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Differential Geometry of Plane Curves Joel Weinberger are included throughoutThis book features plane curves the simplest objects in differential geometry to illustrate many deep and inspiring results in the field in an elementary and accessible way. After an introduction to the basic properties of plane curves, the authors introduce a number of complex and beautiful topics, including the rotation number (with a proof of the fundamental theorem of algebra), rotation index, Jordan curve theorem, isoperimetric inequality, convex
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