**Introduction to Architecture**

**Dimensions: Proportion and Scale**

**PROPORTIONS**

**Scale and proportion play very important roles for architecture. Proportion refers to the proper and harmonious relation of one part to another or to the whole, while scale refers to the size of something compared to a reference standard or to the size of something else (like a human being).**

The mind seeks out mathematical and geometrical relationships or proportions in patterns. Human beings possess a special intuition which makes them perceive simple mathematical proportions in the physical world. This is also true of music. For this reason, since architecture is a composition of forms brought together in proportional relationships, it was called frozen music.

"Proportion" refers to the relative size of visual elements within an image. It also refers to the equality between two ratios in which the first of the four terms divided by the second equals the third divided by the fourth.

PROPORTIONING

**THEORY OF ARCHITECTURE**

a

b

c

d

a c

=

b d

Geometry is inevitable in architectural organization as the means of ordering a design and relating the parts to one another. The first proportional relationship begins in architectural design in the material level and in the level of architectural elements. Many architectural elements are sized and proportioned not only according to their structural properties and function, but also by the process through which they are manufactured. Because the elements are mass produced in factories, they have standard sizes and proportions imposed on them by the individual manufacturers or by industry standards.

Concrete block and common brick for example are produced as modular building units.

Concrete block and common brick are applied in proportional relationships to each

other

Standard door and window units are sized and proportioned to fit into modular

masonry openings.

**SCALE**

While proportion refers to an ordered set of mathematical relationships among the dimensions of a form and space, scale refers to how we perceive the size of something in relation to something else. It is a proportional relationship between two sets of dimensions. In dealing with the issue of scale therefore, we are always comparing one thing to another.

Scale also refers to the mathematical relationship between an object and a measurable quantity (the scale referent). In an architectural drawing, we use a scale to specify the ratio that determines the relationship between the drawing and the actual building. We say that an object is ―full-scale‖ when it corresponds 1 to 1 (1:1) with real life. If the same object is rendered such that any given linear dimension is one-half the length of the original object, we understand this to be at ―half scale‖ or 1:2.

Human scale refers to the size of a form when compared with our own human size. Human dimensions and scale have a determinative effect both in our perception and also in our creation of buildings and spaces. Human scale in architecture is based on the dimensions and proportions of the human body.

b. Human Scale

Psychologists have studied how we perceive visual information and their findings have showed that we perceive and judge the size of something in relation to something else. A thing appears smaller or larger in relation to the size of other things in its environment.

a. Visual Scale

SYSTEMS

Throughout history, it has been realized that a proportion system can assist both the

ordering and also the perception of buildings. Proportioning systems provide an aesthetic rationale for the dimensions of form and space.

They provide a sense of order in the facades and spaces of architectural works. A number of theories of ‗desirable‘ proportions have been developed in the course of history.

THEORIES OF

PROPORTIONS

a. Golden section

b. Regulating lines

c. Classical orders

d. Renaissance theories

e. Modulor

f. Ken

g. Anthrophometry

GOLDEN

SECTION

The Greeks have found out that nature uses a proportion law called Golden section (and Fibonacci Series), which produces things that look pleasing to us. Golden Section is basically described as the law of beautiful proportions. According to this law, two quantities are said to be in the golden section if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one.

A rectangle whose sides are proportioned according to Golden Section is called a Golden Rectangle. If a square is drawn in its smaller side, the remaining portion of the rectangle would be a smaller but similar Golden Rectangle. This operation can be repeated indefinitely to produce a gradation of squares and golden rectangles. In this system, each part remains similar to all of the other parts, as well as to the whole.

If a Golden section rectangle is divided by drawing a square in it, the remaining

rectangle is again a golden section rectangle. If that remaining rectangle is divided again and

this is continued until no more squares could be drawn, in the emerging pattern, the corners of

the rectangles could be connected as to form a logarithmic spiral. It was found that the

patterns of seeds in plants and also nautilus shells follow this logarithmic spiral.

In mathematics, the successive proportions of a series of numbers, which are called

Fibonacci numbers, give the Golden Ratio. In these series, a number is the sum of the two

consecutive numbers before itself. If a Fibonacci number is divided by its immediate

predecessor in the sequence, the quotient approximates golden sectionφ (like: 13/8= golden section φ). The larger the numbers get, the closer it approximates φgolden section. Fibonacci numbers are in the following integer sequence:

A tiling with squares whose sides are successive Fibonacci numbers in length.

REGULATING

LINES

The lines that indicate the common alignment of elements are called regulating lines. They are used to control the proportion and placement of elements in architecture. They reassure the perception of order and fix the fundamental geometry of work.

According to Corbusier, regulating lines guarantee fine proportions and add a rational sense of coherence to the buildings. In this way, the order, the function, and the volume of the space are drawn into one architectural totality.

He explained this as follows:

―The regulating line is a guarantee against willfulness. It brings satisfaction to the understanding. The regulating line is a means to an end. It is not a recipe. Its choice and the modalities of expression given to it are an integral part of architectural creation.‖ (Le Corbusier, Towards New Architecture)

CLASSICAL

ORDER

Classical order is one of the ancient styles of classical architecture, distinguished by its proportions and characteristic details, and mostly by the type of column employed.

Three ancient orders of architecture—the Doric, Ionic, and Corinthian—originated in Greece.

To Greeks and Romans, the Orders represented the perfect beauty and harmony. The basic unit of dimension was the diameter of the column.

RENAISSANCE

THEORIES

The architects of the Renaissance, believing that their buildings had to belong to a higher order, returned to the Greek mathematical system of proportions. Just as Greeks thought music to be the geometry translated in sound. Therefore the Renaissance concern for harmonious proportion.

LE MODULOR

The famous architect Le Corbusier also worked with human proportions and Golden Section. He has developed a theory of proportion and dimensioning system, named Modulor that is based on Golden Section and human proportions. He had formed the proportions of human body according to Fibonacci series and accepted the average human height as 183 cm

ANTHROPHOMETRY

Anthropometry refers to the size and proportions of the human body. Anthropometric proportioning methods search for the functional dimensions for the human body. They say that forms and spaces in architecture are either containers or extensions of the human body and therefore they should be designed according to its dimensions.

KEN

Ken is the Japanese unit of measure. It originally designated the interval between two columns and it was standardized later for residential architecture. Ken was used as the absolute measurement for the construction of buildings and as an aesthetic module that ordered the structure, materials and space of Japanese architecture.

PRESENTATION MADE BY:

RALPH JUNEAL R. BLANCAFLOR

BS IN ARCHITECTURE - 1

MINDANAO UNIVERSITY OF SCIENCE AND TECHNOLOGY