Excellent article by Hugh McCague, York University
A master mason could adeptly and repeatedly apply a few simple geometric operations and tools, such as the mason's large compass, to produce a myriad of sophisticated designs.
Excerpt:
A Mathematical Look at a
Medieval Cathedral
by
Hugh McCague, York University
http://www.maa.org:
Mathematical Association of America
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, Vitruvius'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 compass, 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.
The basic tools for design
were compasses, dividers, straightedges, rulers, and set squares. Both small
and large compasses and dividers were employed. The large compasses could be up
to a meter long. Compasses and dividers were used, of course, for drawing
circular arcs, and the latter was also employed to copy or transfer a given
length.
To implement some larger
designs, string and rope could be used to swing out arcs and set out lengths.
For drawing straight lines, straightedges, rulers, and set squares would have
been employed. However, the central purpose of the set square was, of course,
drawing and checking right angles. Simple combinations of compass positions could
produce a variety of pointed and rounded arch shapes.
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