Typography and mathematics

Renaissance artists' and scholars' fascination with mathematics included the domain of the alphabet, and they assiduously studied the proportions and styles of engraved capitals still visible on classical Roman monuments.

Renaissance artists and writing

The development of geometric perspective in the 1420s convinced artists of the period that the whole of reality could be expressed in numerical formulae, at the same time that the works of Greek mathematicians such as Pythagoras seemed to them to be the high point of ancient civilization (whose perfection, they were convinced, arose from the systematic, rational application of the laws of geometry). The early sixteenth century saw the publication of a number of scholarly studies aimed at discovering the calculations that governed the construction of Roman capitals. These were written by mathematicians (Fra Luca Pacioli, Italy, 1509), artists (Albrecht Dürer, Germany, 1525) and "men of the book" (Geoffroy Tory, France, 1529).

Comparaison of renaissance models

These works are reflected in the progressive achievement of the letterpress process, in which the printed letter gradually pulls away from the influence of writing (and the tools used, such as pen, reed pen, flat brush, etc.). It becomes a visual object more closely related to drawing because of its contour (the accession of punch-cutting to the status of a discipline, with its own design processes and modes of aesthetic evaluation, undoubtedly plays a role in this). This transition, from an "organic" form produced by the nature of the writing tool and the movement of the hand, towards a "constructed" form developed by the outline and slowly refined by the tools of the punch-cutter, brings with it a new rationality, whose source is to be found, as was thought at the time, in the universal laws of mathematical science.

Comparaison of the roman forms of Jenson, Griffo and Garamond

Models from the Classical period

This thought process reaches its culmination in the late seventeenth century with the development of the romain du roi. A scientific committee under the leadership of Abbot Bignon (1662–1743), after considering "the best examples of ancient and modern characters", produced a series of mathematically precise grids (for upper- and lowercase letters in both roman and italic) engraved on copper plates. The artisan responsible for cutting the punches based on these "ideal" drawings, Philippe Grandjean (1665–1714), was forced to adjust some of the more radically theoretical constructs to the realities of his discipline. As Pierre Simon Fournier pointed out a few decades later, in his Manuel typographique (1742), the tiny scale at which a letter is carved in relief and in reverse on the tip of a punch made the committee's typographical recommendations generally inapplicable.

Comparaison between a plate engraved by Simonneau
and a character in a very small font

Another effort by the committee that was equally rational but more long-lived involved the definition of a unit of measurement for letter sizes based on existing typefaces. Up to that point, sizes were defined by a series of proper names (Mignonne, Philosophie, Parangon, Cicéro, etc.). The concept of size was based on the relationship of the letters with each other based on a standard unit. This is still the system used today: the unit is called the point, which has a value of 0.3527 mm).

Optical adjustments

Our eyes play tricks on us. For example, if you line up a rectangle, a circle and a triangle that are exactly the same height, the triangle and the circle will appear smaller than the rectangle. In typography, an uppercase H, A and O on the same line will produce the same effect. For aesthetic reasons, but also for ease of reading, it is important that all of the letters appear to be the same height. The work of the typographer is to offset these optical sensations in order to make the character shapes appear similar. Mathematical precision is not the answer to every design problem; typography calls for a knowledge of other sciences and must factor in other phenomena.

As you do Activity 1, you will see that, for a capital O to appear to be in line with the other letters and to have a uniform thickness, optical adjustments are needed. It's not enough to make an O with two concentric circles (the uppercase O in Futura is an example of this).

Activity 2 shows the impact of handwriting on type design. Even though typographers take science and mathematics into account, achieving high-quality letters is less about science and more about practical experience. The slight lack of symmetry in the layout of these uppercase Garamond Os shows that in the calligraphic gesture, the hand carries more weight in the downward than in the upward stroke, and that the curve bends later in the left-hand portion of the character than in the right.

Teaching guide n°3

LEVEL

Secondary school: themes « Art, techniques, expressions »

High school: themes « Art, sciences and techniques »

RELEVANT AREAS OF INSTRUCTION

French, history-geography, arts, mathematics, physical sciences, technology, art history

DocumentDownload the PDF
of this page

Activity 1

Does the uppercase Futura O consist of two concentric circles ?

Activity 2

Look at a Garamond uppercase O. Is there an axis of symmetry in it? Is it the same for the outside of the O and the inside ?

Drawing geometric forms of a capital H, A and O.