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This lecture covers the historical development of conic sections and gnomonics, focusing on their applications in ancient sundials and astronomical instruments. It explores the use of conic curves in shadow projections and the significance of spherical sundials. The instructor discusses the challenges faced by ancient astronomers and architects in utilizing conic sections for gnomonics, highlighting the rarity of flat sundials in antiquity. The presentation also delves into the practical aspects of constructing sundials, such as the design of spherical sundials and the limitations of ancient gnomonics devices.