The amphitheater of Verona
In th artikel Baroque Oval Churches: Innovative Geometrical Patterns in Early Modern Sacred Architecture Sylvie Duvernoy describes how well-known renaissance architects as Giovanni Battista da Sangallo, Baldassare Peruzzi, Sebastiano Serlio and Andrea Palladio studied the amphitheaters of Verona and Rome. Based on this studies they described how to design oval shaped buildings.
circumference
The Roman designers had to design the building so that they could devide the circumpherence into equal arches to be used as the entrances for the public.
De length l of a circular arch can be written as:
l = 2 x x R x /360° (with R as the radius and as the angle of the circular arch.
The drawings of Peruzzi show that in the amphitheater of Verona each circular arch contains 18 arches. In other words: the four circular arches have an equel lenght.
radii and angles
What are the radii R1 and R2 and the angles 1 en 2 of the circular arches in Verona?
With equal circular arches in a symmetric oval, one can write:
2 x x R1 x 1 = 2 x x R2 x 2 and 1+ 2 = 180°
thus: R1 x 1 = R2 x 2 and 1+ 2 = 180°
finally: R1/R2 = 2/1
In Verona Peruzzi found the ratio R1/R2 = 2/1 = 5/3.
5/3 is a classic ratio known as superbipartiens tertias (tertius).