Daring Diagonal Virtual Museum

The Daring Diagonal: Introduction

Gallery 1.8B

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 What is Diagonality with a Capital D? An Overview

A. Introduction

After peeping out somewhat hesitantly in various cultures over many centuries, Diagonality finally surged onto the world stage at the very end of the 19th century. It soon became what deserves to be called the signature geometry of 20th century art and architecture, and it continues into the 21st century unabated (see Fig. 1.1). While right-angle, curvilinear, and amorphous geometries have certainly been utilized during the modern era, diagonal relationships dominated the scene and did so increasingly as the decades passed through the 20th century and into the 21st. It is curious, however, that the artists, engineers, and architects using diagonals and a host of other angular relationships during this period failed to notice or acknowledge the underlying geometric web that connected their disparate activities. Looking at the “labeled” art movements of the early 20th century, such as Cubism, Rayonism, Constructivism, Vorticism, and Art Deco, it is evident that a diagonal motif undeniably links them all. Diagonality also was utilized in fields not traditionally seen as linked and for that reason in particular, it was never viewed as a singular phenomenon with connective tissue.

Figure 1.1  Hearst Tower, New York. 2003 Sir Norman Foster. Photo: Joel Levinson

Once the concept is understood, the word diagonality is comfortably embraced as an on-the-mark expression referring to a design motif that is both pervasive and culture-shifting. Countless examples of diagonality can be discovered around the world in art museums and on street corners once the mind and the eye are cued to see them. As the German poet, philosopher, and scientist Johann Wolfgang von Goethe (1749-1832) observed, “We see what we know.” Goethe surely meant the obverse as well: We are blind to what has not yet taken residence in our mind. Whether one has learned to see the phenomenon of Diagonality in all its manifestations, those who have actually employed the diagonal motif know that it offers a productive and liberating approach to solving problems in form, pattern, and structure.

A simple illustration will introduce one of the Era of Diagonality’s many modes of expression. Start with the square at the top of Fig. 1.2, noticing that its sides are parallel to the sides of this page. Now rotate the square 45 degrees. A line drawn from the top corner to the bottom corner bisects the square and creates two triangles. Now slide the triangles along the bisecting diagonal but keep the two triangles touching (Fig. 1.3). Imagine that this new angular shape with its two projecting acute corners is the footprint of a building. Some modern buildings constructed since the start of the twentieth century do indeed have this configuration. One example is the triangle-based Church and Center in Hyvinkää, Finland, designed in 1959 by architect Aarno Ruussuvuori (Fig. 1.4). The two triangles composing the building’s footprint are the bases of two pyramids taken to different heights. Another example is the Soviet Pavilion designed in 1925 by the Russian architect Konstantin Melnikov (Fig. 1.5). Not only does Melnikov’s plan mirror our diagram, he also introduces a flight of stairs between the two triangular sections to emphasize the bifurcation and diagonality of the scheme. Angular features of the design, such as the tilted roof panels and the triangulated framing of the sign tower, make this an emblematic project that illustrates the core features of much diagonality in the modern era.

The footprints of most buildings constructed before the twentieth century are simple rectangles (for example, the Temple of Poseidon, Fig. 1.6). Larger buildings were often composed of a combination of squares and rectangles.

Buildings with square corners have a static quality, while modern buildings employing the diagonal motif are dynamic, providing a sense of fluidity, energy, and motion. This book presents the history of this transformation, from the static geometry of the rectangle to the dynamic geometry of the oblique. It is a rich and complex story that begins with the dawn of civilization and involves almost every major period in world history.

As mentioned above, diagonality, as a design motif, is not limited to architecture. It shows up in the visual arts, landscape and urban design, product design, and structural engineering. Its history takes us from the familiar geometry of the right angle to a geometry that is more complex and mysterious, and, in many instances, more functionally advantageous. Manifestations of the diagonal motif appear in the street layouts of cities, in the structural framing of bridges and high-rise buildings, in man-made landscapes, and in furniture design. In this book I explore the connective tissue that unifies seemingly separate and distinct artistic styles and technological developments such as the art movements of the early 20th century, geodesic domes, space frames , and so-called Deconstruction, a development of the 1980s that someone once called piecemeal construction. Diagonality weaves together design trends and developments that in many respects were hitherto regarded as unrelated or, at best, loosely related, such as the patterns used in cut glass and the diagonal grids employed by Frank Lloyd Wright and his many followers.

