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. While the result is technically not a truly logarithmic, or “golden,” spiral, it is a close approximation. More importantly, this is the type of process artists have used to visualize and apply the divine proportion to their paintings throughout the centuries. Here are several examples of how the golden ratio can be applied to works from art history. Courtesy Wikimedia Commons. Photo by Guillaume Baviere. Golden ratio applied by Art & Object. The Parthenon, c. 447 BC. Athens, Greece. According to historians, the golden ratio was first studied by
ancient Greek mathematicians. While some believe the Grecians did associate the ratio with aesthetics and even applied it to achieve beauty (many argue it was intentionally used in the Parthenon) there is little evidence to support this. UFFIZI GALLERY, FLORENCE ITALY. Golden ratio applied by Art & Object. Leonardo da Vinci,
Annunciation, c. 1472. Widespread artistic interest in the ratio (within Western circles) can be justifiably associated with the publication of Divina proportione in 1509. The book, written by mathematician Luca Pacioli and illustrated by Leonardo da Vinci, was widely lauded for its clear writing and stunning illustrations. Many believe these qualities allowed
it to reach and occupy artistic circles. Courtesy of the Metropolitan Museum. H. O. Havemeyer Collection, Bequest of Mrs. H. O. Havemeyer, 1929. Accession Number: JP1847. Golden ratio applied by Art & Object. Katsushika Hokusai, Under the Wave off Kanagawa, also known as The Great Wave, from the series Thirty-six Views of Mount Fuji, 1831. Woodblock print; ink and color on paper. It is important to note that the
logarithmic spiral and the principles behind it are woven into nature and thus extend far past the reaches of the Greeks and Da Vinci. This nineteenth-century Japanese print depicts a wave—a naturally occurring spiral—and serves as a testament to the long non-Western tradition of seeking influence from nature and the beauty it intrinsically offers. UFFIZI GALLERY,
FLORENCE ITALY. Golden ratio applied by Art & Object. Raffaello Sanzio, Madonna of the Goldfinch, 1505 - 1506. In Raffaello Sanzio’s Madonna of the Goldfinch, the principles of the golden ratio can be seen throughout the painting. The outer limits of the spiral follow Madonna’s upper-left side, the far leg of John the Baptist, and the feet of the Christ Child. These three arcs work together to lead the eye through the painting and the ratio as a
whole gives the image a sense of balance and so-called divine proportion. Courtesy Wikimedia Commons. Golden ratio applied by Art & Object. Rembrandt, The Anatomy Lesson of Dr. Nicolaes Tulp, 1632. There is no doubt that the golden ratio runs rampant through the art of the sixteenth century and beyond. The most evident manifestation of the ratio lies in the composition of paintings and cutting of canvases. This Rembrandt painting is a particularly stunning example of the spiral’s manifestation as it is not only shown through a complex yet clear layout of figures and background. The compositional tool has also been used to enhance the story. For example, an unbreakable connection is created between the text in the lower right corner and the students. Courtesy of the
Metropolitan Museum. Robert Lehman Collection, 1975. Accession Number: 1975.1.110. Golden ratio applied by Art & Object. Petrus Christus, A Goldsmith in his Shop, 1449. Oil on oak panel. This painting was created fifty years before the publication of Divina proportione and was painted by a Northern European artist. The art world of this region and
time focused less on mathematical approaches such as one-point perspective and the golden proportion, favoring symbolism and moralistic undertones. And yet, the presence of a golden spiral here can not be denied. Courtesy Wikimedia Commons. Golden ratio applied by Art & Object. Piet Mondrian, Tableau 1, 1921. Painter and art theoretician Piet Mondrian often wove the golden ratio into his work to an astonishing degree. Although the
Modernist originally made figurative art, he pivoted to focus on abstract, geometric work and eventually became well-known for his rectangle-square compositions in particular. He is now considered one of the best and most important artists of the twentieth century. “Without mathematics there is no art,” said Luca Pacioli, a contemporary of Da Vinci. Just as the Golden Section is found in the design and beauty of nature, it can also be used to achieve beauty, balance and harmony in art and design. It’s a tool, not a rule, for composition, but learning how to use it can be a great Art 101 lesson on laying out a painting on a canvas. For those with a deeper understanding yet, the golden ratio can be used in more elegant ways to create aesthetics and visual harmony in any branch of the design arts. As you’ll find in the examples below, it has been used by some of the greatest artists the world has known. Oddly enough, you may also find critics who say that the golden ratio cannot be found in art at all. Such statements often come from Ph.D.s in mathematics who hold a very theoretical viewpoint that nothing in the real world can be a golden ratio. Why? Simply because it has an infinite number of digits. (See a review/rebuttal on art and architecture and design.) Pi does too, so this way of thinking says there are no circles in the real world either. For the rest of us, practical applications of mathematical concepts are a simple and necessary everyday occurrence in the arts, engineering and applied sciences. Leonardo da VinciThe Golden Section was used extensively by Leonardo Da Vinci. Note how all the key dimensions of the room, the table and ornamental shields in Da Vinci’s “The Last Supper” were based on the Golden Ratio, which was known in the Renaissance period as The Divine Proportion. The lines showing Da Vinci’s intricate use of the Divine proportion were creating using PhiMatrix golden ratio design and analysis software:  Note in Da Vinci’s “The Annuciation” that the brick wall of the courtyard is in golden ratio proportion to the top and bottom of the painting: Even the fine details of the