Approximation of Ellipses by Ovals

This lecture explores the historical development of approximating ellipses with ovals, from Serlio's construction of ovals based on triangles to Guarini's ambiguous use of conics. The presentation covers the advantages of ovals over ellipses in monumental architecture, such as amphitheaters and churches, and discusses the challenges in maintaining consistency in machining trajectories. The instructor demonstrates the construction of parallels and circles osculating ellipses, emphasizing the importance of the minimal radius of curvature in machining. The lecture concludes with a detailed examination of the construction of an oval with eight centers, highlighting the intricacies of maintaining valid configurations in machining operations.