The underlying “forces” that at certain times adopted and nourished the use of diagonals and at other times created obstacles are illustrated in the pages that follow. Those positive and negative forces come from fields such as philosophy, mathematics, religion, the mechanics of vision, the structures of both living and nonliving things, and social revolution. The main stage on which the action of this book finally unfolds, however, is the full blossoming of Diagonality during the modern era that began in the late 19th century. At that time, global culture gave birth to and, in turn, was profoundly re-shaped by, this geometric motif.

Figure 1.2  Square and rotated square.

Figure 1.3  Bifurcated square with triangular halves slid along vertical axis.

Figure 1.4  Church and Center in Hyvinkaa, Finland.  1959-1961 Aaron Ruusuvuori, architect P.183. 1959-61 Precedents in Architecture

Figure 1.5  Konstantin Melnikov. USSR Pavilion. Paris Exposition, France. 1925.

Figure 1.6  (Designer unknown) Temple of Poseidon. Paestum, Italy. 460 BCE.

B. Intentional Use Of Diagonals

Diagonality with a capital D, as I define it, involves the intentional use of oblique lines, angular shapes, and crystalline forms. It does not occur when its employment is simply a passive act. An example will help to clarify this. As I mentioned in the Preface, when I and fellow architecture students at the University of Pennsylvania were designing buildings in response to class assignments in 1957-1963, it was clear that the age-old tradition of using right-angle geometry was giving way—in fact, had already given way—to a new angular motif. At the time, wedge-shaped volumes were either added to or subtracted from our otherwise rectangular masses. These design gestures at our university were referred to as Zaps and Zoots. Such deliberate design transformations were beginning to appear in architectural journals. Some years later, when I mentioned Zaps and Zoots to fellow professionals of my vintage, they spoke of Zaps and Zoots as a fad. Whether it was a fad or a more serious step into modernity, it was intentional, a deliberate act of copying or emulating a particular motif.

Diagonality occurs when oblique relationships are utilized from the outset in a deliberate aesthetic act or when oblique relationships are employed because they spring subconsciously from the deep-rooted aesthetic zeitgeist of an era, such as occurred in the 20th century and continues to the present. During the zaps and zoots phase of Diagonality in the 1960s, the use of diagonals in architecture was deemed a fad or a craze. However, as time passed and the use of diagonals in architecture became ubiquitous and ongoing, what had been viewed as a fad was clearly now a trend. In light of Diagonality’s continuing usage and global acceptance, use of the term Phenomenon of Diagonality seems fully justified.

C. Unintentional Use Of Diagonals

When a builder or architect needs to alter an architectural plan in order to accommodate a pre-existing condition—such as when a road cuts across a corner of building site or a rock outcropping slants across one side of a property—the architectural response is to clip off a corner of the plan. The resulting scheme is not an expression of Diagonality as here defined. It is an adjustment forced by circumstances to an otherwise right-angle plan, not an intentional use of Diagonality. The resulting design with a clipped corner never becomes a precursor; it is not picked up by another individual or another generation and replicated as a useful model.

In the fine arts, I do not regard diagonal relationships in a work of art as an expression of Diagonality unless those relationships were employed by the artist in a deliberate, purposeful way.

For example, the ancient Greek sculpture called the Slave presents an array of folds in the slave’s chiton. These folds are not rendered as soft curves but rather as fan-like arrays of angular elements. The sculptor presumably did not have in mind to create a display of diagonality in an intentional manner but rather gave the final work by chance an aesthetic quality that can be referred to as diagonality with a lower-case d.

D. The Phenomenon of Diagonality

Diagonality with a lower-case d refers both to a particular quality of design and, from a societal perspective, to a cultural phenomenon. The quality aspect of diagonality is easily illustrated. In architecture, for instance, if the floor plan, cross-section, side elevation (side view), or structural design of a particular building has many acute and/or obtuse angles and few right angles, one can say that the plan exhibits the quality of diagonality. This is boldly evident in Daniel Libeskind’s Jewish Museum of 1989 in
Berlin (Fig. 1.7). His building is very obviously out-of-square; with its unavoidable attribute of dynamism, it exhibits the quality I call diagonality. This particular example also happens to represent the “Phenomenon of Diagonality.”

