Proportion



Proportion refers to the relative size and scale of the various elements in a design. The issue is the relationship between objects, or parts, of a whole. This means that it is necessary to discuss proportion in terms of the context or standard used to determine proportions.

proports.jpg (66949 bytes)  Leonardo da Vinci, Vitruvian Man , 1513,  25 x 19.2 cm


Our most universal standard of measurement is the human body; that is, our experience of living in our own bodies. We judge the appropriateness of size of objects by that measure. For example, a sofa in the form of a hand is startling because of the distortion of expected proportion, and becomes the center of attention in the room. Architectural spaces intended to impress are usually scaled to a size that dwarfs the human viewer. This is a device often used in public spaces, such as churches or centers of government. The same principle is often applied to corporate spaces through which the enterprise wishes to impress customers with its power and invincibility.  

CLOTHSP.gif (363274 bytes)Claes Oldenburg Clothespin 1976 josefkoudelka_Czechoslovakia.jpg (105091 bytes) Josef Koudelka Czechoslovakia 1968


In contrast, the proportions of a private home are usually more in scale with human measure, and as a result it appears friendlier, comfortable, less intimidating.


Use of appropriate scale in surface design is also important. For example, an overly large textile design can overwhelm the form of a garment or a piece of furniture.


A surprising aspect of proportion is the way ideal proportions can vary for the human body itself. Styles change in bodies as they do in clothing. Prior to the 16th century, for example, the female body ideally had large hips and belly. Only later was a small waistline stressed.


In the 17th century and many other periods, the ideal body was much heavier than we would accept today.


Of course, in the last 25 years the ideal personified by the fashion model has fostered a standard which idealizes exceptionally slender body proportions for women. In this century, sports have provided models for ideal male body proportions. Beginning with the rise of televised football in the 1960's, and the subsequent fitness boom, an increasingly muscular silhouette has been presented as the ultimate male form. This ideal is quite different from that presented in earlier periods.

In addition, artists frequently take liberties with the natural proportions of the human body to achieve their expressive goals. A well known classic example is Michelangelo’s David, in which distortions of proportion are used by the artist to depict both the youthfulness of the boy David, together with the power of the hero about to conquer the giant Goliath. 

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Columbian painter Fernando Botero often used distortions of proportions to create striking effects.

Adán.jpg (17696 bytes) eva.jpg (17781 bytes) Adán and Eva 

BoteroLa danse - 1980.gif (33660 bytes) En el parque1999.jpg (25955 bytes) Hombre1969.jpg (28636 bytes) Fernando Botero La danse, En el parque1999, and Hombre 1969

Modular Proportion  

A proportional system that limits incremental changes of scale to a single unit of measurement is called modular proportion. 

The unit of measure, for instance 1” in a small paper project, is called the modulus of proportion. 

The size of the modulus is arbitrary, but consistent throughout the composition.

6 ˝” cubes with a 1 5/8” modulus is proportionate to 4” cubes divided into 1” modules.

house_kit.jpg (44962 bytes)  

Architects typically build houses using modules of either 16” or 24” to space wall studs, floor joists, and rafters, and to proportion the sizes of their rooms.   

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These figures drive from three parameters: the scale of the human body, the strength of lumber, and the economizing of material. 

Standard 4’ x 8’ pieces of plywood or sheet rock divide evenly by both of these modules.  Just as important, the repeated use of the same modulus supplies proportional order to the architectural design.

modular.jpg (14486 bytes)

The current LEGO stud-and-tube coupling system was patented in 1958 (Design Patent #92683)

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Lincoln Logs

Lincoln Logs were first marketed in the early 1920's by John Lloyd Wright Inc., of Chicago.

Fascinated with the interlocking building system used to construct Tokyo's Imperial Hotel, which had been designed by his famous father, Frank Lloyd Wright, in 1917, architect John Lloyd Wright created the first Lincoln Logs in the very same year. The sets were named after Abraham Lincoln in celebration of the 50th anniversary of the end of the Civil War.

http://www.pbs.org/flw/buildings/imperial/imperial.html

The simple sets could be used for building log cabins that were indeed similar to one Lincoln might have lived in. Later sets became more elaborate and could be used to build forts and other more elaborate structures. Although the conventional Lincoln Log was round, square logs and even bricks were also sold.

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Ratio Proportion

Proportion can also be based on mathematical ratios.  In ratio proportion the relative scale of one element to another is expressed as a ratio. 

The Golden Section, expressed by the ratio 1:1.618, has been utilized in design as far back as construction of the Egyptian pyramids.  Its remarkable and elegantly complex properties appear repeatedly in both architecture and in nature. 

The Golden Section is also known as the Golden Mean, Golden Ratio and Divine Proportion.  It is a ratio or proportion defined by the number Phi = 1.618033988749895...)

It can be derived with a number of geometric constructions, each of which divides a line segment at the unique point where:

The ratio of the whole line (A) to the large segment (B) is the same as the ratio of the large segment (B) to the small segment (C).

In other words, A is to B as B is to C.

This occurs only where A is 1.618... times B and B is 1.618... times C.

This ratio has been used by mankind for centuries.  Its use started as early as with the Egyptians in the design of the pyramids.  The Greeks knew it as the Golden Section and used it in the design of architecture Some of the pyramids indicate an accurate understanding of Pi, but the mathematical knowledge of the Egyptians did not include the ability to arrive at this by calculation. It is possible that this could have been arrived at "accidentally" through a means such as counting the revolutions of a drum.

 Phi and the Great Pyramid

The Parthenon (A,C)

Phi and the Golden Section were used in Notre Dame 3.jpg (609313 bytes) Notre Dame, Paris

As the Golden Section is found in the design and beauty of nature, it can also be used to achieve beauty and balance in the design of art.  This is only a tool though, and not a rule, for composition.

The Golden Section was used extensively by Leonardo Da Vinci.  Note how all the key dimensions of the room and the table in Da Vinci's "The Last Supper" were based on the Golden Section, which was known in the Renaissance period as The Divine Proportion.

"The Last Supper" by Leonardo Da Vincilastsupp.jpg (360635 bytes) Leonardo da Vinci The Last Supper (after cleaning), 1498, 460 x 880 cm

The French impressionist painter Georges Seurat is said to have "attacked every canvas by the golden section," as illustrated here:

seurat8bathers.jpg (233069 bytes) Georges Seurat, Bathers at Asnieres 1883-84 (retouched 1887) 79 x 118 1/2 in

 

Note that successive divisions of each section of the painting by the golden section define the key elements of composition.  This principle is illustrated in the "Golden Ruler™" below:

The horizon falls exactly at the golden section of the height of the painting.  The trees and people are placed at golden sections of smaller sections of the painting.   

Phi Bar

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