The Use of Phi in Painting

Pacioli once said that “without mathematics there is no art”. Leonardo da Vinci’s use of phi in his paintings exemplifies this principle. Phi is known by many names including the Golden Ratio, the Divine Proportion, the Golden Mean, and Mean of Phidias. It is represented by the equation:?=(1+?5)/2 or the irrational number 1.6180339887….
Phi In Art
The use of phi when painting the human form or many natural elements helps the artist to establish the most visually appealing proportions for the contents of the painting. In figurative painting phi is used to create the correct balance between elements of the face, the body and the composition to canvas. The Golden Ratio is evident in many areas of the human body including the ear canal, the separation between the between the pupils as compared with the separation between the eyebrows, the spacing between the mouth, chin, nose and forehead, the ratio between the legs and the torso and the segmentation of the fingers. Although few humans display these exact proportions extensive research by the Marquardt Beauty Analysis has found that the closer a person’s physical appearance aligns to the Golden Ratio the more beautiful he/she is considered to be.
In nature, the Golden Ratio can be found in the shape of our galaxy, the crest of a wave, the branches of a tree, pine cones, flowers, shells and various other elements. In fact the prevalence of the ratio in our world is thought to be the reason for the inherent sense of beauty created when it is used in visual art.
How to Lay Out a Phi Based Canvas
To properly lay out a phi designed canvas draw a diagonal from one corner to the opposite, from that diagonal draw a line at 90 degrees to a third corner. Then draw horizontal and vertical lines through the intersection point. If the grid is not to be subsequently divided the intersection point should be the focal point of the composition (often this is the horizon line). Countless subdivisions can be created to ensure balance throughout the work.
Examples of phi based art can be found in the works of Da Vinci, Raphael, Monet, Dali and countless others. Da Vinci spent years perfecting his “phi framework” and used it throughout his art as well as his design work.
Perhaps Pacioli was referring to the sense of perfection he felt when viewing art designed around phi.

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