Figure 1.7  Daniel Libeskind. Jewish Museum.  Model. Berlin. 1989.

It is not easy to clarify the “Phenomenon” aspect of Diagonality. For one reason, Diagonality never became an art movement as, for example, did Cubism in the first quarter of the 20th century. There was never a group of artists, or architects, or town planners that called themselves diagonalists in the same way that some painters were known as cubists. Nor was there ever a group of designers who associated with others of like interest and collectively explored a design theme in a way they might have called diagonalism or diagonality. Also absent were art historians and design critics who might have labeled a group of designers as diagonalists or have written about the motif in a broad thematic manner. Curiously, there are no manifestos written by proponents of diagonality. This was not the case with at least three other early 20th century movements—Futurism, Rayonism and Constructivism.

There is one barely-qualifying (because of its brevity) exception to the absence of a manifesto that advocates, by name, the notion of Diagonality. That is the short, impassioned article entitled “Michelangelo’s Fortification Drawings: A Study in the Reflex Diagonal,” by Vincent Scully, Jr. This article appeared in the first issue of Perspecta (1952), the Yale Architectural Journal (see Fig. 1.8). Scully, enthralled by the energy and dynamism of the diagonal, wrote in his typically passionate style:

The power of the sensuously felt diagonal to destroy boundaries and to create reflex makes them [Michelangelo’s Fortification drawings (see Fig. 1.9)] live and grow as spatial forms. In this they are similar, for example, to the best of Wright’s diagonally reflex plans… Consequently, if much of the key to architectural design lies in a sensitivity to rectangular, curvilinear and diagonal rhythms, these drawings are important to us, because they demonstrate an intense investigation into the nature of the diagonal carried on under pressure by an architect who was [also] a sculptor and painter…”

The Phenomenon of Diagonality, then, is the global design development characterized by the intentional, oftentimes asymmetrical, use of the diagonal motif in architecture and in many other design disciplines. It came of age in the 20th century and continues to blossom in the 21st.

Figure 1.8  Figure 1.8 Cover, Perspecta #1

michaelangelo, fortification

Figure 1.9  Michelangelo. Fortification Drawing. Perspecta 1, The Yale Architectural Journal. 1952

E. A Movement Absent A Manifesto

Despite Vincent Scully’s obvious enthusiasm for the diagonal, his role as an academic and critic precluded him from drafting a passionate “call to action.” His article was part art history and part manifesto, albeit a manifesto significantly constrained by the academic code of decorum. Nevertheless, his unabashed enthusiasm for diagonality is evident throughout the above-quoted article and his other writings. Had Scully been an artist himself, he could well have been the one to write a compelling exhortation that might have codified the notion of Diagonality for centuries to come. Scully perhaps left that task to his friend Robert Venturi, a world-renowned Philadelphia architect with a strong iconoclastic bent. Venturi, in his influential 1966 book Complexity and Contradiction in Architecture, wrote inventively about diagonality and other design motifs (along with a host of other fresh perspectives on architecture). Although his book was a manifesto of sorts (he himself referred to it as a gentle manifesto), it was not a document solely devoted to this theme and therefore is not the focused declaration of principles that would likely have made Diagonality common parlance in today’s design communities. Venturi’s words and images no doubt helped to bring this motif to somewhat greater prominence and use.

“In Modern architecture, we have operated too long under the restrictions of unbending rectangular forms supposed to have grown out of the technical requirements of the [structural] frame and the mass-produced curtain wall. In contrasting Mies’ and Johnson’s Seagram Building with Kahn’s project for an office tower in Philadelphia it can be seen that Mies and Johnson reject all contradictions of diagonal wind-bracing in favor of an expression of a rectilinear frame. [Figure 1.10] Kahn once said that the Seagram building was like a beautiful lady with hidden corsets. Kahn, in contrast expresses the wind-bracing—but at the expense of such vertical elements as the elevator and, indeed of the spaces for people.”

