Golden Ratio: What it is and How to Apply it to Your Photos

The golden ratio has fascinated mathematicians, painters and sculptors for hundreds of years. It is found in mathematics, nature, architecture, painting and photography, and its name implies beauty, balance and harmony.

Through a series of mathematical calculations based on a numerical series, the parameters of these eye-pleasing proportions are established and applied since antiquity in all kinds of elements that aspired to formal perfection.

From the Parthenon to a photograph following the famous rule of thirds, a conch shell or the petals of a sunflower, the golden ratio is present in very many things around us.

golden ratio conch shell

What is the golden ratio?

The golden ratio is the link existing between a series of numbers based on the golden ratio to which an aesthetic condition is granted. That whose shape respects the golden ratio is considered beautiful. The golden ratio has been successfully applied in multiple projects, designs, buildings, photography, playing an important role in mathematics.

The golden ratio is also known as golden ratio, golden number or divine proportion.

The golden ratio is generated through a numerical series known as the Fibonacci Succession (or series).

Fibonacci, also known as Leonardo of Pisa, was the celebrated mathematician who introduced Arabic numeration to the West (up to that time Roman numeration was used) and who made known the infinite numerical succession whose proportions approximate the golden ratio.

What is the Fibonacci series ?

The Fibonacci series is based on an infinite succession of numbers. Starting with 1,1, the rest of the numbers are the sum of the previous two: 1+1=2, 2+1=3, 3+2=5, 5+3=8, 8+5=13, 13+8=21 and so on to infinity.

If we divide each number in the Fibonacci series with the previous one, this value approximates to the golden number or Phi number, whose value is 1.68033988749894…

If we do the division of the numbers of the Fibonacci series, we obtain results like for example: 89/55= 1.61818182 or 144/89= 1.61797753, which as you can observe correspond to the golden number or Phi.

What is the golden number?

The golden number is an irrational algebraic number. (its decimal representation is infinite and has no period) and is obtained from the ratio or proportion between two segments of a line, that is, from a geometric construction.

This value is 1.618033988749894… and is obtained from the formula:

golden number

The golden number (or Phi number) was discovered in antiquity and possesses many interesting properties, as this ratio is found both in arithmetic figures and in nature. It has also often been associated with the divine.

In the following video you have it perfectly explained:

Fibonacci Series

The golden spiral or Fibonacci spiral

On a visual level, if we apply the Fibonacci series on a rectangle, we obtain a spiral with proportions like the following:

Fibonacci spiral golden ratio

IF you look closely, you will see that the golden spiral is a more complex version of the rule of thirds that is applied in painting and photography.

Examples of golden ratio

The golden ratio has fascinated for hundreds of years all kinds of artistic or mathematical profiles. Its proportions have been found in numerous natural elements, associated with perfection and the divine, it has been applied in architectural works, sculpture and painting.

Let’s see some examples where we can find these proportions linked to the golden ratio or golden number.

The golden ratio in nature

This golden ratio is very present in nature. It is particularly curious, for example, to analyze the petals of a sunflower, where the Fibonacci series is repeated to perfection.

In sunflowers, the first row of petals may contain 21, 34, 55 or 89 petals corresponding in the second row with another 34, 55, 89 or 144. All are numbers and proportions that agree with the Fibonacci series or golden ratio.

And not only in sunflowers we find this pattern, also in petals of different flowers (there are flowers with 3, 5 and 8 petals and also with 13, 21, 34, 55, 89 and 144), in the distribution of leaves on a stem, in the relationship between the nervures of the leaves of trees, in the number of spirals of a pineapple, in the structure of hurricanes, in the relationship between the distance between the spirals of the interior of a snail, in the arrangement of galaxies, etc.

sunflower golden ratio

The golden ratio in the human body

The search for perfect proportions in the human body is commonplace in history. Perhaps one of the most iconic studies of proportions is Leonardo da Vinci’s famous “Vitruvian Man” .

Adolf Zeising also carries out numerous investigations on the golden ratio in nature and later in the human body, which he collects in his work “New doctrine of the proportions of the human body”, where he concludes that the golden ratio governs universally.

The golden ratio in the human body is found, for example, in the distance between the navel and the soles of a person’s feet, with respect to his total height; in the relationship between the length of the head and its width; in the relationship between the phalanges of the fingers, etc.

If you observe, for example, an ear you will see that it is in perfect compliance with the spiral of the Fibonacci series.

The golden ratio in art

The properties of the golden number or the golden ratio have been exploited in all branches of art since Antiquity because of its aesthetic character and its relation to the beautiful, the mystical or the divine.

Pictorial works such as the Gioconda or the Last Supper; of the great Leonardo da Vinci; or the Meninas of Velázquez, fit perfectly in the golden ratio; also the sculptures of Fídias or compositions of musicians such as Debussy or Mozart.

Today you can find it applied in design, in advertising posters or photography, always looking for the proportions of the beautiful and pleasing to the viewer.

The golden ratio in photography

In photography, the golden ratio is used to compose aesthetically pleasing and balanced images, and especially to place the protagonist at specific points in the image where he or she naturally stands out.

The famous rule of thirds, is a simplified version of this Fibonacci series or golden ratio, and indicates the strong points of the image, which translate into the place where the subject stands out most easily.

By dividing the frame into two horizontal and two vertical lines, 4 intersections are created. These intersections are what we know as strong points.

rule thirds flower

The golden ratio in architecture

Phidias, who is credited with the conception of the Parthenon temple, as well as some of the finest sculptures of Antiquity, was a great enthusiast of the golden ratio (in fact the name Phi is in his honor).

Works such as the Parthenon, which aims to unite beauty with the mystical, and his sculptures (preserved or not) were based on the golden number and the golden ratio.

We can also find the golden ratio in architectural works such as the Great Pyramid of Giza or in such famous modern architects as Mies Van der Rohe or Le Corbusier.

In short, the golden ratio is a way of approaching beauty in a universal way. That which is mathematically closest to Phi, we will perceive as beautiful and perfect.

In photography, the golden spiral can help us to compose a photograph pleasing to the eye, as well as to establish the place in which to place our protagonist.

But this notion of beauty and perfection is applicable to architecture, painting, musical scores, people or natural elements.

Did the concept of the golden ratio or the magic number ring a bell? Interesting, isn’t it? Ah, you see Fibonacci spirals everywhere? It’s normal, they are everywhere! Take the opportunity to improve your photographic compositions and experiment with new things.

If you found it interesting, do me a favor and share this content with whoever you think will benefit from it. Thank you very much and see you next time.

Leave a Reply