emblems on the table appear to have been positioned based on golden proportions of the width of the table: Other golden proportions can be found in “The Annunciation” that illustrate the point and give evidence of Da Vinci’s intent. See other examples of Da Vinci’s use of the Divine proportion here and my article on the beautiful golden ratios in his painting “Salvator Mundi.” The golden ratios that Leonardo da Vinci used in the composition of this painting are explored in the video below: Click on the YouTube button and watch it in full screen mode. MichelangeloIn Michelangelo’s painting of “The Creation of Adam” on the ceiling of the Sistine Chapel, look at the section of the painting bounded by God and Adam. The finger of God touches the finger of Adam precisely at the golden ratio point of the width and height of the area that contains them both. Alternatively, you can use the horizontal borders of the width of the painting and get the same result. See my separate article revealing Michelangelo’s use of over two dozen golden ratios in his composition of the paintings on the Sistine Chapel. Click on the photos below to see a larger version of the sample images. RaphaelRaphael’s “The School of Athens” provides another wonderful example of the application of the golden ratio in composition. A small golden rectangle at the front and center of the painting signals the artist’s express intent in the use of this proportion. We find that Raphael used golden ratios throughout the painting, giving it a wonderful visual harmony. BotticelliSome say that Bottocelli composed “The Birth of Venus” such that her navel is at the golden ratio of her height, as well as the height of the painting itself. Some argue this isn’t the case. Close examination shows that you can take the golden ratio point using several different logical variations, and they all come to her navel, as well as the bottom tip of her right elbow:
Perhaps a coincidence in composition, but then again perhaps not. See a more extensive analysis yet of golden ratios in The Birth of Venus. The best evidence is that the canvas itself is a golden rectangle, with the ratio of its height to its width in golden ratio proportion. The dimensions of the canvas is 172.5 cm × 278.5 cm (67.9 in × 109.6 in). The width to height ratio is 1.6168, a variance of 0.08%, only 1/20th of an inch, from the Golden Ratio of 1.618. SeuratThe French impressionist painter Georges Pierre Seurat is said to have “attacked every canvas by the golden section.” In the examples, below the horizons falls exactly at the golden section of the height of the paintings, as are other key compositional elements of the paintings. A more detailed analysis and commentary with dozens of other examples is provided on page Georges Seurat and the Golden Ratio in Art Composition. Edward Burne JonesBelow, Edward Burne Jones, who created “The Golden Stairs” (Click HERE for enlarged view), also meticulously planned the smallest of details using the golden section. Golden sections appear in the stairs and the ring of the trumpet carried by the fourth woman from the top. The lengths of the gowns from the sash below the breast to the bottom hem hits the phi point at their knees. The width of the interior door at the back of the top of the stairs is a golden section of the width of the top of the opening of the skylight. How many more can you find?
Salvador DaliIn “The Sacrament of the Last Supper,” Salvador Dali framed his painting in a golden rectangle. Following Da Vinci’s lead, Dali positioned the table exactly at the golden section of the height of this painting. He positioned the two disciples at Christ‘s side at the golden sections of the width of the composition. In addition, the windows in the background are formed by a large dodecahedron. Dodecahedrons consist of 12 pentagons, which exhibit phi relationships in their proportions (see the Geometry page for details). Note: Insights on the use of the Golden Section by Seurat and Dali were provided by Jill Britton. Art 102 – Painting faces like Da Vinci instead of Picasso … or “Why so long in the face?”Many art teachers and books will tell you that a face can be drawn by dividing the face in halves and thirds, as follows:
That’s a nice approximation, but if you want your faces to have both reality and beauty, use phi. More information on the pervasive appearance of phi in the human face is presented on the Face page, but look at the subtle difference this creates in the length of the nose and overall facial proportions: By the books Reality The mathematical differences in the two approaches are small, but enough to make a noticeable difference:
This explains why portraits drawn “by the books” sometimes look a little “long in the face.” Image source: www.dickblick.com What is the proportion system used by Raphael in the School of Athens?The scale and proportion used in School of Athens is very complex and ironic. The piece uses both one-point and two-point perspective. The proportion of the image is symmetrical and evenly distributed on each side.
Which of the following terms describes a method of measuring human proportions?Anthropometry involves the systematic measurement of the physical properties of the human body, primarily dimensional descriptors of body size and shape.
What type of scale is used to show that the largest person or object is the most important?Scale can refer to any relationship of parts to the whole, but one particular type is of great significance in many periods: Hieratic scale is scale based on relative importance. That is, the more important a figure, the larger he or she is in relation to the figures around him or her.
How did the discovery of the Golden Mean influence Greek art?How did the discovery of the Golden Mean influence Greek Art? The discovery of the Golden Mean made the Greeks fell as if they had found the ideal proportion which was used to control the relationship of the parts in their pottery, architecture, and sculpture.
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Which of these artworks have been composed according to the proportions of the golden section?
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