at something. This reaction happens faster than our awareness, so we don’t even realize it. Design created using the golden ratio positively influences the users’ mind and visual perception and works from the first sight of the product.

I think a field like a User Experience is a good example of how computing often emphasizes elegance and beauty alongside pure practicality. Even programming itself is sometimes referred to as art. The extreme separation of the humanities, arts, and mathematics disciplines is relatively new and has many harmful consequences. I mention this because, in my opinion, combining the concept of the Fibonacci sequence and, for example, trying to understand what beauty is, is objectionable to some. “How can you combine mathematics and humanities? After all, it has nothing to do with each other!” Today, many students majoring in technology or mathematics enroll only in courses that they think will benefit them in the sciences, leaving out the social sciences, humanities, and arts. Likewise, many humanities students try to avoid science and math classes. But it is important to remember that technology is not just a matter of routine procedure and to make students aware of that.

We need thinkers, visionaries, and creative minds who, like the scientists of old, know how to combine fields of knowledge forever more interesting research. Especially given the fact that the sciences are becoming more and more powerful, and by disconnecting them from problems combined with the humanities, we may have quite a problem in the future. I mean there are a lot of philosophical and ethical problems for example with the application of artificial intelligence.

I think that the debates that take place around the Fibonacci sequence and its applications to hundreds of different problems are one of the most interesting examples of how one can have an inter- or multidisciplinary discussion and reach a conclusion that is satisfactory for all.

Literature:

Esposito, E. (2018) “A guide to the Golden Ratio for designers” https://www.invisionapp.com/inside-design/golden-ratio-designers/

Knuth, Donald (2006), The Art of Computer Programming, vol. 4. Generating All Trees – History of Combinatorial Generation, Addison–Wesley, p. 50, ISBN 978-0-321-33570-8

Pearson, C. (2019). Secret Symphony: Intro to Golden Ratio Typography. Pearsonified. https://pearsonified.com/golden-ratio-typography-intro/

Singh, Parmanand (1985), “The So-called Fibonacci numbers in ancient and medieval India”, Historia Mathematica, 12 (3): 229–44, doi:10.1016/0315-0860(85)90021-7