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This lecture explores the historical construction methods of ovals, from Roman amphitheatres to modern architecture, including the use of symmetrical double tangency to create ovals. It discusses the simplicity and persistence of ovals in architecture, despite advancements in mathematical conic sections. The lecture also delves into the architectural works of Borromini, Bernini, Descartes, and Desargues, highlighting the significance of ovals in architectural design.