The Golden Ratio in Art: Truth, Myths and Use

The golden ratio is the proportion of roughly 1 to 1.618, in which the longer part relates to the shorter as the whole relates to the longer. The number is called phi. It has fascinated artists, architects and mathematicians for over two thousand years, but many claims that famous works are built on it are exaggerated.

Facts

What the golden ratio is

Imagine a line divided into two parts, a longer and a shorter. If the longer part relates to the shorter in the same way as the whole line relates to the longer, the division is golden. The ratio is about 1.618, and the number is called phi. A rectangle with sides 1 and 1.618 is called a golden rectangle. If you cut a square off it, what is left is a new, smaller golden rectangle.

Euclid described the division in the Elements, and in the thirteenth century Fibonacci presented the sequence 1, 1, 2, 3, 5, 8, 13 … in which the ratio of consecutive numbers approaches phi. The name golden section only came in the nineteenth century. The explanation is not mystical: it is simply a mathematical ratio with unusual properties.

The Renaissance and Leonardo

In the Renaissance proportions became an ideal. The mathematician Luca Pacioli wrote the book De divina proportione, the divine proportion, in 1509, and Leonardo da Vinci drew the geometric solids that illustrated it. Leonardo and his contemporaries were interested in how mathematics, perspective and beauty are connected; see perspective and the guide to linear perspective.

But Leonardo did not necessarily use phi in the Mona Lisa or The Last Supper. Golden rectangles can be found in them if the diagram is laid on in a certain way, but there is no evidence in his own writings. The same warning applies to The School of Athens by Raphael: the order of the picture is classical and balanced, but any exact formula is unclear.

Myths and what is documented

There are many claims: that the Parthenon in Athens is built to the golden ratio, that the pyramids are, that the human body is. Measurements usually show that the proportions come close but not exactly, and with so many measurements to choose from it is almost always possible to find something that resembles 1.6. This is sometimes called numerology. More about the classical temple is found in the guide to the classical orders.

What is documented is that some artists and architects have used the proportion deliberately. Le Corbusier based his system of measurement, the Modulor, developed from 1943, on human dimensions and the golden ratio; see Le Corbusier. Salvador Dalí painted The Sacrament of the Last Supper in 1955 on a canvas with golden proportions and let a dodecahedron hover over the picture. Georges Seurat and Piet Mondrian have also been mentioned in this context, but scholars disagree there.

How to use it in composition

For a painter or photographer the golden ratio is an aid, not a law. You can place the main subject of the picture about 0.62 of the way across it and so get a balanced but not symmetrical composition. The familiar rule of thirds is a simplified version. Read more about balance and picture surface in the section on composition and in the guide to reading a painting.

The golden ratio also turns up in nature, for example in how the seeds of a sunflower and the scales of cones are arranged in spirals according to Fibonacci numbers. That is an explanation, not a design rule. Today the proportion is used in the design of logos, screens and typography, and in our own eyes: we perceive balanced ratios as harmonious, but taste varies over time and between cultures. See also Dieter Rams and good design in the design section and the Renaissance.

How to recognise it

Exercise

What is the approximate value of the golden ratio?