Selected Bibliography Architecture - Form Space and Order | Page 315

PR O PO RTIO NING SYSTEMS

In truth, our perception of the physical dimensions of
architecture, of proportion and scale, is imprecise. It is
distorted by the foreshortening of perspective and distance,
and by cultural biases, and is thus difficult to control and
predict in an objective and precise manner.
Small or slight differences in the dimensions of a form are
especially difficult to discern. While a square, by definition,
has four equal sides and four right angles, a rectangle can
appear to be exactly square, almost a square, or very much
unlike a square. It can appear to be long, short, stubby, or
squat, depending on our point of view. We use these terms to
give a form or figure a visual quality that is largely a result of
how we perceive its proportions. It is not, however, an exact
science.
If the precise dimensions and relationships of a design that
is regulated by a proportioning system cannot be objectively
perceived in a similar manner by everyone, why are
proportioning systems useful and of particular significance
in architectural design?
Ratio:

a
b

Proportion:

a c
a b c d
=
or
= = =
b d
b c d e

Proportion is the equality between two ratios in
which the first of the four terms divided by the
second equals the third divided by the fourth.

Whole

300 / A R C H I TE C TU R E : F O R M , S PA C E , & O R D E R

Part

The intent of all theories of proportions is to create a sense
of order and harmony among the elements in a visual
construction. According to Euclid, a ratio refers to the
quantitative comparison of two similar things, while
proportion refers to the equality of ratios. Underlying any
proportioning system, therefore, is a characteristic ratio,
a permanent quality that is transmitted from one ratio
to another. Thus, a proportioning system establishes a
consistent set of visual relationships between the parts of a
building, as well as between the parts and the whole. Although
these relationships may not be immediately perceived by the
casual observer, the visual order they create can be sensed,
accepted, or even recognized through a series of repetitive
experiences. Over a period of time, we might begin to see the
whole in the part, and the part in the whole.