Architecture and Mathematics in Roman Amphitheatres

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.