The Geometry of a Piece of String

Abstract

line, n. […] 4. cord for measuring, levelling etc. […] 6. long narrow mark traced on surface. O.E.D.Between the design and the realization of a building there are a number of ‘drawing’ processes, either on the building site or in the workshop, which range from the setting out of the plan to the production of ‘shop drawings’ from which details are derived. Unfortunately, while the latter have survived in sufficient numbers to have attracted scholarly attention, the setting out of the ground plan leaves no trace. Nevertheless, it is that process that determines the building's basic geometry. While much scholarly effort has gone into attempting to divine the geometrical principles behind designs from Antiquity to the Gothic period, it has not always been informed by an understanding of the setting-out process. Without taking the constraints of that process into account, one is reduced to looking for geometrical relationships within the building, and of course one will find some. Clearly, there were geometrical principles behind almost all buildings, if only that they should be rectangular or symmetrical, but the difficulty is that a few simple rules can easily result in a large number of geometrical relationships within the building that were not used, and possibly not even recognized, by their designers. At the very least, therefore, we should consider how to distinguish those relationships that were actually used by the designers and builders from those that are merely epiphenomenal.