Also known as the divine proportion and the golden mean, the golden ratio is a mathematical principle that can be observed in nature and has been applied to man-made things, including art, design, architecture, and music.
Many prominent artists have used the golden ratio in art to make their work more visually appealing. But what is the golden ratio, exactly? Let’s find out.
What is the golden ratio?
The golden ratio is a geometric relationship in mathematics that is achieved when the ratio of two quantities is similar to the ratio of the sum of the two quantities to the greater of the two quantities. The value is an irrational number that has a value of approximately 1.618. The decimal form of the golden ratio stretches into infinity and, like the value of pi, never repeats.
The golden ratio is represented by the phi (“fie”) – a Greek letter – and is also called the golden section, divine section, golden cut, golden number, golden proportion, sacred cut, medial section, and divine section. These terms all mean the same thing. The golden ratio or phi is very useful in quadratic equations, trigonometry, and even in programming software.
If you want to try to visualize the golden ratio, imagine a rectangle that has a length of 1.618 and a width of 1. If I asked you to divide the rectangle such that one part is a rectangle and one part is a square, the sides of the square would have a ratio of 1:1. Meanwhile, the rectangle you are left with will be proportionate to the rectangle you started with and have a ratio of 1:1.618.
You can divide the smaller rectangle again and get a square with a ratio of 1:1 and a rectangle with a ratio of 1:1.618. This will continue on, yielding the exact same ratios, until you run out of space.
We can use the golden ratio to make forms like the golden rectangle, where the ratio of one side, particularly the longer side, to the shorter side is 1:1.618, as well as the golden spiral, which gets wider by a factor of phi or 1.618 every quarter turn. The golden ratio can also be applied to other geometric forms, including triangles, prisms, pyramids, circles, polygons, and more.
Some mathematicians have found that the human face follows the golden ratio. The more closely the proportions of the human face adhere to the golden ratio, the more attractive it is. However, this isn’t true all the time, as each face is distinct and our opinions about what makes a face beautiful vary widely.
The golden ratio in art
Thousands of years ago, someone discovered that when you apply the golden ratio to art, it becomes very appealing to the eye.
Artists began mathematically calculating the proportions in their paintings. Since then, many have used the golden ratio to position their subjects and to balance the smaller elements with the larger elements.
The golden ratio is also applied to the creation of three-dimensional artworks. It is evident in works such as Bird in Space (1927) by Constantin Brancusi and in Three Points (1939-1940) by Henry Moore.
The golden ratio in paintings
Some art experts suggest that the Italian artist Michelangelo may have used the golden ratio when he painted The Creation of Adam (1512), the masterpiece that adorns the ceiling of the Sistine Chapel. Many have observed that if you put a border around the area that contains God and Adam, the finger of God connects with the finger of Adam at the exact golden ratio point of the height and width of that area.
Leonardo da Vinci
Some mathematicians have scrutinized the masterpieces of Leonardo da Vinci and found that he used the golden ratio extensively in his work. In The Last Supper (1495-1498), for instance, the hands of Jesus are placed at the golden mean of half of the height of the painting. Some have calculated that the dimensions of the room and the table in the composition also follow the golden ratio.
Meanwhile, in The Annunciation (1472-1475), the ratio of the wall of the courtyard to the top and bottom of the composition is equal to the golden ratio. The emblems on the table are also in golden ratio to the width of the table.
In The School of Athens (1509-1511) by the Italian Renaissance painter Raphael, there is a small golden rectangle in the middle. The ratio of the height and width of the rectangle is equal to the golden ratio. The golden mean is also evident throughout the painting, in the columns, arches, stairs, and some decorative elements.
Neo-Impressionist master Georges Seurat may have used the golden ratio to organize some of his compositions, including the Bathers at Asnières (1884), where it defines the horizon, balances the scene, and places some of the subjects and points of interest. In Bridge at Courbevoie (1887), the horizon, the mast, and the jetty all seem to have been positioned using the golden ratio.
Edward Burne Jones
The Golden Stairs (1876-1880) is one of the best examples of the use of the golden ratio in paintings. Here, the golden ratio appears over and over again in the stairs. It’s also in the proportions of the women’s dresses and in the rings of the trumpet carried by one of the women.
The Sacrament of the Last Supper (1955) by the Surrealist artist Salvador Dali is another prime example of a painting suffused with the golden ratio. Here, the dimensions of the composition follow the golden ratio as does the dodecahedron dominating the background.
The golden ratio can also be found in the edges of the ceiling and the location of the two disciples flanking Jesus Christ. The position of the table is in golden ratio to the height of the painting.
There are many reasons for the use of the golden ratio in art. It helps balance the weight of the artwork and makes the composition instantly appealing to the viewer. Even when we don’t know that the proportions between the elements of an artwork follow the golden ratio, we’re immediately attracted to that work.