Phi and the Golden Ratio in Art
“Without mathematics there is no art.” Luca Pacioli
Art 101 – Laying out a painting on a canvas
As the Golden Section is found in the design and beauty of nature, it can also be used to achieve beauty and balance in the design of art. This is only a tool though, and not a rule, for composition.
The Golden Section was used extensively by Leonardo Da Vinci. Note how all the key dimensions of the room and the table in Da Vinci’s “The Last Supper” were based on the Golden Ratio, which was known in the Renaissance period as The Divine Proportion.
A more detailed view of Da Vinci’s intricate use of the Divine proportion is available by using PhiMatrix golden ratio design and analysis software:
In Michelangelo’s painting of “The Creation of Adam” on the ceiling of the Sistene 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. Click on the photo to see a larger version of the image.
Some 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:
- Red line – From the very top of her hair to the bottom of her lower foot.
- Green line – From her hairline at the top of her forehead to the bottom of her upper foot.
- Blue line – Her height, as measured from the middle of the feet to the top of her head at the back of the part in her hair.
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 French impressionist painter Georges Pierre Seurat is said to have “attacked every canvas by the golden section,” as illustrated below left.
Note that successive divisions of each section of the painting by the golden section define the key elements of composition. This principle is illustrated in the “Golden Ruler™”below:
The horizon falls exactly at the golden section of the height of the painting. The trees and people are placed at golden sections of smaller sections of the painting.
At right, Edward Burne Jones, who created “The Golden Stairs” at right (Click 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?
In “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 his 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 Geometry 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:
Draw a horizontal line halfway between the eye line and the bottom of the chin. This is the nose line.
Draw a horizontal line one-third of the distance below the nose line and the bottom of the oval. This is the mouth line.
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:
|Reality||By the books|
The mathematical differences in the two approaches are small, but enough to make a difference:
This explains why portraits drawn “by the books” sometimes look a little “long in the face.”
Image source: www.dickblick.com