Sylvie Duvernoy
Università di Firenze
Dipartimento di Progettazione dell'Architettura
Viale A. Gramsci, 42
50132 Florence ITALY

Paul L. Rosin
School of Computer Science
Cardiff University
5 The Parade
Roath, Cardiff CF24 3AA UK

N2006-DuvRosMeasured data from the ruins of the amphitheatre of Pompei, Sylvie Duvernoy and Paul Rosin.

The purpose of research in ancient architecture, or ancient urban design, is usually to unveil a hidden theoretical knowledge, or at least an intentional geometric and/or arithmetic order. This knowledge may be proved either by using the same procedures that ancient designers probably used themselves: diagrams drawn with some kind of manual graphical device, or applying modern procedures provided by contemporary mathematics.

The two approaches may be combined in the same study in order to allow scholars to reach more reliable conclusions. Using techniques from computer science it is possible to carry out a more precise and less subjective analysis of shapes and dimensions, which may also reveal the surprising accuracy with which ancient monuments were designed and laid out. In addition to such an investigation, a simultaneous inquiry on ancient relationships between mathematics and architecture will make possible the verification of the assertions proposed, and will allow us to understand how geometrical shapes could be practically drawn and transformed in architectural forms in the context of the contemporary scientific and cultural knowledge.

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.

About the authors
This email address is being protected from spambots. You need JavaScript enabled to view an architect, having graduated from Paris University in 1982. She later participated in the Ph.D. program of the Architecture School of Florence University and was awarded the Italian degree of "Dottore di Ricerca" in 1998. She presently teaches architectural drawing at the engineering and architecture faculties of Florence University. The research carried forth since the beginning of the post-graduate studies mainly focus on the reciprocal influences between graphic mathematics and architecture. In addition to research and teaching, she always maintained a private professional activity. She is the Book Review Editor for the Nexus Network Journal.

This email address is being protected from spambots. You need JavaScript enabled to view it. is senior lecturer at the Department of Computer Science, Cardiff University. His research interests include the representation, segmentation, and grouping of curves, knowledge-based vision systems, early image representations, low level image processing, machine vision approaches to remote sensing, methods for evaluation of approximations, algorithms, etc., medical and biological image analysis, and the analysis of shape in art and architecture.

The correct citation for this paper is:
Sylvie Duvernoy and Paul L. Rosin, "The Compass, the Straightedge, and the Computer", pp.21-34 in Nexus VI: Architecture and Mathematics, eds. Sylvie Duvernoy and Orietta Pedemonte Turin: Kim Williams Books, 2006.