There are other art historians, in addition to Scully, who have written about the diagonal. One is James S. Ackerman, who discussed the subject in The Architecture of Michelangelo (1961). Two other books more focused on diagonality in modern architecture are Anthony Alofsin’s Frank Lloyd Wright: The Lost Years 1910-1922 (1993) and David DeLong’s excellent book on Bruce Goff’s quirky architecture, Bruce Goff: Toward Absolute Architecture (1988). In The Lost Years, Alofsin devotes an entire chapter to diagonality as a quality of Wright’s design. In his Chapter 9, “A Lesson in Diagonality,” Alofsin writes:

Figure 1.10  Louis I. Kahn and Anne Tyng. Philadelphia City Hall Study. Philadelphia, Pennsylvania. 1957

After 1910, as Wright moved forward with his experiments in primitivism and exploration of ornament, a new force developed in his architecture: a dynamic diagonality that allowed for fresh asymmetrical compositions. The square, its rotation, and its translation into dynamic compositions became a means of artistic expression he pursued at the Imperial Hotel throughout the decade. Wright began to turn, to implode, and, ultimately, to explode the square. (See Fig. 1.11.)

De Long describes Bruce Goff’s use of non-orthogonal elements in his discussion of the architect’s initial design of a house for one his major patrons:

Goff responded by presenting an extraordinary design, one that had a spatial freedom expressed by a composition of nonparallel planes and in which regular geometric shapes of any sort were avoided. Writing of the design, Goff said, “Sometimes we feel the need to go to the other extreme and develop a very free approach—try to emancipate ourselves from geometry, you might say.” Discussing the quality of space that would result, he added, “Now that it is possible to use geometry so freely our spaces may become more active…more dynamic.” [See Fig. 1.12.)

These books are among the few written in English in which diagonality as a geometric motif is discussed at length.

Figure 1.11  11 Midway Gardens, Chicago: cast-concrete block, c. 1914

Joe Price Studio

Figure 1.12  Bruce Goff. Joe Price studio and addition, final plan as built. Bartlesville, Oklahoma. 1966.

F. Antecedents And PrecursorsTo best understand the roots of Diagonality, it is useful to distinguish between Diagonality’s antecedents and its precursors.

Imagine that architects in ancient Egypt had reason to create a triangular room amid a floor plan consisting of otherwise rectangular rooms. The triangular room should be regarded as an antecedent if, say, it is rediscovered and reinterpreted by architects in the 20th century, who then put the concept to use.

If, however, the original triangular room in ancient Egypt immediately starts a trend in that culture involving the design of triangular rooms in other Egyptian buildings, that first triangular room would be described as the precursor of those that followed because subsequent practitioners “built upon” IT.

F. Antecedents And Precursors

To best understand the roots of Diagonality, it is useful to distinguish between Diagonality’s antecedents and its precursors.

Imagine that architects in ancient Egypt had reason to create a triangular room amid a floor plan consisting of otherwise rectangular rooms. The triangular room should be regarded as an antecedent if, say, it is rediscovered and reinterpreted by architects in the 20th century, who then put the concept to use.

If, however, the original triangular room in ancient Egypt immediately starts a trend in that culture involving the design of triangular rooms in other Egyptian buildings, that first triangular room would be described as the precursor of those that followed because subsequent practitioners “built upon” IT.

G. Leaping Ahead: Some Examples Of Diagonality In The Modern World

A fine example of 20th century Diagonality is I. M. Pei’s East Wing of the National Gallery in Washington, DC (designed in 1968 and opened to the public a decade later). In dramatic contrast to the original wing of the building, a classically designed, rectangular structure, Pei’s addition is an angular composition conforming to and echoing its site’s angular shape on the Mall (Fig. 1.13). The acute-angle geometry of the site results in some walls of the building meeting in surprisingly sharp angles. Visitors to the buildings have been so arrested and amazed by the sharpness of the stone corner (see upper left part of the plan) that the knife-edge is marred by a flare of hand oils. It was the disbelief in the sharpness of the corner than demanded it be touched to be believed. It is logical that this building’s geometric motif connected to a revolution that embraced a new geometry because it was during this time that much of Washington, was erupting in political upheaval. Protests against the war in Vietnam, for civil rights, and for freer lifestyles were causing turmoil throughout the nation. In researching Diagonality, I have found evidence that times of social upheaval are correlated with periods of pronounced diagonal expression. At the same time as the Russian Revolution of 1917, for instance, many Russian artistic movements appeared employing diagonals as their dominant geometry (see Fig. 1.14).

