Welcome from Robert Bork

Thank you for visiting “Geometries of Creation.”  This site has been constructed to advance the scholarly conversation about the use of geometry in art. 

I have devoted considerable attention to this topic over the past two decades, because I believe that such research can shed useful light on the processes of artistic creativity, and on the history of art more generally.

The study of artisanal geometry has received less systematic attention than it deserves, at least in my view, partly because it occupies an awkward borderland between two different academic cultures.  Art Historians consider many aspects of artistic creativity and production, but geometry has rarely been among them, in part because the documentary record of geometrical design practices remains disappointingly scanty.  Historians of mathematics, conversely, tend to emphasize the development of genuinely analytical theory, rather than the more informal creative practices of artists and craftsmen.  Although the study of artistic geometry has no really well-established institutional home, the recent proliferation of computer-aided design software now allows researchers to explore the field far more readily than our predecessors could.  The internet, moreover, now facilitates the sharing and exchange of ideas on this subject, both within the academy and more broadly.  I fondly hope that this website, in particular, will help to advance this conversation.  Enjoy!


My Background

My exploration of artistic geometry has emerged naturally from my long-standing interests in art, architecture, and the sciences.  After spending my childhood drawing airplanes and dinosaurs, I fell in love with Reims Cathedral on a family trip to France, and I have been fascinated by Gothic architecture ever since.  Because I also love science and quantitative reasoning, though, I studied mainly physics as an undergraduate at Harvard and as a graduate student at UC Santa Cruz before transferring to Princeton and committing to a career as a medievalist architectural historian.  I have taught in the Art History program at the University of Iowa since 1998, publishing three main books in that time: the first, based on my dissertation, discussed the history of Gothic church spires; the second explored the geometry of Gothic architectural drawings; and the most recent considers the character and fate of late Gothic architecture.  Many of my articles and conference presentations have dealt with geometrical questions, especially in the context of medieval design.  For details on these projects, and on my background, see the links below:

Project Background

This site exists to document and share the results of my ongoing inquiry into the geometry of art and architecture, which has deep roots.  I first became fascinated with Gothic cathedrals because they resemble crystals in having an intricate formal order based on geometrical ideas such as rotation, reflection, and the creation of similar forms on different scales.  As I began to read about these buildings, I learned that they had been designed by master masons who used only simple tools, so in high school I began trying to follow their example by using the compass and straightedge to create my own original design drawings for cathedrals.  In college, I assisted two of my early mentors in surveys of Gothic buildings, working with Miami University’s Sergio Sanabria at Metz Cathedral, and with Columbia University’s Stephen Murray at Amiens Cathedral.  Both of these projects aimed to clarify the history of the buildings in question, and Murray subsequently used the results of his survey as the basis of a geometrical study that he published in an article, a book, and a popular series of educational videos.  I found this work very inspiring, but I decided to pursue a more traditionally art-historical approach in my dissertation, both because I was eager to explore the history of Gothic church spires, and because working with Sanabria and Murray had taught me that careful surveying of Gothic buildings required commitments of time and manpower that I could not easily muster as a graduate student.  While working on the book that emerged from my dissertation, though, I began to recognize the potential of geometrical research into original Gothic design drawings, of which several hundred exist in the German world, and several dozen more in the rest of Europe.  After importing scanned images of these drawings into my computer, I could use the Vectorworks design software as a perfectly precise virtual drafting system, developing and testing hypotheses about how the medieval draftsmen developed their designs.  The first fruit of this work was an article on the early drawings for Strasbourg Cathedral that was published in 2005.  I went on to explore dozens of other Gothic drawings in my 2011 book The Geometry of Creation; the book’s introductory chapter, which explains more about my method, can be found here.  While working on that book project, my colleague Norbert Nussbaum invited me to explore the geometry of the architectural framework around a fifteenth-century painting of the Crucifixion at the Wallraf-Richartz Museum in Cologne, Germany.  I soon found that a simple geometrical system governed not only the frame, but also the arrangement of the figures in the painting itself, and that similar principles appeared in several other closely related paintings.  This struck me as very surprising, because I had always been skeptical of attempts to explain the principles of representational art through geometry; on the rare occasions when I had seen diagrams of this sort, I had not been impressed, since it seemed to me that the choices of reference points in most paintings were far more arbitrary than in the Gothic buildings I studied.  The whole enterprise seemed flawed by imprecision, wishful thinking, and a lack of corroborative evidence.  My work in Cologne convinced me, however, that painters in this milieu really were using geometry in ways that their architectural colleagues would have understood.  In writing my article on those paintings, I wanted to contrast the rigor of my own results with the sloppiness of earlier work that had given the field of artistic geometry a bad reputation.  When I first came across Charles Bouleau’s 1963 book The Painter’s Secret Geometry, I assumed that I had found the perfect foil for my own work, both because the title seemed rather sensationalist, and because the author attempted to apply the same basic geometrical principles to paintings ranging in date from the early Middle Ages to the twentieth century.  After I began to engage more closely with the book, however, I revised my opinion dramatically, since many of Bouleau’s geometrical analyses seemed quite compelling, and even brilliant.  I am not suggesting that his results deserve to be taken on faith; on the contrary, I believe that they deserve rigorous critical scrutiny.  More broadly, I believe that work on the geometry of art deserves to be taken seriously by art historians, and that its results deserve to be incorporated into the larger narratives of art history.  In recent years, I have become increasingly convinced of the importance of this topic, not only because of my early work on the Cologne paintings and my discovery of Bouleau’s book, but also because I have found compelling evidence for the use geometrical composition schemes in a wide variety of paintings, starting with several by Piero di Cosimo that were on view at the National Gallery of Art in Washington when I was there as a research fellow in 2015.   Gothic architecture continues to occupy center stage in my scholarly career, and my most recent research projects thus involve the geometrical analysis of laser-scanned imagery from the cathedrals of ReimsMetz, and Notre-Dame in Paris.  Ultimately, though, I hope to contribute to the discussion of geometry in the arts more generally, and I have created this website to advance that goal.

Contact, Credit, and Comments

In establishing this web site, I aim not only to share ideas, but also to establish active dialog with people interested in geometry and the arts, including scholars, artists, students, and curious readers of all stripes.  If you have questions or comments about the material presented here, therefore, please feel free to write to me at robert-bork@uiowa.edu.  The geometrical schemes described on this site all reflect my original thinking, except where noted otherwise, and I would appreciate being credited if you cite or share this material.  Conversely, I have tried to acknowledge the sources for the images I have used as bases for these analyses.   I should note, also, that this web site will evolve over time, and that much of its content should be understood as work in progress.  For all of these reasons, I will be grateful for your comments and observations.