Geometry has always played a supportive role in the visual arts but never so much so as in this century. It helped in the fashioning of Cubist and Constructivist theory, allowed Mondrian to evolve his own unique form of nonobjective art, and gave impetus and form to the work of many modernist painters. Kandinsky, Klee, Feininger, Albers, Diebenkorn, and Stella, to name only a few, would have produced very different work had they not been able to use perfectly straight lines and precise curves, or circles, squares, and triangles.
Geometry has also been very helpful in the more traditional forms of 20 th-century painting but in a much more subtle way. It has limited itself to providing compositional ''scaffolding'' for largely representational works. The surface effects of paintings by Balthus, Sutherland, Benton, Wood, Hopper, and Hockney, for instance, are always adjusted to carefully designed geometric underpinnings. And even such current New Realists as Estes, Magee, Beckman, and Valerio make certain that their paintings are tightly constructed.
Unfortunately, geometry is also an easy device for circumventing compositional complexities. Altogether too many artists limit their compositional structuring to a few triangles and squares masquerading as pine trees, mountains, and houses and fitting neatly into a tightly designed classical composition derived from one of the Old Masters. Or, just as bad, they think that by neatly arranging a few colorful geometric shapes they are producing significant abstract art.
None of this really works, of course, as can be proven by the thousands of paintings produced every year that qualify neither as abstract nor representational art but that exist in a kind of limbo between those extremes. In order to make it really work, to make geometry and ''realism'' fuse into one integrated image, an artist needs a special kind of formal sensibility - as well as a good eye for significant detail. He or she must, in short, have a genuine talent for design, as well as the ability to make objects interrelate geometrically without losing their individual realities and identities.
No American painter was more successful at doing just that than Charles Demuth (1883-1935). His ability to combine an abstract, geometric approach with precise renderings of actual places and things was so exceptional that his best works are respected by modernists and traditionalists alike. His watercolors of fruit, flowers, and still lifes stand out in any exhibition of this country's finest works on paper, and his precise, elegantly geometric paintings of urban architecture rank among the best American paintings of the early 20th century.
Like so many painters of his day, Demuth was profoundly influenced by the art of Cezanne and the Cubists. Unlike his peers, however, he was not inclined to view his art as an extension of a theory, nor was he inclined to become a formal purist. Like his friends John Marin and Marsden Hartley, Demuth took only as much as he needed from European modernism and then adapted this to fit his own peculiarly American vision of life and of art.
This vision was ideal, pristine, ordered, and discreet. Demuth's paintings and watercolors share Charles Sheeler's sense of New England understatement and orderliness but with a touch more warmth and with considerably less austerity. They do, however, also possess a degree of linear elegance and coloristic sophistication that sets them apart from other American art of the period. Many of his fruit, vegetable, and floral still lifes, in particular, seem more French than American.
On the other hand, Demuth's depictions of colonial churches and modern urban architecture, of factories, grain elevators, smokestacks, and storefronts could only be American. They are too blunt and direct to be anything else. No European would have given hulking factories or huge smokestacks belching smoke the dramatic prominence he gave them. His images of such structures may not be as blatant as those by the Regionalist or American Scene painters of the 1930s, but they do relate more closely to them than to anything being painted in Europe at that time.
Demuth had a remarkable knack for formal distillation, for being able to reduce complex views and buildings to simple forms without removing the subject's very special identity or character. Much of this was due to the great care with which he studied the exact appearance of steeples, brick facades, bell towers, fire escapes, windows - and whatever else he wanted to depict. But it was also due to his extremely sensitive and shrewd application of geometric principles.
Both qualities are very much in evidence in ''Lancaster,'' a smallish work depicting what was originally a cotton mill, and which still stands in Lancaster , Pa., not far from where Demuth lived. Although specifically enough rendered to be identifiable, the subject of this painting also exists as a subtly and beautifully designed modernist image which would lose a good half of its formal identity if its geometric underpinnings were removed.
A 1950 photograph of this building complex underscores the degree to which Demuth modified what he saw in order to fashion a more effective painting. By elevating the water tower and the steeplelike structure, he made both appear higher and more dominant, and by giving the ''steeple'' a more purely colonial look he effected a greater degree of pictorial drama through contrast.
But the major changes occur in the lower half of the painting. Only the vertical building at center left resembles the original, and even it has been dramatically simplified and diminished in importance to emphasize what stands above it. Everything else exists as an interplay of lines and angles. And yet, all these geometric details and effects, these overlappings, facetings, cubistic shiftings, and structurings, contribute significantly and crucially toward establishing the extraordinary aura of calm dignity this painting conveys.