Daring Diagonal Virtual Museum

THe book: the daring diagonal

Gallery 1.8A

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Signature Geometry of the Modern Era



FOR AT LEAST 7000 YEARS, architects and builders around the world regarded the 90-degree right angle as the bedrock geometry of architecture. Conventional construction demanded the use of the consistent and convenient square corner. The floor plans in the ancient Persian complex of Persepolis, for instance, rigidly employ the right angle as its cardinal geometry (Fig. PF 1).

     Although vertical walls and square corners and strictly vertical walls were the norm, occasions arose when a builder was forced to depart from orthogonal (right angle) geometry. Irregular site conditions, such as an intersection where the streets were not perpendicular, forced a builder to create spaces that were not pure rectangles. The Greek house illustrated in Fig. PF 2 shows a plan that ideally would have had all right angles except that site conditions in the non-orthogonal ancient city of Delos very likely demanded that two exterior walls be canted. This layout shows diagonals imposed by external conditions, not an intentional use of diagonals as has occurred as a commonplace in modern times.

     In light of this history, it came as a surprise to me when, during my senior year (1961-62) in the School of Architecture at the University of Pennsylvania, I noticed that fellow students were adding chisel-shaped extensions to their otherwise rectangular plans. These were similar to the geometry used in a 1963 house by the late New York architect Edward Larrabee Barnes (Fig. PF 3). At the time, these triangular extensions seemed slightly perverse, yet alluring.

Figure PF 3  Floor plan and cross section of a house designed by Edward Larabee Barnes, 1963.

     This geometry appeared to be a reaction against conventionality. This expression of angularity dovetailed with cultural developments of that time, mirroring profound changes in American culture in the early 1960s. An anti-establishment and anti-conventional upheaval was beginning to reveal itself throughout the nation and indeed in other communities throughout the world (see Fig. PF 4). This structurally and functionally absurd design for a chair reflects the psychological and social upheaval of the time. It also suggests that diagonality was embraced as a go-to design motif whether it made sense or not, other than as a theme for artistic works.

     The 1960s, variously called the Vietnam Era or the Equal Rights Era, were marked by protests and social turbulence. People sought to shed convention and bristled at the rigid order of things. A new geometric patterning that felt like it slashed across the orthogonal grid ushered new life and forms into an architecture ripe for change. Anti-orthogonal architecture became something of a banner waved by those advocating and practicing a radical departure from traditional design. This defiant and emerging geometry perfectly suited what was becoming, for some, the psychedelic and experimental behavior of that stormy era (see Fig. PF 5).

Figure PF 5  Drawings for Plug-in city.  Peter Cook and Archigram.  1964


     The use of diagonal shapes and angular relationships during this period was, for me, both puzzling and fascinating. Something new and compelling was in the air, something daring and ripe with the potential for foundational change (see Fig. PF 6).  Oddly, no one was discussing this sweeping architectural transformation.

Figure PF 6  Study for a sculpture for an architectural setting, James Rosati, 1965

     Inexplicably, the pervasive use of what I choose to call diagonality received little recognition or serious discussion by design professionals, scholars, and critics. How was it possible that something as significant as diagonality could be overlooked and under-examined?  For six decades, I have engaged in numerous exchanges with architects and artists of all stripes around the world and amassed a large body of information dealing with this little-recognized cultural phenomenon.  My mounting collection of evidence provides repeated confirmation that 20th-century art and architecture underwent a dramatic transition as indicated by how we designed buildings, drew pictures, decorated vases, engineered bridges, planned cities and gardens, and even configured jet fighters (Fig. PF 7). All of this did not come from nothing. It was a natural, albeit swift, evolution from centuries of prior, more stately, change.

Figure PF  8  Goldenberg House (project).  Louis I. Kahn, 1959

     During the three years of my professional apprenticeship in the 1960s, I couldn’t help but observe that the diagonal was undeniably influencing the architectural geometry of buildings constructed across the country and indeed around the world. The Goldenberg House, designed by visionary Philadelphia architect and Penn professor Louis I. Kahn, is an example of diagonal motifs superimposed on an otherwise orthogonal scheme (Fig. PF 8).  By the late 1970s, it was in fact unusual to find almost any significant new building that did not incorporate some form of diagonality. Some designers, indeed, had embraced diagonality as the dominant expressive motif in their work (Fig. PF 9).

Figure PF 10  Grammar school design project, Joel Levinson, University of Pennsylvania.  1960

Robert Venturi, another member of the Philadelphia School and one of my professors at Penn, assigned a class project to design a grammar school. My scheme consisted of three classroom wings, each in rectangular form but defining a triangular open-air courtyard in the middle (Fig. PF 10).  Each wing ended with rectangular stair towers and toilet cores.  In the spirit of designs being developed in his own office (Fig. PF 11), Venturi suggested that wedge-shaped ends to each classroom wing be considered rather than the clashing rectangular forms I had drawn. This approach extended the triangular theme. The wings now dovetailed with one another in a more geometrically harmonious fashion. Venturi was at the time finalizing his landmark book Complexity and Contradiction in Architecture, in which he frequently refers to diagonals in the works of other architects.  But he did not draw these together into a broader notion of diagonality.

Figure PF 12 Kimball Residence, 1989, Joel Levinson, architect.

     Despite my fascination with the emergence and formalities of diagonality, this oblique geometry did not come naturally to me in my own work. In 1989, all that changed when a client engaged me to design a house with many angles and curves. I gleefully embraced the assignment and discovered that I could, myself, successfully employ the challenging geometry of diagonality throughout the design (Fig. PF 12).

     In the decades since my graduation, I have collected hundreds of articles that reflected examples of diagonality in architecture, city planning, and the arts in general, in both modern and long-ago times (see examples in Figs. PF 13 and PF 14).  I actively searched for cultural developments that might relate to and help illuminate the roots and significance of this emergent design phenomenon. The cumulative effect of my research and analysis led me to the conclusion that diagonality should be regarded as the Signature Geometry of the Modern Era.

     I have established a Web site with extensive detail and in-depth essays that go beyond what can be covered in this book. Its address is ddvm.org, and parts of it will be cited at appropriate places in the Daring Diagonal Virtual Museum.

Figure PF 12 Rendering of Central Chinese Television Tower, Beijing China, Rem Koolhaas, Ole Scheeren/Office for Metropolitan Architecture, projected completion 2008, © OMA/Rem Koolhaas

Figure PF 1  Ancient Persian complex of Persepolis

Figure PF 2  House of the Lake, Delos, Greece. ca. 300 – ca.100 BC

Figure PF 4  Chair transformation 1960s

Figure PF 7  F-117A Nighthawk Stealth Combat Aircraft.  US Air Force, Lockheed Martin. Circa 1982

Figure PF  9 Adult Learning Research Center, Bryn Mawr, Pennsylvania designed by Romaldo Giurgola.

Figure PF  11 Figure PF 8 Headquarters Building, North Penn Visiting Nurse Association, Ambler, Pennsylvania, USA, Venturi and Short, 1960

Figure PF 13  Mannheim, Germany, fortress plan and citadel, 1606