Figure 1.13  I.M. Pei. East Wing of National Gallery of Art. Washington DC. 1968.

Figure 1.14  Russian Avant Garde art by El Lissitsky. 1919

Figure 1.15  Maya Lin, Vietnam Veteran’s Memorial. Washington DC. 1983

Another example is the popularity of octagon-shaped buildings in the United States during a twenty-year period in the midst of the industrial revolution. This is not to say that the industrial revolution caused the proliferation of octagonal architecture but simply to suggest that a mood of revolutionary change was in the air, spawning a desire for change on various fronts including the appearance and functioning of buildings.

The Vietnam Veterans Memorial (Fig. 1.15), designed by Maya Lin and, like Pei’s East Wing, built on the Washington Mall, is another, and more poetic, example of the diagonal motif in 20th century architecture. The Memorial’s footprint is a V cut into the level grass plane of the Mall. The legs of the V point toward the Washington Monument and the Lincoln Memorial. Visitors follow a ramp that slopes down along one leg of the V, then rises back to the plane of the Mall. At the point where the black polished wall changes direction, one begins to rise out of the shadows of the earth and into the brighter light of day and vistas of hope. This excellent, understated memorial reflects the designer’s keen intelligence and poetic use of the diagonal motif.

The city of Washington, itself a paradigm of diagonal city planning and a steppingstone to 20th-century Diagonality, is a fitting home for the East Wing of the National Gallery and the Vietnam Veterans Memorial. Around 1791, a Frenchman, Pierre L’Enfant, designed the city based in part on Baroque planning tenets (Fig. 1.16). Other urban and landscape plans shaped by and/or characterized by bold diagonals are described and analyzed in later chapters, including the highly diagonalized layout of Versailles (Fig. 1.17), executed in the middle of the seventeenth century and a project that directly influenced L’Enfant when he lived at Versailles.

Figure 1.17  Andre le Notre. Versailles. France. 1660.


Figure 1.16  L’Enfant’s plan for Washington.

Throughout the 20th century, the diagonal was also employed extensively in the fine arts. It was oftentimes used to express movement and temporality as in Marcel Duchamp’s “Nude Descending a Staircase” with its cascade of fan-shaped forms (Fig. 1.18). Another example, a composition of crisscrossing black stripes by abstract expressionist Franz Kline (Fig. 1.19), expresses a different quality of modern life. His rough-edged slashes convey a mood of change and unrest, qualities that portended societal developments that began to unfold in the decade just following Kline’s experiments with this motif.

Figure 1.18  Marcel Duchamp. Nude Descending a Staircase, No.2. 1912.

Figure 1.19  Franz Kline. Mohoning. 1956

H. The Psychology Of Diagonality

The subject of Diagonality is intimately involved with the working of the human mind and the mechanics of vision. The concepts of vertical and horizontal axes, for example, are etched in our consciousness like crosshairs. These orientations are reinforced by constant reminders such as the vertical axes of trees and columns and the always-horizontal line of the aptly named horizon at sea. The angled line has historically been viewed as teetering, off-balance. Non-vertical objects and structures frequently appear as though they are about to fall over.

Oblique relationships have been the subject of several interesting scientific investigations over the last hundred years, particularly as they relate to visual perception and cognition. David Olson, a Canadian, found that children cannot reliably replicate the orientation of a diagonal line before the age of seven. He found, too, that some adults have trouble with the concept of diagonals, far more than with vertical and horizontal orientations. Another researcher, Herman Witkin, investigating the perception of verticality, found connections between how individuals perceive what is upright and how they function in society. It is evident that connections of Diagonality to visual perception and emotions add a rich dimension to its study.

