This particular skill, stereotomy (from the Greek words for stone and cutting), would have been a principal point of difference between how Michelangelo would have approached sculpting the Pieta in St Peter’s, Rome (1499), and crafting the Medicean-Laurentian Library in Florence (commenced in 1523). Shaping implies a reductive process: from a block of stone, for example, material is chiselled roughly, finely, and abraded to release the artifice. Typically, it is the engineer who is called upon to engage with the mathematics of architecture. Felix Candela’s use of several hyperbolic paraboloids used in combination
The development of four intersecting ‘hypars’ with curved edges. Modelling implies the reverse: lumps of pliable material are cajoled and caressed to the satisfaction of the artist. In making this claim it will self-contradict, showing how taking up such geometries has
thus far blurred the distinction between architects, engineers and sculptors. He asks whether the application of doubly ruled surfaces like these might help us to make a significant distinction between architecture and sculpture. The emphasis on geometry as part of the architect’s skill set became more sophisticated from the Renaissance up until the modern epoch of iron and steel construction: the earlier congruence between architecture and engineering design thinking fell away as each profession charted quite different paths to practice. This article looks at one set of geometries – doubly ruled surfaces, and proposes that their attendant facilitation for construction purposes, even if obviated by file to factory production may yet point to a useful distinction between the fundamentals of architecture (Vitruvian trinity) and the aesthetic priorities of sculpture. As a force of destiny, together they have further distanced the designer from any role as stereotomer. Plastic arts traditionally describe the work of the sculptor and the way they manage material through shaping or modelling. He was the first to determine through calculation that the entire shell was in compression: in ordinary circumstances hyperbolic paraboloid roof forms do not experience significant tensile stress. In this article Mark Burry looks at a specific set of geometries – doubly ruled surfaces – that have been most explicitly developed by ‘structural artists’ Antoni Gaudi, Vladimir Shukhov and Felix Candela. Parameters of a hyperbolic paraboloid
A hyperbolic paraboloid is a saddle-shaped doubly ruled surface that has a convex curve as a section across one axis and a concave curve in the other. Figure 1. Candela used this process for engineering his structural shells made from relatively lightly reinforced concrete. Where there is evidence of a healthy presence of descriptive geometry retained in departments (for example in certain schools in Spain and in Budapest), far from being defended from any unspoken accusation of being an anachronism, its role is actively promoted as an enabler of different types of conversations around spatiality, as a tool to cement a strong sense of the architectural tradition in the emerging architect, and as a philosophical link back to the Greeks. Descriptive geometry allows the general description of the composition to be more readily templated so that individual components could be worked without physical reference to each other. With the exceptions of a relatively few schools of architecture worldwide, since early in the 20th century most have reduced any emphasis on descriptive geometry in their curricula due to a combination of the increased technical specialisation away from the hands-on involvement of the architect, two generations of rationalist ideology favouring the orthogonal, vertical and planar, and the advent of advanced computation especially for engineers. Figure 2.

Updated: 30.10.2014 — 13:51