Graphics Reference
In-Depth Information
PROPORTION
a (38%)
b (62%)
4-5
Removing the square from a golden rectangle
leaves another golden rectangle.
Divided space is perceived as a system of proportional relationships.
To work effectively with the typographic grid is to understand that it
also is a system of proportions. A grid ratio, which is a mathematical
relationship between two or more grid measurements, governs the
size and placement of typographic elements. The ratio X:2X (one unit
to two units), for example, indicates the basic grid ratio. This stepped
progression of X:2X establishes an underlying proportional system
among the parts (Fig.
4-4
).
Designers most often rely upon an innate sense of proportion.
But it is helpful also to consider models that have been handed down
over centuries. The most familiar of these is the golden section, which
is a law of proportionality found frequently in nature and the human
body, and used throughout centuries in art, architecture, design, and
music. First developed by Vitruvius, the golden section is basically
a relationship or ratio between two numbers (or objects) wherein the
ratio of the smaller number to the larger number is the same as the sum
of both numbers. The algebraic expression of this relationship is a:b =
b:(a+b). Stated numerically, the ratio is 1:1.618, and stated in percentages
the ratio is 38 percent to 62 percent (Fig.
4-5
). The golden section, which
can easily be constructed from the square (Fig.
4-6)
, dominated as the
proportional system for the design of medieval manuscripts (Fig.
4-7
).
The Fibonacci sequence is another important proportional model.
Closely related to the golden section, this is a mathematical sequence
wherein a number is the sum of the two preceding numbers; in other
words, you add the two current numbers to get the third number. The
progressive series of mathematical relationships found in the Fibonacci
sequence can be observed throughout nature, from seashells and pine
cones to the arrangement of seeds on flowering plants (Fig.
4-8
).
0 +1 = 1
1+1 = 2
1+2 = 3
2+3 = 5
3+5 = 8
5+8 = 13
8 +13 = 21
13+21 = 34
21+34 = 55
34+55 = 89
etc.
4-6
The golden rectangle can be drawn by making
a square, dividing it in half, and striking an arc from
the half-point of one side of the square to the opposite
corner of the square.
3
5
1
1
T
The whole duty of typography, as with calligraphy, is to com-
2x
13
municate to the imagination, without loss by the way, the
thought or image intended to be communicated by the author.
And the whole duty of beautiful typography is not to substitute
for the beauty or interest of the thing thought and intended to
be conveyed by the symbol, a beauty or interest of its own, but,
on the one hand, to win access for that communication by the
clearness and beauty of the vehicle, and on the other hand
3x
counterform
x
The whole duty
of typography
8
characteristic
2x
2x
picture writing
4-4
This exploratory composition
exhibits modular relationships among
elements. (Designer: Debra Thompson)
4-7
Medieval manuscript (psalterium)
from the twelfth century. Shown is a
page of text with three-line and one-line
initials proportioned according to the
golden ratio.
4-8
The golden spiral winds through a series of
conjoined golden rectangles. The spiral is linked to
many forms in nature and is related to the Fibonacci
sequence.
