The golden ratio

Andy introduced us to the concept of ‘the golden ratio’ as an alternative to ‘the rule of thirds’.
The rule of thirds is a basic rule for composition of photographs. You need to imagine lines going through the frame at 1/3 and 2/3 of the way through both horizontally, vertically to create a grid:

The aim is to line things up with the lines on the grid, either vertically or horizontally, or fill up each section with a different, area or object of interest, or to fill 1/3 of the image with one thing and 2/3 with something else. This is supposed to give a more aesthetically pleasing image.
The golden ratio is a mathematical way of capturing aesthetics. TThe first known use of the ratio was by the ancient Egyptians when they designed the pyramids.  The ratio was also used by ancient Greeks in their buildings such as the Parthenon at the Acropolis.

During the Renaissance European artists revisited ancient art for inspiration and utilised the ratio in sculptures and paintings. For example, Leonardo da Vinci applied the golden ratio when he painted the Mona Lisa.

One of the most interesting graphic forms of the golden ratio is the nautilus shell and the way the shell starts from a central origin and then spirals outward around itself until it reaches the opening of the shell.

The golden ratio can be depicted in a rectangular form in which the rectangle is made up three smaller rectangles. Add enough golden rectangles and you can create the spirals of a nautilus shell.

(Source: http://photoinf.com/Golden_Mean/Edwin_Leong/Camera_Hobby_-_e-Book_on_the_Golden_Ratio.htm)

Le Corbusier was one of the most important architects of the 20thC – he was a pioneer of modern architecture with a vision for creating a utopia for the masses through his urban planning. He was also an artist who explored Cubism before rejecting it in favour of Purism. The golden ratio was used extensively by Le Corbusier in his architecture.

How does this relate to photography? In simple terms, a photographer can apply the golden ratio by using it to think about where to place objects in the composition.

"Using the Golden ratio forms a fluid line for the eye to trace through the picture, where the Rule of Thirds is more static. Your viewer's gaze will invited along the line of the spiral which creates a more symmetrical visual flow and a compelling experience. You want to place the subject (or focal point) of your photograph in the tightest end of the spiral, and the other elements of the picture should roughly follow the path of the spiral. The Golden Spiral can be rotated in the frame or transposed from top to bottom so you can create more variety when you are composing pictures.

This idea is best suited for landscape photography where the lines are long and dramatic but it can also be effective in close-ups and portraits. Once you understand the basic form of the Golden Spiral, this idea becomes intuitive and thus easy to apply. You don't need difficult mathematical calculations to produce an compelling picture.
Taking pictures using the Golden Spiral is a more fluid and visually compelling way to structure your photos than the more static Rule of Thirds. With practice this method becomes intuitive. It will create a more symmetrical visual flow, especially in landscape photography. Have fun experimenting with it!" (Extract from http://EzineArticles.com/?expert=Tracy_Crowe).