PRINT March 1974

A Humanist Geometry

ROBERT MANGOLD HAS WORKED QUIETLY and steadily over the last decade toward a reductive but confident kind of painting, as though moved by constructive doubt. Early in the 1960s Mangold painted flat, hieroglyphic works like Red October, 1962, with firmly curving forms in black, white, and gray, set smartly against an uninflected ketsup-colored ground. A couple of years later came Mangold’s Walls, those literally architectural reliefs in which colorism retracted in favor of a play of real light and cast shade, over forms whose shapes and proportions were as innately abstract as those of a building. As mimetic carpentry, the wall pieces evoke the highly patternistic architectural photography of American early modernism, such as Charles Sheeler’s board-and-batten Pennsylvania Barn or Stairwell, both from 1915, or his Shaker Window, c. 1935.1 Sheeler himself had said, on seeing Piero della Francesca’s frescoes at Arezzo, “. . . You saw pictures that were really planned like a house.”2 In even more general terms Sheeler’s Precisionism is like Mangold’s reticent formality.

Mangold’s paintings are intrinsically architectural in character and altogether independent of the architectural facts of a containing room. They are composed of compressive units that hang together in a unitary whole, like blocks in a wall or voussoirs in an arch, and resemble the vertical planes of architectural design—especially facades and planar ornamental features of classicistic architecture and its theory. This is most obvious in the semicircular paintings of the later 1960s, which compare with semicircular tympana—over doors or under arches—in both Italian Romanesque and also early and high Italian Renaissance architecture. Fig. A represents one of the tympana under the facade arcade of S. Miniato al Monte, at Florence (c. 1062, facade finished 12th century), while Fig. B is a device used as a tympanum over the door of Alberti’s S. Andrea, Mantua (begun 1470), and then, on a larger scale, over the whole central block in Bramante’s design for S. Maria di S. Satiro, Milan (c. 1480). Fig. G shows a “thermal window,” so called because it derives from the monumental baths (thermae) of ancient Rome, which was used often by Palladio in the 16th century, as for example over the doorway of S. Francesco della Vigna, Venice (1562), and which was revived in eighteenth-century England.3 Types A and C especially bear a resemblance to Mangold’s linear subdivisions of the semicircular format, and to those works from the mid-’60s that read as detached but self-sufficient sections of a thermal-window form.

The semicircularity of Mangold’s 1/2 Manilla Curved Area (Trisected), 1967, and similar works from 1967 and 1968, is distinctly Classical. It could be argued that the semicircular format is, in fact, the most Classical format in Western painting. Raphael’s Vatican frescoes evidence it, although it developed earlier in the Renaissance. In The School of Athens we see it in planar analogy with the Roman (and modern Bramantesque) arch—and its spatial projection, the barrel vault—underscoring its relation to Roman architectural Classicism. In the Disputà Raphael generates his own pictorial answer to the architectural source, a spatial semicircle (of figures in heaven) in analogy with the overall shape of the painting. At the opening of the 17th century the semicircular format asserts itself in the most germinal, and one of the most monumental, of all classicistic landscapes, Annibale Carracci’s Flight into Egypt of about 1604. Furthermore, with Raphael and Annibale and all their heirs, Mangold shares in the specifically Classical (and form-bound) tradition of starting a work with systematic preparatory designs.

Even in modern art the semicircular format carries with it a timeless geometrical purity, whether in Duchamp’s Glider Containing a Water Mill (in Neighboring Metals), 1913–15, at the Philadelphia Museum—which Ozenfant was happy to use as a link between Dada and Purism4—or in Matisse’s Barnes Foundation panels.

Nowadays, Mangold’s semicircular format cannot but call to mind Stella’s Protractor series that began in 1967, just as the oblongs cut through with trapezoids in Mangold’s Untitled Frame Set A, 1970, relate to Stella’s geometrical figures with cutout centers of 1963, and to framelike pictorial rhombuses and trapezoids in asymmetrical works by Stella of 1966 and 1967. Similarly, Mangold’s Manilla Neutral Area, 1965—a modified square with a long shallow angular slice off the lower right-hand corner and a small protruding rectangle at the upper left—suggests both the small squarish, keylike corner cuts and long vertical, inset edge cuts in such paintings by Stella as Kingsbury Run and Marquis de Portago of 1960. The quadrant of Cool Gray Area with Curved Diagonal, 1966, by Mangold, obviously suggests Stella’s quadrant Kufa Gate type. These parallels are all the more interesting in light of William Rubin’s comment that Stella’s Protractors, although antitectonic, are that painter’s first works “that might be termed unremittingly architectural in both size and scale.”5

