The choir of Notre-Dame of Paris: An inquiry into twelfth-century mathematics and early-Gothic architecture

The cathedral of Notre-Dame of Paris has been studied from the perspective of Art History, but never from the point of view of the changes in mathematics during the twelfth century. When the builders undertook the construction of the choir of Notre-Dame, Paris was a burgeoning center of intellectual activity. The city was known as a place for the study of theology and the arts. Some prominent figures such as Hugh of Saint-Victor and Thierry of Chartres taught in Paris during the first half of the twelfth century. These scholars composed treatises that inform us about mathematics contemporary to the construction of the cathedral of Notre-Dame. In this dissertation I analyze these writings and compare their mathematical content to the calculations that the builders made to design the plan of the choir of Notre-Dame. Central to these calculations are mensuration and computations with right-angled triangles. These are the same mathematics as those that a twelfth-century pupil learned during his curriculum in the arts. As I show, by the middle of the twelfth century, there is no separation between the science of the builder and the mathematical knowledge of the Parisian elite.;I begin by presenting the intellectual context in which the choir of Notre-Dame was built. In chapter one, I explain how the twelfth century is a period in which arts and sciences flourished and how it is also a time of intense building activity in Paris. In the same section, I introduce the type of mathematics known to twelfth-century Western scholars. Chapter two first deals with writings which inform us about the concept that medieval intellectuals had of the link between geometry and building practice. In the second section of this chapter I detail the mathematics present in medieval scientific treatises. In the third chapter, I explain how with these mathematics the choir of Notre-Dame was designed. I show how besides Biblical numbers, a careful choice of values minimizing calculation errors dictated the dimensions of this early-Gothic choir.