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Mathematics in, of and for Architecture: A Framework of Types

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Architecture and Mathematics from Antiquity to the Future

Abstract

A majority of the many different types of applications of mathematics in architecture are present, in some rudimentary way at least, in even the earliest myths of this discipline. The more extensive set of application types in use today shares a clear lineage to these ancestral cases. The specific formulas used by architects and engineers may have changed, and, amongst other things, their capacity to work with non-orthogonal geometries has also improved, but the fundamental purpose of the application of mathematics in architecture has endured throughout history. The purpose of the present chapter is to examine and to begin to identify the different ways in which mathematics is used in architecture.

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Notes

  1. 1.

    “Well building hath three Conditions. Commoditie, Firmenes and Delight” (Wotton 1624: 1).

  2. 2.

    A common and reasonable concern that has been raised with the standard design process model is that design is not necessarily a linear or systematic process. Design is often characterised as an ‘ill-defined’ or ‘wicked’ problem (Brown et al. 2010). Design problems, unlike many mathematical ones, rarely have a single ideal solution. Instead, design involves handling a range of challenges that are described by scientists and engineers as either ‘non-trivial’ or ‘sub-optimal’. Design involves balanced compromise between issues, some of which may be described with great rigour (like structural stability and material strength) while others cannot (like the symbolic power of a building, or the message its iconography communicates to society). This is why the design process model, which may be appropriate for simple or formulaic buildings, is much less useful for more complex building types.

  3. 3.

    For some complex building types, a much higher level of performance is specified in the architectural brief including lighting levels, acoustic reverberation times and structural bearing capacities. In the last few decades it has also become common for technically advanced buildings, like hospitals, to rely on a relative performance brief. For example, a client might state that a new oncology centre for Rome must function at least as well as the recently completed oncology centre in Sydney, but accommodate a 25 % growth in treatment capacity. Such a brief involves both the measuring of the properties of the reference structure and then the interpretation and interpolation of these performance criteria into the new design with increased capacity.

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Authors and Affiliations

  1. School of Architecture and Built Environment, University of Newcastle, Callaghan, New South Wales, 2308, Australia

    Michael J. Ostwald

  2. Kim Williams Books, Corso Regina Margherita, 72, 10153, Turin, (Torino), Italy

    Kim Williams

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  1. Michael J. Ostwald
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  2. Kim Williams
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Correspondence to Michael J. Ostwald .

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  1. Kim Williams Books, Torino, Italy

    Kim Williams

  2. School of Architecture and Built Environment, The University of Newcastle, Callaghan, Australia

    Michael J. Ostwald

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Ostwald, M.J., Williams, K. (2015). Mathematics in, of and for Architecture: A Framework of Types. In: Williams, K., Ostwald, M. (eds) Architecture and Mathematics from Antiquity to the Future. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-00137-1_3

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