Part 3: How the golden mean caught on with artists

After considering the Parthenon and Leonardo Da Vinci, let's see if we can continue taking a rational look at the claims about "phi," (or the "golden mean" or "golden ratio") that has been so popular with artists.

The story gets more complex in the nineteenth and twentieth centuries as artists begin to consciously adopt it in their work, and so it gets harder to separate fact from fiction. Let's start with what we know for sure.

One of the nineteenth century champions of the golden mean was German psychologist Adolf Zeising (1810-1876) who found the golden mean in nature, especially in branching patterns, leaves, and seed patterns. These manifestations of the ratio are acknowledged by even the most skeptical scientists.

Over the years scientists have found other places where the golden mean turns up. In 2010, the journal Science published a paper about how these numerical patterns appear in crystals at the atomic scale.

The golden mean appears most often in terms of numerical relations, such as the Fibonacci numbers that appear in flowerheads, seeds, and shells.

Zeisler promoted the idea that the golden mean could be found in the Parthenon and the works of Leonardo. He made broad claims that the golden ratio was: 

"the universal law in which is contained the ground-principle of all formative striving for beauty and completeness in the realms of both nature and art, and which permeates, as a paramount spiritual ideal, all structures, forms and proportions, whether cosmic or individual, organic or inorganic, acoustic or optical; which finds its fullest realization, however, in the human form." 

Whether or not Zeisler's ideas had a solid grounding in observable fact, they caught on with artists and mystics. 

A group of painters led by Jacques Villon and called "Section d’Or," (French: “Golden Section”) held exhibitions in Paris between 1912 and 1914. They included Juan Gris, Robert Delaunay and Giro Severini and several others, though not all used the mathematical principles. Later artists such as Salvador Dali also claimed to use golden mean principles. 

In the 1920s, Jay Hambidge, a student of William Merritt Chase, published a book called Dynamic Symmetry  which presented a grid system based on the golden mean. The system was picked up by artists such as Maxfield Parrish, whose preliminary drawing for the famous painting "Daybreak" is above. Here's one person's analysis of the structure behind Daybreak. 

Above: Architects' Data (German: Bauentwurfslehre) First published in 1936 by Ernst Neufert,

Golden mean principles were adopted in extremely different aesthetic quarters in the twentieth century. Many readers of this blog have encountered golden mean principles in the context of contemporary realist ateliers.

The methods were also embraced by the Bauhaus school (literally "House of Construction"), founded by Walter Gropius in Germany between World War I and II, and run by influential architects such as Ludwig Mies van der Rohe. 

The Swiss architect Le Corbusier, who championed the international style of building design, used the golden ratio and the Fibonacci series as a central tenet of his work and teaching. He described the patterns as:

 "rhythms apparent to the eye and clear in their relations with one another. And these rhythms are at the very root of human activities. They resound in man by an organic inevitability, the same fine inevitability which causes the tracing out of the Golden Section by children, old men, savages and the learned."

Many Bauhaus teachers emigrated to America, where their ideas about the golden section became incorporated in university art educations, where they are taught to this day. 

Tomorrow we can evaluate claims of Zeisler and Le Corbusier about whether the golden mean really does appear in natural forms such as the human figure.
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Book: The Elements of Dynamic Symmetry (Dover Art Instruction)
Book: Bauhaus 1919-1933 (Taschen 25)
Book: Maxfield Parrish by Coy Ludwig
Photos of planet, hand, etc. from here

Coneflower from "Math Surrey" 

GurneyJourney series: Mythbusting the Golden Mean

Part 1: Debunking claims about The Parthenon

Part 2: The golden mean and Leonardo
Part 3: How the golden mean caught on with artists
Part 4: The golden mean and the human body
Part 5: Last question about the golden rectangle