P164 – Research Point – The Golden Section

Find out about the golden section. Find at least six examples by a range of artists and look at how they have used the golden section in the composition of their pictures.

First the maths bit! (courtesy of Wikipedia):

“In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure illustrates the geometric relationship. Expressed algebraically, for quantities a and b with a > b > 0,

 \frac{a+b}{a} = \frac{a}{b} \ \stackrel{\text{def}}{=}\ \varphi,

where the Greek letter phi (φ) represents the golden ratio. Its value is:

\varphi = \frac{1+\sqrt{5}}{2} = 1.6180339887\ldots.

The golden ratio is also called the golden section (Latin: sectio aurea) or golden mean.

GoldenRectanglesA golden rectangle with longer side a and shorter side b, when placed adjacent to a square with sides of length a, will produce a similar golden rectangle with longer side a + b and shorter side a. This illustrates the relationship  \frac{a+b}{a} = \frac{a}{b} \equiv \varphi.”

Okay, that’s straight forward but what’s that got to do with art? To be honest, I don’t know – and I suspect no one knows. Perhaps it’s just the way our brains are wired. Whatever the reason, the simple fact is that buildings,  paintings, in fact almost anything built or made which uses the Golden Section is aesthetically pleasing – it just looks right!

It has been used for centuries in architecture and design. The ancient Parthenon in Athens is built as a series of golden rectangles:

gold08

Meanwhile the CN Tower in Toronto contains the golden section in its design. The ratio of its total height of 553.33 meters to the height of the observation deck at 342 meters is 1.618.

Toronto SkylineEven Star Trek’s USS Enterprise uses the golden section!

 But these are not paintings!

bottocelli-birth-of-venus-golden-ratio-large-1024x656“The Birth of Venus, painted by Sandro Botticelli between 1482 and 1485, is one of the most famous pieces of the 15th century Italian art. The canvas is a golden rectangle. There are many golden sections within the painting. For example, the horizontal golden ratio line from the top to the bottom crosses exactly at the top of the sea shell while the horizontal golden ratio line from the bottom to the top crosses at the horizon line and directly through Venus’ navel. Meanwhile, the vertical golden ratio line from the left side to the right side falls exactly at the point at which the goddess of Spring Hora’s thumb and finger are touching, and the vertical golden ratio line from the right side to the left side falls at the point where the land on the horizon meets the sea.

In a similar way, there are golden sections in Botticelli’s The Annunciation:

Botticelli-Cestello-Annunciation-1489

The Mona Lisa by Leonardo da Vinci can be divided into several golden rectangles. Her face, for example, fits one. Indeed, like the Birth of Venus, the dimensions of the painting are themselves a golden rectangle.

Math a18

6-mona-lisa

Da Vinci’s Annunciation also uses several golden sections. For example the brick wall of the courtyard is at exact golden ratio proportions in relation to the top and bottom of the painting.

da-vinci-the-annunciation-divine-proportion

It is estimated that about a third of the paintings of George Suerat, the French Post-Impressionist painter well known for his development of pointilism, use the golden section. For example, horizons are often on a golden section or a key feature is placed on the intersection of two golden ratios. As a photographer, I often place an important compositional detail on the intersection of thirds, but the use of the intersection of golden ratios looks so much better. Here are a handful of Suerat’s paintings:

Seurat-Auf-einer-Wiese-sitzendes-Bauernmädchen
Seurat-Figures-assises-1024x655 Seurat-Frau-mit-Sonnenschirm Seurat-Knabe-mit-Pferd

Some of Turner’s paintings seem to have references to the golden section.

fighting

In The Fighting Temeraire, the intersection of two golden sections coincides with the point midway between the sail of an older boat and the chimney of the modern tug which is towing the ancient warship away to be broken up.

steam

Secondly, in Rain, Steam and Speed – The Great Western Railway, the train is at the intersection of two golden sections.

slaver

Finally, in The Slave Ship, the ship and the horizon are along the golden section.

Salvador Dali used the golden section in his painting The Sacrament of the Last Supper. He framed his painting in a golden rectangle, positioning the table exactly at the golden section of the height of his painting and the two disciples at Christ’s side at the golden sections of the width of the composition. I believe that the duodecahedron used by Dali has links with the golden section.

lastsupper

About this point, I discovered some downloadable software called Phi Matrix. This allows quick analysis of images according to the golden section. I chose a couple of artists at random – Picasso and Vermeer – and I looked at some of their paintings to see if the golden section was apparent. With Picasso, some compositional features in one or two works were close to intersections, but rarely spot on:

picasso picasso2

With Vermeer’s The Geographer, the eyes were on a golden section, but this was the only painting I could find which did have such a section, although I did not analyse them all by any means.

geographer2

One out of three dozen? This got me thinking whether it was intentional or unintentional use of the golden section. There was only one way to find out and that was to analyse one of my own works – Self Portrait in the style of Andre Derain. I’d based this on a portrait of Henri Matisse by Derain which I’d copied at a painting course. As you can see, my eyes are on a golden section (and my mouth is almost on another).

selfportrait-derainNow I know that I did not set out to use the golden section in this painting. However, I based it on a photograph which I liked. Why did I like the original photograph? Perhaps, as I said at the beginning, it’s just the way our brains are wired. Perhaps I liked the photograph because it was aesthetically pleasing because the eyes were on a golden section.

 

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About notes to the milkman

I'm a printmaker based in the North West of England, living in Bolton and printing at Hot Bed Press in Salford. Please visit my website johnpindararts.weebly.com
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5 Responses to P164 – Research Point – The Golden Section

  1. Reblogged this on notes to the milkman and commented:

    This is a research piece I did for my OCA Drawing 1 course.

  2. I am not certain I agree with the theory which seems based in symmetry but I did enjoy this post very much! Nice work in your painting!

  3. seascapesaus says:

    I am inclined to think it is intuitive placement, but who knows. A tutor once showed evidence of pre-Renaissance (and later) painters using the golden section and attributed early use of it to subliminal designs of the cross. Perhaps asymmetry is also cultural. I understand that Chinese people would arrange two or four flowers whereas my inclination would be to use one or three.

    • I’ve been a photographer far longer than I’ve been an artist so I’ve been brought up on the rule of thirds, together with foreground, middle and distance, but I’ve always been told to photograph odd numbers of things. It just looks better to my Western eye.

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