The golden ratio has been assigned many definitions and different names throughout history. If we review old texts, we can find references and denominations such as the golden number, the phi number (not pi number), the golden section, the golden measure or the divine proportion. The discovery of this proportion or number caused a whole movement in the sciences and the arts. It even obsessed artists, designers, architects, and all kinds of professionals in search of visual perfection for centuries.
What is the golden ratio?
The golden ratio (also sometimes called the golden number, the Phi number, the golden section or the divine proportion), is a ratio between two numbers that equals 1.618. It is usually represented by the Greek letter Phi (Φ).
Since ancient times, man has studied and theorised about aesthetics, composition, proportions and beauty in nature and in the human body. In his studies, he came to the conclusion that everything seems to be made up of patterns and that these patterns could determine whether or not something is beautiful. Thus, he came to study the golden ratio.
This proportion was considered aesthetically pleasing, perhaps because it is a proportion that humans have found consistently present in the patterns of nature and that we somehow understand. The ratio has fascinated mathematicians, artists and engineers alike over the centuries, so much so that it has come to be regarded as the mathematical representation of beauty.
What is the Fibonacci sequence?
To know the origin of the golden ratio we need to go back many centuries (see below for its history). In the 16th century, Leonardo Pisano, also known as Fibonacci, was a famous Italian mathematician, who helped to spread throughout Europe the Arabic numbering system with decimal base that we still use today.
Fibonacci’s great discovery was the Fibonacci sequence, which later gave rise to the golden ratio. This proportion would come to be associated with beauty and nature, and would be used in art and painting for generations. I’m sure the name rings a bell from your childhood maths class. We are talking about an infinite number sequence.
This numerical sequence is as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc.
In the Fibonacci sequence, the sum of two consecutive numbers always results in the next number. Moreover, the relationship that exists between each pair of numbers is increasingly closer to a specific number: the golden number. That is to say, if we divide each number in the sequence with its previous number, the result obtained gets closer and closer to the value of the golden number and the difference is smaller and smaller as we take higher values in the sequence.
The golden ratio has so far been represented by the Greek letter φ or Φ (phi), after the Greek sculptor Phidias. It was not discovered as a unit value, but as a ratio or proportion. The value of the golden ratio is 1.618034 and we will learn why this number is given these interesting properties.
The golden rectangle and the golden spiral
Many artists, architects, designers and craftsmen have applied the geometry of the golden ratio to their projects and creations to enhance the harmony of objects, design or architecture. This can be seen today in many designs, buildings, photographs, nature itself and other compositions.
So how does this succession of numbers or proportion apply to our disciplines? To better understand the golden ratio and how it came to be applied to art, we need to explain the creation of the golden rectangle and the golden spiral.
Let’s look at it in 3 quick steps, so you can get a good understanding of these two rules or tools.
- If we transfer two values from the numerical sequence above, we would get a rectangle with the proportion of the golden rectangle:
- We draw a square to divide the rectangle into two non-equal parts. Then, we have to draw another square in the small part and so on.
If we keep the same division as the one we can find in the Fibonacci sequence, and we draw a circle inside the perfect squares (inside them I mark their diameter which coincides with the numerical sequence), the result would be the following:
- To obtain the famous “golden spiral“, it would be enough to join the different vertices or to draw semicircles inside all the perfect squares.
In practice, the golden ratio is shown in the form of a spiral, known as a “golden spiral”. This logarithmic spiral is constructed from the evolution of a golden rectangle, whose proportionality is equal to the golden ratio.
Both the golden rectangle and the golden spiral can be used nowadays as another form of composition when developing our creativities in graphic design or any other artistic discipline.
History of the golden ratio
The first known written mention of the golden ratio dates back to 300 BC in the classical Greek work Elements by Euclid. In this classic work of mathematics and geometry, the ratio is recognised, although it is not yet called the golden ratio.
But before this date, in older civilisations, probably as early as Ancient Egyptian times, the proportion had been applied in the design and construction of the Great Pyramid of Giza. The pyramid shows that the Egyptians applied the golden ratio with incredible mathematical accuracy.
Later, in 500 BC, Phidias, the most famous Greek sculptor and mathematician of the classical world, studied Phi and applied it to the design of sculptures and reliefs. Such as his well-known works for the Parthenon in Ancient Greece and in some of his column designs.
After him, it was Plato who considered the golden ratio to be the mathematical relationship most closely linked to the physics of the cosmos and a key to understanding it. The golden ratio would be linked to the patterns of the universe and the galaxies, and would be given this mystical character.
The golden ratio has always been considered harmonious and pleasing to the eye. This may be because it is so prevalent in nature. Tree leaves or pine cones tend to grow in patterns that approximate the golden ratio, as do sunflowers and roses. Also some seashells such as nautiluses grow in a ratio very close to the golden ratio, in a golden spiral pattern.
Although the Fibonacci sequence was discovered around 1200 by the Italian mathematician Leonardo Pisano, better known as Leonardo Fibonacci, the golden ratio received its name later in 1509 from Luca Pacioli’s De Divina Proportione, which included illustrations by Leonardo Da Vinci. It was Da Vinci who first referred to it as the golden ratio, from which the name “the divine proportion” was also derived.
