A Mathematical Look at a Medieval Cathedral
By Hugh McCague
Math Horizons (April 2003)
Introduction: If you wish to design and build a cathedral, you’d better know some mathematics. The application of mathematics has been central to the design and execution of art and architecture from the Classical era through the Middle Ages and still today. The renown of the Greek prescriptive sculptural instructions, the Canon of Polykleitos, attests to this. The celebrated Roman architectural and engineering manual, Virtruvius’s De Architectura, also emphasized the importance of mathematics in fulfilling the purpose of building. Medieval stonemasonry was itself reverently known as the Art of Geometry. Our focus here will be on the mathematics known and used by medieval stonemasons, in particular in the construction of Durham Cathedral in Northeast England.
One of the main applications of mathematics in medieval architecture was practical geometry. Practical geometry did not concern itself with axioms, deductions, theorems and proofs. Its approach was more empirical and time-tested. Generally, medieval masons including master masons would not have been able to read more abstract or speculative mathematical treatises in Latin, even if they were allowed access to them in the libraries of bishops and monasteries. However, a master mason could adeptly and repeatedly apply a few simple geometric operations and tools, such as the mason’s large compas, to produce a myriad of sophisticated designs as attested to by extant late medieval design manuscripts, by full-scale working drawings still etched on some church floors and walls, and by the cathedrals themselves.