Aside from Stella, there are also similarities between Mangold’s semicircular, protractorlike shapes and recent wall drawings by Sol LeWitt. To extend Robert Pincus-Witten’s distinction between Stella and LeWitt to LeWitt and Mangold, however, is uncommonly difficult.6 Why? Because of the combination in Mangold of an insistent crispness of form with an almost unnecessarily pleasing, muted color. With Mangold there is a balance between firmness and conserved delectation that could almost be called polite.

Color in Mangold is significant but unobtrusive, in accordance with the emphasis on form. Mainly, it distinguishes one uniformly monochromatic painting (the black, drawn lines hardly interrupt the field at all) from another. But it has more perceptual charm than that might suggest. One of the new paintings is something like battleship gray, one an umbrous orange, one light green, and one a kind of dark brick red. All these colors have about them an air of intrinsic, preesthetic chromatism. They seem to belong to neutral or natural art-making materials, like colors of modeling clay. Even the drawings share in the same taste, for the intrinsic charm of the creamy manilla paper seems noticed and liked as well as heightened by the more aggressively colored pencil line. In other words, Mangold gravitates toward a color of substantiality in a way that is almost as important to his painting as the texture of metals is to the sculpture of elemental materials.

The semicircular paintings may further be juxtaposed with Mel Bochner’s contemporaneous Degrees: (Straight Line), 1968. Bochner’s device is fundamentally the purely diagrammatic visualization of a geometrical idea—that a straight line can be described as an angle (of 180°)—and as such it has a certain antisensuality; the straightness of the line itself has a taut and real geometrical thinness (like a line in naval rigging), just as Mangold was at that time combining drawn lines with literally dug-in grooves. The wide slice through a circle (further subdivided, as in a thermal window) of Mangold’s 1/2 Manilla Curved Area (Divided) can be compared with the incomplete circles in Robert Smithson’s slate sculptures of 1973, such as Slate Grind No. 3, although then we deal with radically different sensibilities. But comparison with Bochner and Smithson makes all the clearer the fact that, even where there are morphological similarities, Bochner’s and Smith-son’s works are categorically sculptural. Even Bochner’s conceptualistic wall piece deals with materiality and circumstantial space. Mangold’s commitment is just as categorically to the painted plane, even in the early (monochromatic) reliefs. Some relief art is sculpture, and some hovers between sculpture and painting, but some—like Mangold’s—is painting, period.

Of all contemporary artists, however, Ellsworth Kelly is in closest affinity with Robert Mangold. Compare, for instance, the inward press of the surrounding border in Mangold’s Distorted Circle Within Polygon III, 1972,with Kelly’s Black and White, 1960. A remarkable similarity exists between Mangold’s Untitled (Pink), 1973, and Kelly’s Yellow Piece, 1966: both are monochromatic squares with quadrant arcs in two diagonally opposite corners, although Kelly shapes the canvas by cutting off these corners where Mangold uses a drawn graphic line—a line that also produces a mild ambivalence when it suggests that Untitled consists of two overlaid forms with opposed diagonals. Kelly’s superb White Plaque: Bridge Arch and Reflection, of 1954–55, with its upward- and downward-projecting round forms (each slightly more than a semicircle), adumbrates such works by Mangold as Untitled (Red), where a cinching-in of the square shape midway up breaks the circle into a distinct pair of upper and lower semicircles.

Kelly is surely most important as a precedent for the architecturally abstract mode in Mangold’s work. Kelly drew representationally upon architecture for abstract painting motifs, exploiting the traditional and continuous abstractness of architectural form. Also, Kelly’s reliefs based on architectural motifs, such as Window, Museum of Modern Art, Paris, 1949, and, even more, Saint-Louis II, 1950—both deriving from literal and preexisting configurations on the walls of buildings—provide an important antecedent for Mangold’s physical modification of the surface by a cut-in line. Mangold came to abandon the recessed linear groove, but for both artists it provided essential experience in both the antitangibility of line—the way it might be less than, or literally deeper than, the surface in order to affect that surface in a shaping way—and then, in turn, in the reconciliation of the intrinsic weakness of pure line to the sovereignty of the surface.

