This lecture covers the definitions and properties of a sphere, including its metric and geometric definitions, the generation of the sphere by rotating a circle around its diameter, and the symmetry properties of the sphere. It also discusses the tangent plane to the sphere at a point, containing tangents to curves passing through that point. The lecture emphasizes the sections of a sphere by planes, highlighting that every section is a circle. Additionally, it explores the concept of meridians and parallels on a sphere, as well as the relationship between tangents and great circles passing through a point.
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