These proportions are generally said to be the most pleasing aesthetically. The ratio of the Golden Section has been used in the construction of many works of art for centuries - paintings, buildings, design and in mathematics.
With a rectangle, the formula is based on the ratio of the long side plus the short side to the long side, which needs to be the same as the ratio of the long side to the short side.It works out as a ratio of 1:1.6180339887 . . . .
35mm film with dimensions of 24mm x 36mm is very close to this ideal proportion.
Digital cameras usually have the same proportions but smaller in size. The rectangle can then be divided up to the same proportions, as this illustration demonstrates.
The Golden rectangle can be divided up with four lines to continue the proportions within the rectangle.
The grid can be placed over an image. With the horizon positioned on one line and the scarecrow at an intersection, the result gives a very balanced picture.
The proportions of this ratio have a long history. Mathematicians have had fun with the formula and the properties of the ratio and shape since the ancient Greeks.
The proportions have been used frequently by architects for centuries and they are said to give buildings a harmonious and calm aspect.The result can be more successful than the Rule of Thirds but photographers should not be bound rigidly to the theme, rather using it more as a guideline.
Graphic designers and illustrators can find it more useful at the planning stage. They can also make use of the 'golden triangle' and 'golden spiral' principles. The spiral aims to lead the eye into the centre of the composition. They certainly can be good aids for balancing an image.
PowerRetouche have a very good plug-in for drawing these divine proportions.