Proportion (architecture)

In classical architecture, proportions were set by the radii of columns.

Proportion is a central principle of architectural theory and an important connection between mathematics and art. It is the visual effect of the relationships of the various objects and spaces that make up a structure to one another and to the whole. These relationships are often governed by multiples of a standard unit of length known as a "module".[1]

Proportion in architecture was discussed by Vitruvius, Alberti, Andrea Palladio and Le Corbusier among others.

Proportion in Roman Architecture

Vitruvius's Theory

Architecture in Roman antiquity was rarely documented except in the writings of Vitruvius's treatise 'De Architectura'. Vitruvius served as an engineer under Julius Caesar during the first Gallic Wars (58 - 50 BC). The treatise was dedicated to the emperor Augustus. As Vitruvius defined in the first chapters of the treatise, he mentioned the three prerequisites of architecture are firmness (firmitas), commodity (utilitas), and delight (vernustas), which requires the architects to be equipped with a variety kind of learning and knowledge of many branches. Moreover, Vitruvius identified the 'Six Principles of Design' as order (ordinatio), arrangement (dispositio), proportion (eurythmia), symmertry (symmetria), propriety (decor) and economy (distributio). The word symmetria actually has a very different meaning as we interprets today. Among the six principles, proportion interrelates and supports all the other factors in geometrical forms and arithmetical ratios.[2]

The Vitruvian Man developed by Leonardo da Vinci based on the description of Vitruvius's ideal ratio of human body.

Symmetria as translated to symmetry in modern language, which does not mean symmetrical in forms in ancient language, but more closely related to the 'mathematical harmony'[3] and measurable proportions. Vitruvius tried to describe his theory in the make up of human body, in which he referred as the perfect ratio. The principles of measurement units digitus, foot and cubit also came from the dimensions of a Vitruvian Man. More specifically, Vitruvius used the total height of 6 feet of a person, and each part of the body takes up different ratio. For example, the face is about 1/10th of the total height, and the head is about 1/8th of the total height.[3] Based on these ratios, Vitruvius was able to support that the composition of classical orders were actually mimicking the human bodies. Which ensures the aesthetic harmonization when people viewing columns.[2]

Classical architecture

In classical architecture, the module was established as the radius of the lower shaft of a classical column, with proportions expressed as a fraction or multiple of that module.[4]

Le Corbusier

Commemorative coin illustrating Le Corbusier's Modulor

In his Le Modulor (1948), Le Corbusier presented a system of proportion which took the golden section and a man with a raised arm as the scalable modules of proportion.