On serlio’s constructions of ovals

In his celebrated Tutte l'Opere d'Architettura published over the period 1537-1575 Sebastiano Serlio introduced four techniques for constructing ovals which have thereafter been applied by many architects across Europe. Using various geometric forms (i.e. the triangle, square, and circle) as a basis they produced ovals made up from four circular arcs. This paper analyses both Serlio' s constructions and some of the many possible alternatives and evaluates their accuracy in terms of the ovals' approximations to an ellipse.