
Proportion is a mathematical concept, important in all the visual arts, but most significant in the field of architecture, where it is traditionally considered one of the essential variants in a built structure for the creation of visual effect. The proportion, the relationship of one part to another, and of one part to the whole, usually in terms of size, has clearly been a consideration in architecture since Neolithic times. Early built structures, such as Stonehenge, which were built as religious sanctuaries, can be seen to have a careful rhythmic sequence between full and empty spaces, which has been compared to the proportion of the colonnades of archaic Greek temple architecture. In certain examples of early Egyptian tomb architecture it is thought that the proportions were modelled by way of allusion to the symmetrical concepts of the solar system, and the relationship of planets and their orbits.
For textual evidence of the significance of the concept of proportion to designers of buildings in the late classical period there is Vitruvius\'s treatise De Aedificatoria. â€˜Proportion consists in taking a fixed module, in each case for the parts of a building and for the whole, by which method symmetry is put into practice. For without symmetry and proportion no temple can have a regular plan; that is it must have an exact proportion worked out after the fashion of a wellshaped body â€¦in like fashion the members of temples ought to have the dimensions of their magnitudeâ€¦â€™ In Vitruvius\'s treatise, and in much subsequent discussion right into this century, most notably in the writings of Le Corbusier, the proportions of a building to its parts were conceived of in terms of the human body, and of the ideal shapes which it was thought could be demonstrated between the whole human body and its parts. These ideal forms were the simple shapes of the square and circle, and by extension the cube and the sphere, based on absolute regularity from the centre: as Vitruvius says: â€˜If a man lies on his back with hands and feet outspread, and the centre of a circle is located in his navel, then his hands and feet will touch the circumference: a square can be produced in the same way â€¦ the height of a body from the sole of the foot to the crown of the head being equal to the outstretched arms.â€™
The human analogy can also be used for an analysis of medieval Gothic architecture. The historian Frankl (1910  1962) observed: â€˜Even a Gothic cathedral is a system of supportsâ€¦[in which]â€¦proportion plays a decisive role, but this is precisely the proportion of the skeleton, of the spidery membersâ€™, he also wisely observes that â€˜proportions adapted to the human body, in all its variety, range between the extremes of thinness and bloated fatnessâ€™.
In the 20th century, an understanding of proportion was seen as part of the search for the pure, mathematical and geometric root of beauty in functionalist terms. Le Corbusier and his school within the Modern movement were the most faithful to the notion of a module, part derived by analogy with the human body, which has enormous practical value in modern industrialized societies with the mass prefabrications of parts. JM
Further reading G. Raymond, Proportion and Harmony of Line and Colour in Painting, Sculpture and Architecture; , Le Corbusier, Le Modulor. 
