Most photographic and print publication work involves operating within rectangular frames. The relationship of width to height is the aspect ratio, expressed as, for example, 1:1 for a square, 1:1.5 for a 6 x 9 book, or 1:2 for a sheet that is twice as wide as it is tall. Conventionally, the width is stated first: that 6 x 9 book is in portrait format, whereas a 9 x 6 book would be landscape, bound on the short side, and most inconvenient to read.
A special case is the golden section or golden ratio, a rectangle with the proportion 1:1.618 (between 3/5ths and 5/8ths). In this rectangle the smaller dimension is to the larger as the larger is to the sum. In other words, 1 is to 1.618 as 1.618 is to 2.618. And as 2.618 is to 4.236, and so on. This relationship, which can be extended indefinitely, was known since classical times, and it underlies the Fibonacci Series and the modular architecture of Le Corbusier, among other expressions. Gustav Theodor Fechner, a German scientist, studied people’s responses to rectangular shapes in 1876 and concluded that the golden section is the most pleasing, though his methodology and results have been questioned. But other aspect ratios also have historic and aesthetic associations.