It is hard to resist the conclusions that early civilizations harbored subconscious taboos associated with the diagonal and that when these were finally swept aside, Diagonality penetrated the world’s subconscious, not as a word but as a yet unnamed way of seeing. Angularity, for some, became a fundamental component of their psychological makeup. Of course, my assertion that Diagonality penetrated the world’s subconscious at the start of the 20th century does not mean that it was entirely missing from earlier periods in history. The walkways and roadways at Versailles, as mentioned earlier, provide a splendid example of what one must assume was an intentional use of diagonals, not just a passive happenstance. The diagonal allées were deliberate, artful features in the manipulation of a grand landscape for the aggrandizement of royalty.

What distinguishes Diagonality in the 20th century from antecedents in preceding centuries is that 20th century diagonality permeated all design disciplines, not just one or two. Hard to explain, however, is the fact that this motif has been wholeheartedly embraced without designers having had a commonly accepted term to refer to the model, to this pervasive motif – until now.

Figure 1.20  El Lissitsky. Speaker’s Platform. 1920

Figure 1.21 The Brooklyn Bridge New York.  1883

It was, however, the 19th century that truly set the stage for the explosion of Diagonality during the 20th century. Cast-iron structural frames with diagonal bracing were used to frame vast exhibition halls. Triangulated steel colliery towers rose out of the landscape, foreshadowing and possibly inspiring the angled commemorative towers and speakers’ platforms of the Russian Avant-garde. [Figure 1.21] Iron and steel were also used to create diagonally braced bridge trusses and suspension structures such as the Brooklyn Bridge. When Lewis Mumford, a 20th century social and architectural historian, first saw the angled suspension cables slanting off the massive Gothic-styled stone towers of the then ‘new’ Brooklyn Bridge, he sensed ‘the dawning of a new age.’ [Figure 1.22] These examples all speak to the technological advances over the last 150 years that made triangulated structures more feasible and affordable.

* * * *

For as long as I have been studying this subject, I have wondered whether I was imagining a phenomenon that does not really exist. James S. Ackerman, in his book about Mannerism and Michelangelo (1961), states, “I believe that while the concept of Diagonality can facilitate criticism, it can also obstruct our perception by urging us to find in the work of art what our definition of it states we must find.” Ackerman concludes his commentary by saying, “In short, my approach has been guided by the conviction that generalization on style should emerge from, rather than guide the examination of works of art themselves.”

The chapters in this book are organized chronologically for the most part. but license is occasionally taken within each chapter to arrange the material thematically. In this respect the significance of an entry takes priority over its exact place in time. Each entry, whether building, city, artwork, or treatise, is based upon either my personal examination of the work or my interpretation of sometimes conflicting historical information about it.

The book should also be regarded as a celebration of a design motif that has been little understood but widely used for well-over a century. I can remember my excitement when, driving in Madrid in 1998, I saw two twin office towers leaning over the roadway (Fig. 1.22). The silver, black, and red graphics of the design, and the leaning masses of the towers themselves seemed to boldly proclaim a new era in design. The theory of Diagonality was dramatically confirmed: the Signature Geometry of the 20th century was manifest.

Diagonality has provided our modern civilization with a liberating new perspective that has served as a catalyst for seeing all manner of things from a new vantage. This is a gift to mankind: a powerful new design tool that continues to unleash a host of exceptionally free forms of expression. I have to believe that one day Diagonality will be seen as an empowering design modality close to or equal in significance to the transforming geometry provided centuries earlier by the arch, the dome, the barrel vault, and the flying buttress.

Figure 1.22 One of two Gate of Europe towers also known as KIO Towers. Philip Johnson and John Burgee, architects. 1989-96

Ackerman, J. S. (1961). The Architecture of Michelangelo. Chicago and London, The University of Chicago Press.          

Alofsin, A. (1993). Frank Lloyd Wright: The Lost Years, 1910-1922: A study of Influence. Chicago and London, The University of Chicago Press.

De Long, D. G. (1988). Bruce Goff: toward absolute architecture. New York, The Architectural History Foundation and The MIT Press.

Kostof, S. (1991). The City Shaped : Urban Patterns and Meanings Through History. Boston, Toronto, London, Bullfinch Press.

Scully, J., Vincent J. (1952). “Michelangelo’s Fortification drawings: A Study in the Reflex Diagonal.” Perspecta 1: 38-45.

Venturi, R. (1966). Complexity and Contradiction in Architecture. New York, The Museum of Modern Art with the Graham Foundation for Advanced Studies in the Fine Arts