The Compass, the Ruler and the Computer: An Analysis of the Design of the Amphitheatre of Pompeii

  • Sylvie Duvernoy
  • Paul L. Rosin


The present study demonstrates the complementarity of the two methodologies—analysis with modern digital tools, and classical simulation with ancient tools—in the case study of Roman amphitheatres. The geometrical analysis and the arithmetical analysis both converge to the same conclusion. Furthermore they corroborate the conclusions suggested by the numerical analysis with modern mathematics (i.e., the manipulation of computer science). Therefore, the coherence of the results coming from our different approaches allows us to assert that the geometrical pattern of Pompeii’s amphitheatre is a rare example of elliptic shape in architecture. Furthermore, its geometry and dimensions also show some of the finest evidence of direct application of the latest discoveries in mathematical knowledge and science in architectural design in classic antiquity.


Mathematical Knowledge Geometrical Pattern Classic Antiquity Natural Integer Arithmetical Order 
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.



All images and photographs in this chapter are by the authors.


  1. Densmore, D., ed. 1998. Apollonius of Perga. Conics, Books I-III. Santa Fe, NM: Green Lions Press.Google Scholar
  2. Duvernoy, S. 2014. Architecture and Mathematics in Roman Amphitheaters. Chap. 13 in vol. 1 of this present publication.Google Scholar
  3. Fitzgibbon, A., Pilu, M. & Fisher, R. 1999. Direct least-square fitting of ellipses. IEEE Transactions on Pattern Analysis and Machine Intelligence 21(5): 476–480.CrossRefGoogle Scholar
  4. Golvin, J. C. 1988. L’Amphithéâtre Romain. Paris: ed. Pierre Paris.Google Scholar
  5. Hart, V. & Hicks, P., eds. 1996. Sebastiano Serlio on Architecture: Books I-V of “Tutte L’Opere D’Architettura et Prospetiva”. New Haven: Yale University Press.Google Scholar
  6. Heath, T. 1981. A History of Greek Mathematics. New York: Dover.Google Scholar
  7. Kimberling, C. 2004. The shape and history of the ellipse in Washington, D.C. In Proceedings of Bridges Conference, R. Sarhangi and C. Séquin, eds. Accessed 25 November 2013.
  8. Papaodysseus, C. et al. 2005. Identification of geometrical shapes in paintings and its application to demonstrate the foundations of geometry in 1650 B.C. IEEE Transactions on Image Processing 14 (7): 862–873.MathSciNetCrossRefzbMATHGoogle Scholar
  9. Press, W. H., Flannery, B. P., Teukolsky, S. A. and Vettering, W.T. 1990. Numerical Recipes in C. Cambridge: Cambridge University Press.Google Scholar
  10. Rosin, P. L. 1998. Ellipse fitting using orthogonal hyperbolae and Stirling’s oval. Graphical Models and Image Processing 60 (3): 209–213.CrossRefzbMATHGoogle Scholar
  11. ———. 1999. A survey and comparison of traditional piecewise circular approximations to the ellipse. Computer Aided Geometric Design 16 (4): 269–286.MathSciNetCrossRefzbMATHGoogle Scholar
  12. ———. 2001. On Serlio’s constructions of ovals. Mathematical Intelligencer 23 (1): 58–69.MathSciNetCrossRefzbMATHGoogle Scholar
  13. Serlio, S. 1545. Il primo libro d’architetettura di Sebastiano Serlio. Venice: Francesco de’ Franceshi Senese.Google Scholar
  14. Siegal, S. & Castellan, N. J. 1988. Non-Parametric Statistics for the Behavioural Sciences. New York: McGraw Hill.Google Scholar
  15. Trevisan, C. 2000. Sullo schema geometrico costruttivo degli anfiteatri romani: gli esempi del Colosseo e dell’arena di Verona. Disegnare Idee Immagini 1819: 117–132.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Politecnico di MilanoMilanItaly
  2. 2.School of Computer Science and InformaticsCardiff UniversityCardiffUK

Personalised recommendations