This thesis deals with the mathematical knowledge of the geometry, which were used in the Gothic period. This is mainly the knowledge that was reflected in the architecture. It is also concerned with the geometrical modeling of the Gothic architectural elements using computer systems of dynamic geometry and potential use of these figures in the mathematics, because the visible connection between theory and practice is very good motivation. The thesis briefly introduces characteristic features of the Gothic style and also describes the historical background that enabled the rise of this new style. This work shows closer also how Gothic building was technically built up. Part of this work is dynamic geometric computer models, which were made with using the gathered information. The interactivity of these models helps students to get better insight into the principles of Gothic architecture elements and also into geometric relationships used in these elements.

Reims Cathedral holds a great deal of significance for the history of Gothic architecture, as well as the larger history of France as the coronation church. Given the historic significance of Reims, it is not surprising that much scholarship has been dedicated to the building’s sculpture, glass, and architecture. Most studies dealing with the cathedral’s architecture are based on stylistic and archaeological analysis, augmented by the use of surviving documents related to the construction. Although much fruitful work has been done in this vein, important questions about the building’s chronology and design still remain unresolved. The extent to which the design of the cathedral was established at the start of its construction, for example, continues to be disputed. The most recent monograph on the cathedral, published by Alain Villes in 2009, suggests that dramatic revisions to the overall plan and elevation were introduced during the course of its construction, going beyond the alterations to the façade designs that many previous authors have noted, but his theses remain controversial. Subsequently, Robert Bork has produced geometric models of the cathedral, which suggest that its plan was more coherent and unified. Additionally, French archaeologist Walter Berry has conducted new excavations, which further reveal additional archaeological evidence not yet taken into account by other Reims scholars. My dissertation, “Measuring the Past: The Geometry of Reims Cathedral,” examines the architectural design from a geometric perspective, augmented by archaeological, stylistic, and historic evidence. The primary contribution that my dissertation makes to art history is the development of a new, modern plan of the cathedral. I developed this plan by taking thousands of measurements using handheld devices and laser mapping, which I then incorporated into a single data set. This work allowed Bork and me to further refine the underlying geometry that created the cathedral’s layout and proportions. This new plan indicates that a master plan devised by the first architect governed the whole church, with subsequent modifications affecting its articulation rather than its overall layout. In addition to explaining how this plan was originally conceived, my dissertation also examines the anomalies and mistakes made during construction, which at times forced minor deviations from the plan. Some of these building errors and the obvious attempts to correct them give clues to the order of construction, in addition to supporting the notion that the masons repeatedly returned to the uniform scheme. This allows me to reassess the scholarship written about the cathedral and the complex history of the building project, while resolving some of the disputes over the cathedral’s construction and design.