Abstract
In order to understand how the new typological pattern for amphitheaters was first drawn, and how it was transformed into a variety of archetypal models during its historical evolution, measured surveys were made of the amphitheaters of Pompeii, Roselle, and Veleia. The analysis of their curves evidences three different geometric diagrams deriving from three different answers to the same query. The design of amphitheaters involves two of the classic problems of ancient mathematics: the quadrature of the circle and the trisection of the angle. The curve of the outer perimeter has to be approximated by an irregular polygon in order to determine the position of the vertices from which the stairs would come down the steps of the cavea, dividing it into wedge-shapes of more or less identical size. Aesthetic demands and arithmetic necessities had to converge toward coherent and scientific geometric patterns. One of these would later be called “the perfect oval” by the architects of the Renaissance.
First published as: Sylvie Duvernoy , “Architecture and Mathematics in Roman Amphitheaters”, pp. 81–93 in Nexus IV: Architecture and Mathematics, eds. Kim Williams and Jose Francisco Rodrigues, Fucecchio (Florence): Kim Williams Books, 2002.
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Notes
- 1.
The architectural design unit in Pompeii’s amphitheater is equal to 12 ft of approximately 29.25 cm.
- 2.
This hidden underground curve could not be measured during the survey of the monument. Nevertheless, its position is known by the gates that lead to the corridor. Its elliptic shape is the only assumption included in the geometric pattern proposed here, while all other conclusions come from accurate measurements.
- 3.
The architectural design module in Roselle corresponds to 12 ft of 29.38 cm.
- 4.
A circle having a radius of seven (or multiple of seven) will allow simple calculations for perimeter or area, and the results will be expressed through round numbers only.
- 5.
An approximate image of this tool is published in Loria (1914).
References
Catalano, G.M. 1990. Il compasso conico – Uno strumento per tracciare qualsiasi conica con moto continuo. Disegnare 1 (October 1990).
Duvernoy, Sylvie. 2000. Due anfiteatri repubblicani: Roselle e Veleia. Disegnare 20/21 (June-December 2000).
Loria, Gino. 1914. Scienze esatte nell’antica Grecia. Milan: Hoepli.
Vitruvius Pollio. 2009. On Architecture. Richard Schofield, trans. London: Penguin Classics.
Further Reading
Bartoli, Maria Teresa. 1998. Le ragioni geometriche del segno architettonico. Florence: Alinea.
Duvernoy, Sylvie and Paul L. Rosin. 2014. The Compass, the Ruler, and the Computer. Pp 525–540 in Kim Williams and Michael J. Ostwald eds. Architecture and Mathematics from Antiquity to the Future: Volume II the 1500s to the Future. Cham: Springer International Publishing.
Golvin, Jean Claude. 1988. L’amphithéâtre romain, essai sur la teéorisation de sa forme et de sa fonction. Paris: Centre Pierre.
Wilson Jones, Mark. 1993. Designing amphitheaters. Mitteilungen des deutschen archäologischen Instituts-Römische 100 (1993): 391-441.
Zerlenga, Ornella. 1996. Il tracciamento delle «forme ovali» nella trattatistica del XVI secolo. La pratica del filo e del compasso. XY 27/28.
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Duvernoy, S. (2015). Architecture and Mathematics in Roman Amphitheatres. 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_13
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