Generation of Architectural Forms Through Linear Algebra

  • Franca Caliò
  • Elena Marchetti


Our efforts are aimed at applying a mathematical taxonomy or a geometrical model to significant classes of classical or modern architectural structures. Mathematical formulas are used to describe them, even though it is very clear that such formulas have not influenced the creativity of the designers. The purpose of our exercise is simply to better highlight the shape of the architectural object, to extract from it an inherent rule, to make evident its structural rigor. The final result of this exercise is a three-dimensional geometrical model, that is, a description of the geometrical object (a locus, or set of points) expressed through geometric analytical formulae, and its subsequent display on media such as paper or computer screen. The approach involves establishing a few basic elementary shapes, imposing movements and deformations on them, to determine a final shape dynamically; then giving the equations and supplying the related graphical representations.


Translation Vector Cartesian Space Vector Point Architectural Form Algebraic Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Caliò, Franca, Elena Marchetti and E. Scarazzini. 1995. Operazioni e Trasformazioni su Vettori (software). Milan: Città Studi Edizioni.Google Scholar
  2. Caliò, Franca and E. Scarazzini. 1997. Metodi Matematici per la Generazione di Curve e Superfici. Milan: Città Studi Edizioni.Google Scholar
  3. Foster and Partners. 1997. Norman Foster: Selected and Current Works. Mulgrave: Images Publishing.Google Scholar
  4. Furer, R. 1990. Untergewichtig, aber Hochrangig (Zumthors Kapelle in Sogn Benedetg). Architese 6 (1990): 29–33.Google Scholar
  5. Jodidio, P. 2001. Foster. Cologne:TaschenVerlag.Google Scholar
  6. Marchetti , Elena. 1998. Appunti di Istituzioni di Matematiche (Linee e superfici). Milan: Città Studi Edizioni.Google Scholar
  7. Steinmann, M. 1989. On the Work of Peter Zumthor. Domus 710 (Nov. 1989): 44–53.Google Scholar
  8. Zumthor, P. 1998. Peter Zumthor Works. Baden: Lars Muller.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MathematicsPolitecnico di MilanoMilanItaly

Personalised recommendations