As a curiosity, since the publication of The Divine Proportion, the golden ratio has been taken as the divine proportion. It was claimed that Fibonacci’s succession and its golden number were related to something more spiritual than geometry. As a consequence of the publication and reception of the book, many myths about the application of the proportion appeared.
Renaissance artists used it in their paintings and sculptures to enhance the harmony and beauty of their creations. Those artists understood at the time that proportion is an aspect to be taken care of in front of the viewer, to gain harmony and highlight the beauty of things. However, it was not associated with the term Phi until the 20th century. It was the mathematician Mark Barr who used the Greek letter Φ to designate the proportion.
Part of the curiosity about this rule lies in speculation that this number is said to recur very often in nature. Supposedly we could even detail a perfect golden spiral, or the proportions of the Fibonacci sequence in plants, insects, fruits, etc. Some even argue that the golden ratio was the foundation on which the entire natural world was built. Since the proportion was present in nature, it was even said to be a manifestation of nature. Hence the golden ratio was said to be the most natural manifestation of beauty. It was thought that anything designed or made according to these proportions would have an intrinsic beauty.
Terminology related to the golden ratio
What is the golden point?
The golden point is the point of origin of a golden ratio. To make it easier to understand, the golden point is the strong point from which the golden spiral starts. For example, the vortex of the galaxy above. This point often marks where to focus attention in painting, photography or design.
What is the golden number?
The golden number, is the number that expresses the relationship between the numbers in the Fibonacci sequence. We are talking about the number 1.618034. It is the mathematical basis on which the golden spiral is built, and which we relate visually to the golden ratio.
What is the golden rectangle?
A golden rectangle is a rectangle whose sides are ruled by two consecutive numbers of the Fibonacci number sequence. It can be a very practical tool for proportion and composition, along with the golden spiral.
What are the golden circles?
The golden circles are the result of drawing circles inside the perfect squares found in the division of the golden rectangle, with the Fibonacci number sequence.
It can be a very practical way to apply this rule in your designs.
The golden ratio in logo design
When designing logos, many graphic designers are always looking for the “ideal proportions” in which the protagonist of the visual identity can be captured. This does not mean that the golden ratio is always the best proportion to follow when designing logos. But it is worth knowing some examples of well-known logos that have been designed following the Fibonacci sequence.
Once again we will be able to see that in graphic design nothing is the result of chance.
A practical way to apply the golden ratio in your design is to draw several circles respecting the proportion of the numbers of the Fibonacci sequence. Then distribute them so that they form the basis of your creation. Some logos that have used the golden ratio in their design are for example the Apple logo, Twitter, Pepsi or the National Geographic logo.
The most effective and attractive logos are those that are well proportioned. To get your message across quickly, using this rule can help potential customers and users connect with your logo.
The golden ratio can be used to distribute the elements of your logo. It can also be applied to the placement of the images that appear in the logo.
Another option is to use elements of the golden ratio such as the golden rectangle and the golden spiral, to create the main basic shapes of your logo. Combining all of these shapes in a single design creates a harmonious, balanced and coherent result.
How to use the golden ratio to hierarchise typography
You can also use the golden ratio when including typography in your design. Keeping this ratio in mind will help you to hierarchise and distribute the text on your poster, article, website or invitation.
Hierarchy is the visual control of information in the layout of a design and directly influences the order in which the human eye perceives what it sees. In graphic design we use hierarchy to achieve cohesion and structure, visual order, create direction, generate emphasis and also to guide the viewer’s reading.
It has happened to all of us at one time or another, that we do not know how to define the exact size that should be between the typography of a headline. Using the golden ratio, we will be able to get very accurate relationships for the sizes of the texts. In this way we can establish a functional, coherent and harmonious hierarchy.
To do this, all we have to do is choose 3 numbers in a row from the fibonacci sequence and assign each of these numbers to the sizes of the typefaces.
Another way would be to multiply the size of your smallest text by 1.618 to find out what size the most important fonts in your design should be. If you have already decided what size you want the headline to be, you can divide that size by 1.618 to find out what size to use for the rest of the text. This will beautify your creation in a scientific and mathematical way.
A simple calculation will make your design proportionate, harmonious and much more effective and attractive. This is essential so that the person receiving the design can better perceive the content and the message.
All of this, bearing in mind that you should try to ensure that the dimensions of your typography are also proportional in terms of the space you should leave between lines.
Conclusion.
In graphic design, we will be able to find good designs that use this proportion and achieve a beautiful and harmonious result. However, the golden ratio is not the key to composition and therefore we should not always design around it. We have to value it for what it is, just another rule of composition and proportion. We should give it the same attention we give to other rules, such as the rule of thirds, balance of weights, patterns, symmetry…
Hola, soy Roberto Vidiella.
I am the founder and Creative Director of VIDI. I am passionate about graphic design, and through this blog, I try to deepen my knowledge and share what I have learned during my career. If you leave me a comment, you help me to keep learning and improving, and I’m really excited about it!