A fundamental principle underlying painting and other art forms is the concept of ratio — how a work is divided and how its various elements interact. One of the most fundamental models of visual organization is the golden ratio, also known as the divine proportion.
An early representation of this concept dates back to a Greek geometric formula from as far back as the 5th century BC. This relatively straightforward mathematical constant has persisted over the centuries, partly because of its prevalence in the natural world. From plant leaves to galaxies, spirals often follow the golden ratio's growth rate. This concept has deep roots in Western art, with even Leonardo da Vinci providing illustrations for "De divina proportione", a 1509 text by the mathematician Luca Pacioli. Here are several paintings that incorporate the divine proportion.
The Starry Night by Vincent van Gogh
This famous painting "The Starry Night" not only revolves around the linear core of the golden ratio, with the left third of the painting featuring dark, swaying trees in the foreground, counterbalancing the right two-thirds gently depicting a village in the background. However, it's the starry spirals of the night sky overhead that truly dominate, alluding to the primordial flow of galaxies, making it one of the world's most renowned works of art.
Girl with a Pearl Earring by Johannes Vermeer
Whether by Vermeer's conscious design or not, overlaying a Fibonacci spiral onto "Girl with a Pearl Earring" highlights the fact that this seemingly simple portrait is also a complex geometric composition. The young woman's unique posture—her head turned over her shoulder, gazing at a painter positioned almost behind her — creates a line of tension that starts around her eyes, revolves over the top of her head, and descends through her headscarf. The dark, empty background introduces rectangular blocks of space that evoke the golden ratio. The subject's open, profoundly human expression is intricately constructed within this complex formal framework.
Bathing at Asnieres by Georges Seurat
Best known for his use of pointillism—where dots replace lines, effectively "fooling" the human eye into perceiving radiant images—Seurat also employed the golden ratio to underpin his compositions. Similar to "The Starry Night", "Bathing at Asnieres" adopts a left-to-right linear "rule of thirds" composition. It guides the viewer's eye from the hats of two figures sitting on the grass to a boy standing in the water. Yet, these figures, in harmony with the trees and smoke rising from one of the smokestacks in the background, create an overall sense of rotation—a feeling that the human figures are part of a larger whole.
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The Golden Stairs by Sir Edward Burne-Jones
"The Golden Stairs" incorporates an understated, tight spiral effect—a detail that may easily go unnoticed amidst the more conspicuous top-to-bottom circular structure of the painting. At first glance, the artwork is dominated by the half-circle of women descending the stairs. However, within this composition, starting with the small tree beneath the stairs (standing out due to its dark green contrast with the surrounding light colors), a counter spiral ascends the staircase's firm line. It then curves through the women themselves, culminating in the bold square of blue sky—an additional focal point on the canvas.
The Great Wave off Kanagawa by Katsushika Hokusai
The most famous composition by a painter renowned for geometrically precise drawings, this work captures one of the Earth's most common yet vibrant spiral forms. Each ocean wave builds itself up in accordance with the golden ratio, only to crash into oblivion eventually. This inherent certainty forms the centerpiece of "The Great Wave". The composition's underlying geometry is further emphasized by the placement of the pyramid-like Mount Fuji in the background, just off-center. Above it, the sky—a rectangular expanse of negative space—stands ready to absorb the force of the wave, about to turn in on itself, all while carrying the frail, almost imperceptible human-made boats with it.
These paintings not only showcase the artists' creativity but also highlight the integration of mathematical principles in crafting visual splendor, revealing the intricate connection between art and mathematics.
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FAQs
For instance, in 'The Birth of Venus', Botticelli uses the Golden Ratio to position Venus at the centre of the painting, creating a balance between the other elements in the artwork. This canvas print accurately captures the balance and harmony in Botticelli's masterpiece.
How is the golden ratio used in famous paintings? ›
It is believed that Leonardo da Vinci used the golden ratio in the proportions of the table, the placement of the figures, and the overall composition of the painting. The horizontal and vertical lines in the painting are believed to follow the golden ratio, creating a sense of balance and harmony.
Which famous painter used golden ratio in his famous work? ›
Discover the ways Leonardo used the Golden Ratio in some of his most famous works of art. Da Vinci created the illustrations for “De Divina Proportione” (On the Divine Proportion), a book about mathematics written by Luca Pacioli around 1498 and first published in 1509.
How is the golden ratio used in Starry Night? ›
This famous painting "The Starry Night" not only revolves around the linear core of the golden ratio, with the left third of the painting featuring dark, swaying trees in the foreground, counterbalancing the right two-thirds gently depicting a village in the background.
How is the golden ratio used in the Mona Lisa painting? ›
A famous example of the application of the golden ratio is Mona (Figure 4, [6]) Lisa. "Mona Lisa's face is a perfect golden rectangle, according to the ratio of the width of her forehead compared to the length from the top of her head to her chin." ...
How was the golden ratio used? ›
The golden ratio has been used to analyze the proportions of natural objects and artificial systems such as financial markets, in some cases based on dubious fits to data. The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other parts of vegetation.
How to use the golden rule in art? ›
You can create your own golden ratio image by dividing the width and height by 1.618. Artists throughout time used this technique. Draw diagonal lines from each corner and line. Position the elements within your composition on this structure.
Did Picasso use the golden ratio? ›
Pablo Picasso & the Golden Ratio & Fibonacci Numbers: It has been said that the postmodern movement neglected classcial rules of composition, but as seen here, Picasso embraced the golden number PHI and the golden rectangle, PHI grid, and golden harmonies.
How do you use golden ratio in images? ›
In photography, the golden ratio can be used to create balanced and aesthetically pleasing compositions. This is achieved by dividing the frame into thirds, both horizontally and vertically, and placing the subject or key elements of the image at the intersection points of the lines.
What is golden ratio in stars? ›
The objects were found in data from the Kepler space telescope by looking for stars with two characteristic pulsation frequencies that have a “golden ratio” of approximately 1.62.
In 1509, Luca Pacioli's dissertation presented the idea that 1.618 formed the basis for the Divine Proportion or Ratio. It was used extensively during the Renaissance to achieve balance and beauty in art. Leonardo Da Vinci's The Last Supper is often cited as an example of the golden ratio's application in art.
How is the golden ratio used in the Last Supper? ›
In 1955, Dalí painted The Sacrament of the Last Supper. This great work contains the golden ratio in two ways. The proportions of the painting correspond directly to the golden ratio. It also features a huge dodecahedron harmoniously dominating the background of the scene.
How did Michelangelo use the golden ratio? ›
In 2013, I reported that Michelangelo used the golden ratio in his painting “The Creation of Adam” in the Sistine Chapel. This Divine Proportion appears at the point at which Adam's finger is touched by the finger of God, as God breathes life into Adam.
Which artists seem to have used the golden ratio in their works of art? ›
Sixteenth-century Europe witnessed some of the more clear-cut examples of the golden ratio in action. Italian artists such as Leonardo da Vinci, Michelangelo, and Raphael all demonstrated the use of this central proportional relationship in their paintings.
Why did artists such as Leonardo da Vinci use the golden ratio? ›
By incorporating the golden ratio in their paintings, artists like Da Vinci aimed to create compositions that were visually appealing and pleasing to the viewer. They believed that using this ratio would help them achieve a sense of balance and harmony in their artwork.
What is the famous golden ratio? ›
The golden ratio is an irrational number that approximately equals 1.618. For artistically-minded people, the ratio—or better yet, the divine proportion—might be easier to understand visually. This is easiest to demonstrate with the golden spiral, which is often depicted and constructed within a rectangular frame.
