Phi and the Golden Section in Art

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 Section, which was known in the Renaissance period as The Divine Proportion.

The French impressionist painter Georges Pierre Seurat is said to have "attacked every canvas by the golden section," as illustrated here:

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. 

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:

1. Draw a horizontal line halfway between the eye line and the bottom of the chin. This is the nose line.

2. 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