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Explore the rich history and fundamental concepts of Greek geometry in this 51-minute lecture from the Math History series. Delve into the ancient Greeks' love for geometry and their significant contributions to the field, including Euclid's Elements and Apollonius' study of conics. Learn about the systematic treatment of planar and three-dimensional geometry, culminating in the five Platonic solids. Discover the importance of constructions using straightedge and compass, and examine key topics such as definitions, postulates, Euclid's approach, equilateral triangles, heptagons, polytopes, and the Golden Rectangle. Gain valuable insights into this foundational subject that shaped mathematics for over 2000 years.