The implications of Classicism in Mangold’s earlier semicircular paintings, and the architectural aspect of his work, come to the fore in a group of new paintings and drawings recently shown at the John Weber Gallery. The new works deal with the combination of the circle and the square, or, more accurately, with the adjustment of whole or modified circles to squares. They are an elegant and articulate outgrowth of the earlier works, and they relate even more vividly than before to Classicizing architectural ideas. This is clear if we consider a sequence of representations of the Vitruvian Man, that famous Renaissance architectural image of the geometrical harmony between the proportions of the human body and the quasi-mystic fusion of square and circle (earthly and divine). The works in question are illustrations of the passage (III.1.i) in Vitruvius’ Ten Books of Architecture, where the ancient Romantheorist affirms the analogy between anatomy and geometry by claiming that a man with his arms extended could fit into both a circle and a square.7 A whole tradition of illustrations of the idea developed in the Renaissance. I show schematic versions (minus the figure) of some of the most significant ones in Figs. D-G.

The first (Fig. D) is by Francesco di Giorgio (I 5th century), in a manuscript that once belonged to Leonardo da Vinci; in this diagram the circle touches the upper rim of the square, cuts down a little below the bottom (as though accidentally), and is cut off, left and right, where it would extend beyond the square. In Leonardo’s own version (Fig. E), the most famous of all the illustrations, the circle exactly meets the bottom of the square, as though in correction of Francesco di Giorgio, but it also extends in three segments beyond the square, at the top (the largest segment) and at the sides; also, two small corners of the square extend beyond the rim of the circle at the top, with two larger ones at the bottom. Compared with the earlier disposition, in this arrangement the square is less dominant over the circle, which now rises in buoyant equality with it. The arrangement in Fra Giocondo’s 1511 edition of Vitruvius (Fig. F) is more resolved than Francesco’s, but more simple-minded and static than Leonardo’s: the circle and square simply coincide. In our fourth case, from Cesariano’s 1521 Vitruvius (Fig. G), the circle again exactly fits the square, but another square also fits exactly within it, and the whole pattern is crossed by a pair of diagonal lines (which intersect at the navel of the man).

The Renaissance Vitruvius illustrations seem pertinent because these configurations can be found in the work of Mangold, and particularly because his latest works are preoccupied with the relation of circle to square. Fig. D suggests those works which read as square truncations of an implied circle, such as Light Neutral Area, 1966, or 1/2 Manilla Curved Area (Divided), 1967. Fig. E suggests works where the corners of the square lie beyond a circular canvas, such as Circle Painting No. 5 (Purple), 1973. Fig. F resembles the exact fit of the circle in a square in Untitled (Gold), 1973, although there only a semicircle is drawn. And Fig. G calls to mind both the oblong X Paintings of 1969 and the square/within a circle/within a square of Untitled (Brown), 1973. Mangold’s paintings often play against the perfect fit of circle to square, the general presumption from which they all diverge.

The question of deviations from geometric regularity and consequent warpage or illusionism is urgent in Mangold’s new works on canvas and paper. The new drawings, in colored pencil, present perfect circles, to the inside of which modifications of a square relate. In one example the idea is to have two sides of equal length (for a square) and two longer ones: the longer ones cross—not at a right angle, either—generating a second small modified square against the circle rim. The whole has a Fritz Glarner-like twist against the geometric grain. Because of the deviation from orthogonality, the resultant irregular quadrilaterals have a tense relation to the circle (where optical overtones can occur) and to the plane; this would be even tenser if the reassuring steadiness of the circle didn’t intervene. This is not really a problem of illusionism, since we do not—at least on paper—imagine such forms as squares subsequently wrenched in space. Instead there is a more charming, subjunctive suggestion of the possibility of distortion. A parallel for this can be found in numerous square-seeming forms in the work of Kasimir Malevich—forms which are visibly not squares at all but which don’t lose the square Gestalt. The “square” within Malevich’s Suprematist Composition: White on White, c. 1918 (The Museum of Modern Art), is not even a rectangle, let alone a square, having two sides of equal length and one shorter, and another longer, than the others; even so, that form is generally—and not unreasonably—described as a square.

