Geometry has played a major role in twentieth-century art. No era before ours produced as many paintings with ruler and compass. And none ever argued so vehemently that art could be made out of circles, squares, and triangles.
The mechanically drawn line and compass-created arc threatened for a while to dominate modernist art. Constructivism, Cubism, Futurism, and Neo-Plasticism were all deeply indebted to geometry. Not, perhaps, to its deeper meanings but certainly to its outward manifestations.
Geometry even had its effect upon free-form, fanciful, and representational art, much of whose imagery was subject to the strictest geometric scaffolding. Even such an anti-modernist as Thomas Hart Benton took pride in the fact that his paintings were as tightly constructed as any Cubist work.
Although geometry's dominance has abated somewhat in recent years, its lessons have not been forgotten. Frank Stella and Sam Gilliam are doing interesting things with circles and straight lines, and any number of other painters and sculptors are ''packaging'' their creative enthusiasms within modified geometric forms.
There is at least one artist, however, whose creative ideals are as deeply and totally rooted in geometry as ever, and whose art is continuing to venture into areas previously considered the exclusive domain of logic and mathematics.
Hans Hinterreiter is a Swiss Constructivist who uses mathematics to discover new geometric patterns which then become the basis for tightly controlled and richly colored paintings. These often appear in serial form, one image appearing over and over in a wide variety of color combinations. Although the surface effect is ornamental and decorative, Hinterreiter's intentions go much deeper.
His wish is to create pictorial equivalences of the laws that act invisibly through matter. Or (as he himself has written), ''parables of the creative substrate of the visible world, of its inner dimensions, which interest us moderns more than its surface.''
This desire to fashion artistic icons that represent and illuminate certain universal laws is, of course, not new. It was on the minds of artists as far back as the ancient Egyptians and Greeks, and as recently as our own Brancusi and Mondrian. Architecture, in particular, has often been seen as a formal distillation and representation of universal law.
What differentiates Hinterreiter's creative quest from most others, however, is the extraordinary degree to which it is both rooted in scientific inquiry and tempered by aesthetic sensibility. He doesn't permit his mathematical probings and calculations to stand as they are, but modifies and extends them according to artistic considerations. In this he is as much poet as scientist, as much communicator as theorist.
Hinterreiter is very emphatic about this. Although he insists it's possible to develop an art based on mathematical thinking, he also insists there is a ''zone of freedom'' above natural law where only sensibility can guide the artist, and where feeling and intellect must join forces if there is to be art.
Interestingly enough, it is color, acting in counterpoint to his geometric explorations, that generally provides this added ''aesthetic'' dimension. And yet his approach to color is also scientific and systematic, and was originally given impetus by the color theories of Wilhelm Ostwald.
Here again, however, he tempers method with intuition and sensibility. Color must be lyrical as well as logical, for whatever the mathematical basis of his forms, his ultimate goal is to create images that have spatial, emotional, and ''spiritual'' resonances - that are, in effect, coloristic poetry.
To achieve this, Hinterreiter first establishes the geometric structure of his composition. This involves a complex process of dividing an element such as a triangle, square, or hexagon into several parts, isolating and extending these to create intricate geometric networks, and repeating and varying the results until the entire pictorial field is filled.
Once this pictorial skeleton or scaffolding is completed, color enters the picture to provide emphasis, establish major and minor formal relationships, and to evoke the particular ''tone'' or resonance Hinterreiter has in mind.
This is the difficult part, the moment when the work's identity moves from geometry to art. Or, failing that, to ornament or design.
My first reaction to Hinterreiter's paintings was that they were merely handsome designs, and too decorative to be art. That impression has changed considerably, however, as I've seen more of them, and have compared them to works which are merely designs. The best of his works are indeed art, for they are exceptionally poetic, and have dimensions that touch the spirit as well as enchant the eye.
Even so, I'm not yet fully convinced of their depth and importance. There is a degree of calculation about some that diverts my attention away from the work and its deeper intentions, and toward the artist's intellectual capacities and skills. These neither involve me nor engage my humanity - although I am enchanted and touched by others.
Perhaps I should let the artist have the last word. In discussing his kind of art, he writes: ''For the first time in the history of art, conscious and determined, we go a similar way as music had gone several hundred years ago. We renounce copying and the remotest imitation of the external world, which even until recently was the fashion among abstract painters. In view of the personal character of our figuration material, we will devote ourselves exclusively to the inner life of the soul, as the musician does. But our means are visual. We will no longer study the surface of things, their skins, but rather their inner, natural laws. We will become explorers and designers; yet not as engineers, since not utility but beauty and psychological expression are our goals.''