The Balance Problem Set

Problem 5 Tutorial: Balanced Proportion

Question: Of the three architectural images below which is the best example of balanced proportion?

Building A

Building B

Building C

Tutorial:

Proportion

Proportion is the ratio of one part of a building to another. For example, a room that is eight feet wide by thirteen feet long has the ratio 8 to 13.

Although proportion may be measured mathematically, aesthetic judgement is usually rendered on visual evidence and is culture specific. The assumption is that a well proportioned building is one that is balanced. One of the key factors in the quality of an interior space will be found in its proportions.

Throughout history, architects have sought to create pleasing compositions by inventing proportional systems. Following are three examples of these systems.

Ancient Greek proportional systems

Ancient Greek proportional systems were based on mathematical ratios, but were then carefully adjusted to compensate for optical illusions. These ratios were seen as evidence of a perfect universe that could be demonstrated in mathematics, music, and in the human body; and therefore their application was expected in architecture.
	The dimensions of a Greek temple are based on the radius of the shaft (the module). One could construct an entire temple based on one part and the ratio. The "most perfect proportions" or the Golden Section was the ratio of 1 to 1.618.
The Parthenon is based on a ratio of 1 to 2.25, but there have been many refinements in dimension to compensate for optical distortion. For example, a long horizontal member will appear to sink or curve downward in the middle. To counteract this tendency, the Greeks curved horizontal members upward.

Renaissance proportional systems

Renaissance proportional systems were based on ancient Greek and Roman systems. Many Renaissance architects drew their own illustrations for the text of the Ten Books of Architecture by the Roman architect Vitruvius. The two most influential illustrations were those of the human body, legs and arms outstretched in a perfect circle and square and of the orders. The orders included the three Greek orders; Doric, Ionic and Corinthian, and the two Roman orders; Tuscan and Composite

Da Vinci drawing

Five Roman orders

The Modulor

The twentieth century architect to most frequently use a proportional system was Le Corbusier. The Modular is the proportioning system developed by Le Corbusier based on the Fibonacci series (1,1,2,3,5,8,13). He believed these proportions to be evident in the human body. The Fibonacci series is also the closest approximation in whole numbers to the Golden Section. The purpose of the modular was to "maintain the human scale everywhere". The entire building "Unite d'" was based on the Modular proportioning system.

Modular man

Unite d',
Marseilles, France,
(1946-52)

Problem 5 | Answer | Problem 6

Aesthetics | Balance Problems | vocabulary | The Architecture Project

The Architecture Project
University of Arizona
Tuesday, September 2, 1997
lapointe@u.arizona.edu