Are Mangold’s bulged or broken circles, or skewed squares, really distorted at all? Not if by that we mean to imply that they eclipse a truer, purer, more timeless and unqualified form that they might have revealed. Yes, if we simply mean that they are activated . . . into identity. Mangold’s warpage consists more in the vitalization of a form—at the worthwhile expense of its conceptual generality—than in an anticanonic violation of it. These are not distortions and not cues to illusion. They take just so much weight off the conceptual circle and put it onto the perceptual circle.

Illusionism did occur in 1969 and 1970, especially in the (gently) bulging X Paintings of 1969. And the same holds true for the cutout “frame” paintings of 1970—rectangular outside and trapezoidal within—which exaggerate the cut-away center in Stella’s 1963 polygonal works by reducing the painted (masonite) surface to an almost sarcastic mat or (modernist) edge around the wall showing through from behind. That kind of thing has been left behind.

There is a dryness and absence of anxiety in Mangold’s work that may derive from its tendency to set a curious but thoroughly manageable problem for itself within the Classical territory of painting and then to just go ahead and solve it. Nothing wrong with that, although it can get a little like playing chess against yourself. One such device involves first subjecting a regular geometrical figure to irregularity and then somehow accommodating it. In the drawings it is the “improper” square that requires attention. In the impressive new painting Untitled (Blue-Gray), 1973, it is the circle, there broken into a loose, springy, gasketlike ring about to uncoil. The strict square of the canvas is given: no question of asymmetry there. But there is a second, drawn square within the broken circle and that needs somehow to be accommodated to the wayward ring. The clever handling of this neat little dilemma results in a composition in which the inside square seems placed carefully with regard both to the outside square of the rim and to the ring as well, in much the same way as El Lissitzky centers a horizontal rectilinear form with respect both to an open springlike hoop and to an overall rectangle, in his Proun No. 95, c. 1920–23, recently shown in the Guggenheim’s Futurism show. To say that is only to say that Mangold’s firm, direct, sharp-looking paintings are architectural in still another way.

Joseph Masheck



1. See Charles Millard, “The Photography of Charles Sheeler,” in Charles Sheeler, National Collection of Fine Arts, Washington, 1968, and illustrations on pp. 80, 81, 151. For Mangold’s Brown Wall, Gray Window Wall, and Yellow Wall Section I, see Diane Waldman’s Guggenheim Museum catalogue, Robert Mangold, New York, 1971, where other works not illustrated here can also be found.

2. Quoted in Henry Geldzahler, American Painting in the Twentieth Century, New York, 1965, p. 139.

3. For S. Miniato, see Kenneth John Conant, Carolingian and Romanesque Architecture 800 to 1200, Harmondsworth, England, 1959, p. 133(a); for the other churches, Rudolf Wittkower, Architectural Principles in the Age of Humanism, 3rd ed., London, 1962, pls. 19b, 32c, 33a.

4. See Amédée Ozenfant, Foundations of Modern Art, rev. ed., trans. John Rodker, New York, 1952, p. 116.

5. William S. Rubin, Frank Stella, New York, 1970, p. 131. For my response to the protractor type, involving the architecture of Frank Lloyd Wright, see Joseph Masheck, “London Commentary: Frank Stella at Kasmin,” Studio International, February, 1969, pp. 90–91.

6. Robert Pincus-Witten, “Sol LeWitt: Word <—> Object,” Artforum, February, 1973, p. 71, warning that an insistence on the similarity between Stella and LeWitt might deny such important differences as “color sensibility against theoretical didacticism, feeling and emotionalism against keen rationalism, sensibility against theory, object against concept.”

7. See Wittkower, Architectural Principles, pp. 13–19, with pls. 2a, 2b, 3a, 4. Mangold’s Circle in and out of a Polygon II, 1973, half square, half circular in form, with a semicircle drawn on the square half fused to a half hexagon drawn on the round half, also relates in Renaissance architectural theory to Leon Battista Alberti’s system of constructing regular polygons within a circle, illustrated in his De Re aedificatoria, written c. 1450; see ibid., pp. 3ff, with fig. 1 on p. 4. In the XVI century Sebastiano Serlio devoted much attention to these matters in Book I (“De Geometria”) of his treatise, see his Tutte l’Opere d’architettura, Venice, 1619, repr. Ridgewood, NJ., 1964.