Synopsis
Points and lines in the plane.- Circles and spheres.- The sphere by itself: can we distribute points on it evenly?.- Conics and quadrics.- Plane curves.- Smooth surfaces.- Convexity and convex sets.- Polygons, polyhedra, polytopes.- Lattices, packings and tilings in the plane.- Lattices and packings in higher dimensions.- Geometry and dynamics I: billiards.- Geometry and dynamics II: geodesic flow on a surface.
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